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[ "Generative Adversarial Networks (GANs) have proven to be a powerful framework for learning to draw samples from complex distributions.", "However, GANs are also notoriously difficult to train, with mode collapse and oscillations a common problem.", "We hypothesize that this is at least in part due to the evolution of the generator distribution and the catastrophic forgetting tendency of neural networks, which leads to the discriminator losing the ability to remember synthesized samples from previous instantiations of the generator.", "Recognizing this, our contributions are twofold.", "First, we show that GAN training makes for a more interesting and realistic benchmark for continual learning methods evaluation than some of the more canonical datasets.", "Second, we propose leveraging continual learning techniques to augment the discriminator, preserving its ability to recognize previous generator samples.", "We show that the resulting methods add only a light amount of computation, involve minimal changes to the model, and result in better overall performance on the examined image and text generation tasks.", "Generative Adversarial Networks BID6 (GANs) are a popular framework for modeling draws from complex distributions, demonstrating success in a wide variety of settings, for example image synthesis BID14 and language modeling .", "In the GAN setup, two agents, the discriminator and the generator (each usually a neural network), are pitted against each other.", "The generator learns a mapping from an easy-to-sample latent space to a distribution in the data space, which ideally matches the real data's distribution.", "At the same time, the discriminator aims to distinguish the generator's synthesized samples from the real data samples.", "When trained successfully, GANs yield impressive results; in the image domain for example, synthesized images from GAN models are significantly sharper and more realistic than those of other classes of models BID16 .", "On the other hand, GAN training can be notoriously finicky.", "One particularly well-known and common failure mode is mode collapse BID0 BID35 : instead of producing samples sufficiently representing the true data distribution, the generator maps the entire latent space to a limited subset of the real data space.When mode collapse occurs, the generator does not \"converge,\" in the conventional sense, to a stationary distribution.", "Rather, because the discriminator can easily learn to recognize a modecollapsed set of samples and the generator is optimized to avoid the discriminator's detection, the two end up playing a never-ending game of cat and mouse: the generator meanders towards regions in the data space the discriminator thinks are real (likely near where the real data lie) while the discriminator chases after it.", "Interestingly though, if generated samples are plotted through time (as in FIG0 ), it appears that the generator can revisit previously collapsed modes.", "At first, this may seem odd.", "The discriminator was ostensibly trained to recognize that mode in a previous iteration and did so well enough to push the generator away from generating those samples.", "Why has the discriminator seemingly lost this ability?We", "conjecture that this oscillation phenomenon is enabled by catastrophic forgetting BID20 BID30 : neural networks have a well-known tendency to forget how to complete old tasks while learning new ones. In", "most GAN models, the discriminator is a binary classifier, with the two classes being the real data and the generator's outputs. Implicit", "to the training of a standard classifier is the assumption that the data are drawn independently and identically distributed (i.i.d.) . Importantly", ", this assumption does not hold true in GANs: the distribution of the generator class (and thus the discriminator's training data) evolves over time. Moreover,", "these changes in the generator's distribution are adversarial, designed specifically to deteriorate discriminator performance on the fake class as much as possible. Thus, the", "alternating training procedure of GANs in actuality corresponds to the discriminator learning tasks sequentially, where each task corresponds to recognizing samples from the generator at that particular point in time. Without any", "measures to prevent catastrophic forgetting, the discriminator's ability to recognize fake samples from previous iterations will be clobbered by subsequent gradient updates, allowing a mode-collapsed generator to revisit old modes if training runs long enough. Given this", "tendency, a collapsed generator can wander indefinitely without ever learning the true distribution.With this perspective in mind, we cast training the GAN discriminator as a continual learning problem, leading to two main contributions. (i) While", "developing systems that learn tasks in a sequential manner without suffering from catastrophic forgetting has become a popular direction of research, current benchmarks have recently come under scrutiny as being unrepresentative to the fundamental challenges of continual learning BID3 . We argue", "that GAN training is a more realistic setting, and one that current methods tend to fail on.(ii) Such", "a reframing of the GAN problem allows us to leverage relevant methods to better match the dynamics of training the min-max objective. In particular", ", we build upon the recently proposed elastic weight consolidation BID15 and intelligent synapses BID39 . By preserving", "the discriminator's ability to identify previous generator samples, this memory prevents the generator from simply revisiting past distributions. Adapting the", "GAN training procedure to account for catastrophic forgetting provides an improvement in GAN performance for little computational cost and without the need to train additional networks. Experiments", "on CelebA and CIFAR10 image generation and COCO Captions text generation show discriminator continual learning leads to better generations.", "We observe that the alternating training procedure of GAN models results in a continual learning problem for the discriminator, and training on only the most recent generations leads to consequences unaccounted for by most models.", "As such, we propose augmenting the GAN training objective with a continual learning regularization term for the discriminator to prevent its parameters from moving too far away from values that were important for recognizing synthesized samples from previous training iterations.", "Since the original EWC and IS losses were proposed for discrete tasks, we adapt them to the GAN setting.", "Our implementation is simple to add to almost any variation of GAN learning, and we do so for a number of popular models, showing a gain in ICP and FID for CelebA and CIFAR-10, as well as BLEU scores for COCO Captions.", "More importantly, we demonstrate that GAN and continual learning, two popular fields studied independently of each other, have the potential to benefit each other, as new continual learning methods stand to benefit GAN training, and GAN generated datasets provide new testing grounds for continual learning." ]

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[ "Generative Adversarial Network Training is a Continual Learning Problem." ]

[ "Many problems with large-scale labeled training data have been impressively solved by deep learning.", "However, Unseen Class Categorization (UCC) with minimal information provided about target classes is the most commonly encountered setting in industry, which remains a challenging research problem in machine learning.", "Previous approaches to UCC either fail to generate a powerful discriminative feature extractor or fail to learn a flexible classifier that can be easily adapted to unseen classes.", "In this paper, we propose to address these issues through network reparameterization, \\textit{i.e.}, reparametrizing the learnable weights of a network as a function of other variables, by which we decouple the feature extraction part and the classification part of a deep classification model to suit the special setting of UCC, securing both strong discriminability and excellent adaptability.", "Extensive experiments for UCC on several widely-used benchmark datasets in the settings of zero-shot and few-shot learning demonstrate that, our method with network reparameterization achieves state-of-the-art performance.", "The rich and accessible labeled data has fueled the revolutionary successes of deep learning in various tasks, e.g., visual recognition BID7 ), object detection BID20 ), machine translation BID1 ), etc.", "However, requiring numerous annotated data severely limits the applicability of deep learning algorithms to Unseen Class Categorization (UCC) for which we only have access to a limited amount of information, which is frequently encountered in industrial applications.", "Recently, an increasing number of approaches have been proposed to solve UCC with the help of either attribute descriptions (zero-shot learning (ZSL)) BID9 ; BID30 ) or one/a few labeled samples for each class (few-shot learning (FSL)) BID22 ; BID29 ).Previous", "approaches to UCC mainly have the following characteristics and limitations: (i) To obtain", "powerful discriminative feature representation, they often train a deep classification model employing state-of-the-art multi-class classification techniques. However, such", "models are hard to be adapted to new classes with limited supervision information due to the high volume of model parameters and the gradual updating scheme. (ii) To ensure", "the consistency of training and test settings and adaptability to new classes, previous methods often train a deep model in an episode fashion BID26 ), sometimes along with some specially designed meta-learning updating rules BID4 ). With episode-based", "training, the model acquires adaptability to new tasks after many training episodes using the knowledge it grasps during the training. However, the episode-based", "training strategy severely limits the model's capability of extracting discriminative features, because it does not fully exploit the diversity and variance of all classes within the training dataset. The trained model treats the", "classes in each episode as new classes and attempts to separate them. Therefore, it does not have", "memory of the competing information of these classes against all the other ones in the whole dataset beyond the current episode. Due to the neglect of this", "global (dataset-wise rather than episode-wise) discriminative information, the feature extraction capability of the model is suppressed, thus limiting the UCC performance.To address these issues, we propose to secure both powerful discriminability of feature extraction and strong adaptability of model classification through network reparameterization, i.e., reparametrizing the learnable weights of a network as a function of other variables. We decouple the feature extraction", "module and the classification module of a deep classification model, learn the former as a standard multi-class classification task to obtain a discriminative feature extractor, and learn the latter employing a light deep neural network that generates generic classification weights for unseen classes given limited exemplar information. We train the classification weight", "generator by following the episode-based training scheme to secure the adaptability. Our method can be flexibly applied", "to both ZSL and FSL, where the exemplar information about unseen classes are provided in the form of either the semantic attributes or one/a few labeled samples. Extensive experiments show that our", "proposed method achieves state-of-the-art performance on widely-used benchmark datasets for both tasks.", "In this paper, we propose a flexible framework for unseen class categorization with limited information provided about these classes.", "We secure two key factors, a powerful feature extractor and a flexible classifier, through network reparameterization.", "We decouple the feature extraction module and the classification module of a deep model for UCC.", "The feature extraction module is learned in a standard multi-class classification framework and the classification weight vector is generated by a network from exemplar information of the unseen classes.", "We train the classification weight generator in an episode-by-episode fashion to enable it flexibility for new tasks.", "Applying our framework for zero-shot learning (ZSL), we achieve much better results especially for the generalized ZSL setting than the state-of-the-art owing to our incorporation of inter-class separation information for learning the mapping from semantic space to visual space.", "For few-shot learning (FSL), we also achieve remarkable performance gains relative to existing methods due to the flexible scheme that make it possible a powerful feature extraction model and a flexible weight generation model." ]

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[ "A unified frame for both few-shot learning and zero-shot learning based on network reparameterization" ]

[ "Proteins are ubiquitous molecules whose function in biological processes is determined by their 3D structure.\n", "Experimental identification of a protein's structure can be time-consuming, prohibitively expensive, and not always possible. \n", "Alternatively, protein folding can be modeled using computational methods, which however are not guaranteed to always produce optimal results.\n", "GraphQA is a graph-based method to estimate the quality of protein models, that possesses favorable properties such as representation learning, explicit modeling of both sequential and 3D structure, geometric invariance and computational efficiency. \n", "In this work, we demonstrate significant improvements of the state-of-the-art for both hand-engineered and representation-learning approaches, as well as carefully evaluating the individual contributions of GraphQA.", "Protein molecules are predominantly present in biological forms, responsible for their cellular functions.", "Therefore, understanding, predicting and modifying proteins in biological processes are essential for medical, pharmaceutical and genetic research.", "Such studies strongly depend on discovering mechanical and chemical properties of proteins through the determination of their structure.", "At the high level, a protein molecule is a chain of hundreds of smaller molecules called amino acids.", "Identifying a protein's amino-acid sequence is nowadays straightforward.", "However, the function of a protein is primarily determined by its 3D structure.", "Spatial folding can be determined experimentally, but the existing procedures are time-consuming, prohibitively expensive and not always possible.", "Thus, several computational techniques were developed for protein structure prediction (Arnold et al., 2006; Wang et al., 2017; Xu, 2019) .", "So far, no single method is always best, e.g. some protein families are best modeled by certain methods, also, computational methods often produce multiple outputs.", "Therefore, candidate generation is generally followed by an evaluation step.", "This work focuses on Quality Assessment (QA) of computationally-derived models of a protein (Lundstrom et al., 2001; Won et al., 2019) .", "QA, also referred to as model accuracy estimation (MAE), estimates the quality of computational protein models in terms of divergence from their native structure.", "The downstream goal of QA is two-fold: to find the best model in a pool of models and to refine a model based on its local quality.", "Computational protein folding and design have recently received attention from the machine learning community (Wang et al., 2017; Xu, 2019; Jones & Kandathil, 2018; Ingraham et al., 2019b; Anand & Huang, 2018; Evans et al., 2018; AlQuraishi, 2019) , while QA has yet to follow.", "This is despite the importance of QA for structural biology and the availability of standard datasets to benchmark machine learning techniques, such as the biannual CASP event (Moult et al., 1999) .", "The field of bioinformatics, on the other hand, has witnessed noticeable progress in QA for more than a decade: from earlier works using artificial neural networks (Wallner & Elofsson, 2006) or support vector machines (Ray et al., 2012; Uziela et al., 2016) to more recent deep learning methods based on 1D-CNNs, 3D-CNNs and LSTMs (Hurtado et al., 2018; Derevyanko et al., 2018; Pagès et al., 2018; Conover et al., 2019) .", "In this work, we tackle Quality Assessment with Graph Convolutional Networks, which offer several desirable properties over previous methods.", "Through extensive experiments, we show significant improvements over the state-of-the-art, and offer informative qualitative and quantitative analyses.", "GRAPHQA predicts local and global scores from a protein's graph using message passing among residues with chemical bond or spatial proximity.", "CASP QA algorithms score protein models by comparison with experimentally-determined conformations.", "For the first time we applied graph convolutional networks to the important problem of protein quality assessment (QA).", "Since proteins are naturally represented as graphs, GCN allowed us to collect the individual benefits of the previous QA methods including representation learning, geometric invariance, explicit modeling of sequential and 3D structure, simultaneous local and global scoring, and computational efficiency.", "Thanks to these benefits, and through an extensive set of experiments, we demonstrated significant improvements upon the state-of-the-art results on various metrics and datasets and further analyzed the results via thorough ablation and qualitative studies.", "Finally, we wish that Quality Assessment will gain popularity in the machine learning community, that could benefit from several curated datasets and ongoing regular challenges.", "We believe that richer geometric representations, e.g. including relative rotations, and raw atomic representations could represent an interesting future direction for learning-based Quality Assessment.", "Global Distance Test Total Score (GDT TS) Global Distance Test Total Score (GDT TS) is a global-level score obtained by first superimposing the structure of a decoy to the experimental structure using an alignment heuristic, and then computing the fraction of residues whose position is within a certain distance from the corresponding residue in the native structure ( figure 7 ).", "This percentage is computed at different thresholds and then averaged to produce a score in the range [0, 100], which we rescale between 0 and 1 (table 2).", "Table 2 i", "2.5Å x x 5 6.3Å x 20% 60% 80% 100% Local Distance Difference Test (LDDT) Local Distance Difference Test (LDDT), is a residue-level score that does not require alignment of the structures and compares instead the local neighborhood of every residue, in the decoy and in the native structure.", "If we define the neighborhood of a residue as the set of its contacts, i.e. the set of other residues that lie within a certain distance from it, we can express the quality of that residue as the percentage of contacts that it shares with the corresponding residue in the native structure.", "Figure 8: Example of LDDT scoring for residue 7: the residues within a radius R 1 are { 6, 8, 10 } the native structure (left) and { 6, 8 } for the decoy (right); at a radius R 2 we have { 3, 6, 8, 9, 10, 11 } the native structure (left) and { 3, 6, 8, 9, 10 } for the decoy (right)." ]

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[ "GraphQA is a graph-based method for protein Quality Assessment that improves the state-of-the-art for both hand-engineered and representation-learning approaches" ]

[ "We study the problem of training machine learning models incrementally using active learning with access to imperfect or noisy oracles.", "We specifically consider the setting of batch active learning, in which multiple samples are selected as opposed to a single sample as in classical settings so as to reduce the training overhead.", "Our approach bridges between uniform randomness and score based importance sampling of clusters when selecting a batch of new samples.", "Experiments on\n", "benchmark image classification datasets (MNIST, SVHN, and CIFAR10) shows improvement over existing active learning strategies.", "We introduce an extra denoising layer to deep networks to make active learning robust to label noises and show significant improvements.\n", "Supervised learning is the most widely used machine learning method, but it requires labelled data for training.", "It is time-consuming and labor-intensive to annotate a large dataset for complex supervised machine learning models.", "For example, ImageNet (Russakovsky et al., 2015) reported the time taken to annotate one object to be roughly 55 seconds.", "Hence an active learning approach which selects the most relevant samples for annotation to incrementally train machine learning models is a very attractive avenue, especially for training deep networks for newer problems that have littel annotated data.", "Classical active learning appends the training dataset with a single sample-label pair at a time.", "Given the increasing complexity of machine learning models, it is natural to expand active learning procedures to append a batch of samples at each iteration instead of just one.", "Keeping such training overhead in mind, a few batch active learning procedures have been developed in the literature (Wei et al., 2015; Sener & Savarese, 2018; Sinha et al., 2019) .", "When initializing the model with a very small seed dataset, active learning suffers from the coldstart problem: at the very beginning of active learning procedures, the model is far from being accurate and hence the inferred output of the model is incorrect/uncertain.", "Since active learning relies on output of the current model to select next samples, a poor initial model leads to uncertain estimation of selection criteria and selection of wrong samples.", "Prior art on batch active learning suffers performance degradation due to this cold-start problem.", "Most active learning procedures assume the oracle to be perfect, i.e., it can always annotate samples correctly.", "However, in real-world scenarios and given the increasing usage of crowd sourcing, for example Amazon Mechanical Turk (AMT), for labelling data, most oracles are noisy.", "The noise induced by the oracle in many scenarios is resolute.", "Having multiple annotations on the same sample cannot guarantee noise-free labels due to the presence of systematic bias in the setup and leads to consistent mistakes.", "To validate this point, we ran a crowd annotation experiment on ESC50 dataset (Piczak, 2015) : each sample is annotated by 5 crowdworkers on AMT and the majority vote of the 5 annotations is considered the label.", "It turned out for some classes, 10% of the samples are annotated wrong, even with 5 annotators.", "Details of the experiment can be found in Appendix A. Under such noisy oracle scenarios, classical active learning algorithms such as (Chen et al., 2015a) under-perform as shown in Figure 1 .", "Motivating from these observations, we fashion a batch active learning strategy to be robust to noisy oracles.", "The main contributions of this work are as follows: (1) we propose a batch sample selection method based on importance sampling and clustering which caters to drawing a batch which is simultaneously diverse and important to the model; (2) we incorporate model uncertainty into the sampling probability to compensate poor estimation of the Noise channel is assumed to be a 10-symmetric channel, where ε is the probability of label error.", "importance scores when the training data is too small to build a meaningful model; (3) we introduce a denoising layer to deep networks to robustify active learning to noisy oracles.", "Main results, as shown in Fig. 3 demonstrate that in noise-free scenario, our method performs as the best over the whole active learning procedure, and in noisy scenario, our method outperforms significantly over state-of-the-art methods.", "In this paper we have proposed a batch sample selection mechanism for active learning with access to noisy oracles.", "We use mutual information between model parameters and the predicted class probabilities as importance score for each sample, and cluster the pool sample space with JensonShannon distance.", "We incorporate model uncertainty/confidence into Gibbs distribution over the clusters and select samples from each cluster with importance sampling.", "We introduce an additional layer at the output of deep networks to estimate label noise.", "Experiments on MNIST, SVHN, and CIFAR10 show that the proposed method is more robust against noisy labels compared with the state of the art.", "Even in noise-free scenarios, our method still performs the best for all three datasets.", "Our contributions open avenues for exploring applicability of batch active learning in setups involving imperfect data acquisition schemes either by construction or because of resource constraints.", "Under review as a conference paper at ICLR 2020 A ESC50 CROWD LABELING EXPERIMENT", "We selected 10 categories of ESC50 and use Amazon Mechanical Turk for annotation.", "In each annotation task, the crowd worker is asked to listen to the sound track and pick the class that the sound belongs to, with confidence level.", "The crowd worker can also pick \"Unsure\" if he/she does not think the sound track clearly belongs to one of the 10 categories.", "For quality control, we embed sound tracks that clearly belong to one class (these are called gold standards) into the set of tasks an annotator will do.", "If the annotator labels the gold standard sound tracks wrong, then labels from this annotator will be discarded.", "The confusion table of this crowd labeling experiment is shown in Figure 5 : each row corresponds to sound tracks with one ground truth class, and the columns are majority-voted crowd-sourced labels of the sound tracks.", "We can see that for some classes, such as frog and helicopter, even with 5 crowd workers, the majority vote of their annotation still cannot fully agree with the ground truth class." ]

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[ "We address the active learning in batch setting with noisy oracles and use model uncertainty to encode the decision quality of active learning algorithm during acquisition." ]

[ "Artistic style transfer is the problem of synthesizing an image with content similar to a given image and style similar to another.", "Although recent feed-forward neural networks can generate stylized images in real-time, these models produce a single stylization given a pair of style/content images, and the user doesn't have control over the synthesized output.", "Moreover, the style transfer depends on the hyper-parameters of the model with varying ``optimum\" for different input images.", "Therefore, if the stylized output is not appealing to the user, she/he has to try multiple models or retrain one with different hyper-parameters to get a favorite stylization.", "In this paper, we address these issues by proposing a novel method which allows adjustment of crucial hyper-parameters, after the training and in real-time, through a set of manually adjustable parameters.", "These parameters enable the user to modify the synthesized outputs from the same pair of style/content images, in search of a favorite stylized image.", "Our quantitative and qualitative experiments indicate how adjusting these parameters is comparable to retraining the model with different hyper-parameters.", "We also demonstrate how these parameters can be randomized to generate results which are diverse but still very similar in style and content.", "Style transfer is a long-standing problem in computer vision with the goal of synthesizing new images by combining the content of one image with the style of another BID8 BID12 BID0 .", "Recently, neural style transfer techniques BID9 BID15 BID11 BID20 BID19 showed that the correlation between the features extracted from the trained deep neural networks is quite effective on capturing the visual styles and content that can be used for generating images similar in style and content.", "However, since the definition of similarity is inherently vague, the objective of style transfer is not well defined and one can imagine multiple stylized images from the same pair of content/style images.Existing real-time style transfer methods generate only one stylization for a given content/style pair and while the stylizations of different methods usually look distinct BID27 BID13 , it is not possible to say that one stylization is better in all contexts since people react differently to images based on their background and situation.", "Hence, to get favored stylizations users must try different methods that is not satisfactory.", "It is more desirable to have a single model which can generate diverse results, but still similar in style and content, in real-time, by adjusting some input parameters.One other issue with the current methods is their high sensitivity to the hyper-parameters.", "More specifically, current real-time style transfer methods minimize a weighted sum of losses from different layers of a pre-trained image classification model BID15 BID13 (check Sec 3 for details) and different weight sets can result into very different styles (Figure 6) .", "However, one can only observe the effect of these weights in the final stylization by fully retraining the model with the new set of weights.", "Considering the fact that the \"optimal\" set of weights can be different for any pair of style/content ( Figure 3 ) and also the fact that this \"optimal\" truly doesn't exist (since the goodness of the output is a personal choice) retraining the models over and over until the desired result is generated is not practical.", "Our main contribution in this paper is a novel method which allows adjustment of each loss layer's contribution in feed-forward style transfer networks, in real-time and after training.", "This capability allows the users to adjust the stylized output to find the favorite stylization by changing input parameters and without retraining the stylization model.", "We also show how randomizing these parameters plus some noise added to the content image can result in very different stylizations from the same pair of style/content image.Our method can be expanded in numerous ways e.g. applying it to multi-style transfer methods such as BID11 , applying the same parametrization technique to randomize the correlation loss between the features of each layer and finally using different loss functions and pre-trained networks for computing the loss to randomize the outputs even further.", "One other interesting future direction is to apply the same \"loss adjustment after training\" technique for other classic computer vision and deep learning tasks.", "Style transfer is not the only task in which modifying the hyper-parameters can greatly affect the predicted results and it would be rather interesting to try this method for adjusting the hyper-parameters in similar problems.", "Convolution 3 1 C SAME ReLU Convolution 3 1 C SAME Linear Add the input and the output Upsampling -C feature maps Nearest-neighbor interpolation, factor 2 Convolution 3 1 C SAME ReLUNormalization Conditional instance normalization after every convolution Optimizer Adam (α = 0.001, β 1 = 0.9, β 2 = 0.999)" ]

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[ "Stochastic style transfer with adjustable features. " ]

[ "Recent work has shown that deep reinforcement-learning agents can learn to follow language-like instructions from infrequent environment rewards.", "However, this places on environment designers the onus of designing language-conditional reward functions which may not be easily or tractably implemented as the complexity of the environment and the language scales.", "To overcome this limitation, we present a framework within which instruction-conditional RL agents are trained using rewards obtained not from the environment, but from reward models which are jointly trained from expert examples. ", "As reward models improve, they learn to accurately reward agents for completing tasks for environment configurations---and for instructions---not present amongst the expert data.", "This framework effectively separates the representation of what instructions require from how they can be executed.\n", "In a simple grid world, it enables an agent to learn a range of commands requiring interaction with blocks and understanding of spatial relations and underspecified abstract arrangements.", "We further show the method allows our agent to adapt to changes in the environment without requiring new expert examples.", "Figure 1: Different valid goal states for the instruction \"build an L-like shape from red blocks\".Developing", "agents that can learn to follow user instructions pertaining to an environment is a longstanding goal of AI research BID33 . Recent work", "has shown deep reinforcement learning (RL) to be a promising paradigm for learning to follow language-like instructions in both 2D and 3D worlds (e.g. BID11 ; BID5 , see Section 4 for a review). In each of", "these cases, being able to reward an agent for successfully completing a task specified by an instruction requires the implementation of a full interpreter of the instruction language. This interpreter", "must be able to evaluate the instruction against environment states to determine when reward must be granted to the agent, and in doing so requires full knowledge (on the part of the designer) of the semantics of the instruction language relative to the environment. Consider, for example", ", 4 arrangements of blocks presented in Figure 1 . Each of them can be", "interpreted as a result of successfully executing the instruction \"build an L-like shape from red blocks\", despite the fact that these arrangements differ in the location and the orientation of the target shape, as well as in the positioning of the irrelevant blue blocks. At best (e.g. for instructions", "such as the * Work done during an internship at DeepMind.† Now at Facebook AI Research.aforementioned one), implementing such an interpreter is feasible, although typically onerous in terms of engineering efforts to ensure reward can be given-for any admissible instruction in the language-in potentially complex or large environments. At worst, if we wish to scale", "to the full complexity of natural language, with all its ambiguity and underspecification, this requires solving fundamental problems of natural language understanding.If instruction-conditional reward functions cannot conveniently or tractably be implemented, can we somehow learn them in order to then train instruction-conditional policies? When there is a single implicit", "task, Inverse Reinforcement Learning (IRL; BID20 BID36 methods in general, and Generative Adversarial Imitation Learning BID12 in particular, have yielded some success in jointly learning reward functions from expert data and training policies from learned reward models. In this paper, we wish to investigate", "whether such mechanisms can be adapted to the more general case of jointly learning to understand language which specifies task objectives (e.g. instructions, goal specifications, directives), and use such understanding to reward language-conditional policies which are trained to complete such tasks. For simplicity, we explore a facet of", "this general problem in this paper by focussing on the case of declarative commands that specify sets of possible goal-states (e.g. \"arrange the red blocks in a circle.\"), and where expert examples need only be goal states rather than full trajectories or demonstrations, leaving such extensions for further work. We introduce a framework-Adversarial", "Goal-Induced Learning from Examples (AGILE)-for jointly training an instruction-conditional reward model using expert examples of completed instructions alongside a policy which will learn to complete instructions by maximising the thus-modelled reward. In this respect, AGILE relies on familiar", "RL objectives, with free choice of model architecture or training mechanisms, the only difference being that the reward comes from a learned reward model rather than from the environment.We first verify that our method works in settings where a comparison between AGILE-trained policies with policies trained from environment reward is possible, to which end we implement instructionconditional reward functions. In this setting, we show that the learning", "speed and performance of A3C agents trained with AGILE reward models is superior to A3C agents trained against environment reward, and comparable to that of true-reward A3C agents supplemented by auxiliary unsupervised reward prediction objectives. To simulate an instruction-learning setting", "in which implementing a reward function would be problematic, we construct a dataset of instructions and goal-states for the task of building colored orientation-invariant arrangements of blocks. On this task, without us ever having to implement", "the reward function, the agent trained within AGILE learns to construct arrangements as instructed. Finally, we study how well AGILE's reward model generalises", "beyond the examples on which it was trained. Our experiments show it can be reused to allow the policy to", "adapt to changes in the environment.", "We have proposed AGILE, a framework for training instruction-conditional RL agents using rewards from learned reward models, which are jointly trained from data provided by both experts and the agent being trained, rather than reward provided by an instruction interpreter within the environment.", "This opens up new possibilities for training language-aware agents: in the real world, and even in rich simulated environments BID4 BID34 , acquiring such data via human annotation would often be much more viable than defining and implementing reward functions programmatically.", "Indeed, programming rewards to teach robust and general instruction-following may ultimately be as challenging as writing a program to interpret language directly, an endeavour that is notoriously laborious BID32 , and some say, ultimately futile BID33 .As", "well as a means to learn from a potentially more prevalent form of data, our experiments demonstrate that policies trained in the AGILE framework perform comparably with and can learn as fast as those trained against ground-truth reward and additional auxiliary tasks. Our", "analysis of the reward model's classifications gives a sense of how this is possible; the false positive decisions that it makes early in the training help the policy to start learning. The", "fact that AGILEs objective attenuates learning issues due to the sparsity of reward states within episodes in a manner similar to reward prediction suggests that the reward model within AGILE learns some form of shaped reward BID21 , and could serve not only in the cases where a reward function need to be learned in the absence of true reward, but also in cases where environment reward is defined but sparse. As", "these cases are not the focus of this study, we note this here, but leave such investigation for future work.As the policy improves, false negatives can cause the reward model accuracy to deteriorate. We", "determined a simple method to mitigate this, however, leading to robust training that is comparable to RL with reward prediction and unlimited access to a perfect reward function. Another", "attractive aspect of AGILE is that learning \"what should be done\" and \"how it should be done\" is performed by two different model components. Our experiments", "confirm that the \"what\" kind of knowledge generalizes better to new environments. When the dynamics", "of the environment changed at test time, fine-tuning using frozen reward model allowed to the policy recover some of its original capability in the new setting.While there is a large gap to be closed between the sort of tasks and language experimented with in this paper and those which might be presented in \"real world\" situations or more complex environments, our results provide an encouraging first step in this direction. Indeed, it is interesting", "to consider how AGILE could be applied to more realistic learning settings, for instance involving first-person vision of 3D environments. Two issues would need to", "be dealt with, namely training the agent to factor out the difference in perspective between the expert data and the agent's observations, and training the agent to ignore its own body parts if they are visible in the observations. Future work could focus", "on applying third-person imitation learning methods recently proposed by BID26 learn the aforementioned invariances. Most of our experiments", "were conducted with a formal language with a known structure, however AGILE also performed very well when we used a structure-agnostic FiLM-LSTM model which processed the instruction as a plain sequence of tokens. This result suggest that", "in future work AGILE could be used with natural language instructions." ]

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[ "We propose AGILE, a framework for training agents to perform instructions from examples of respective goal-states." ]

[ "We present Multitask Soft Option Learning (MSOL), a hierarchical multi-task framework based on Planning-as-Inference.", "MSOL extends the concept of Options, using separate variational posteriors for each task, regularized by a shared prior.", "The learned soft-options are temporally extended, allowing a higher-level master policy to train faster on new tasks by making decisions with lower frequency.", "Additionally, MSOL allows fine-tuning of soft-options for new tasks without unlearning previously useful behavior, and avoids problems with local minima in multitask training.", "We demonstrate empirically that MSOL significantly outperforms both hierarchical and flat transfer-learning baselines in challenging multi-task environments.", "A key challenge in Reinforcement Learning (RL) is to scale current approaches to higher complexity tasks without requiring a prohibitive number of environmental interactions.", "However, for many tasks, it is possible to construct or learn efficient exploration priors that allow to focus on more relevant parts of the state-action space, reducing the number of required interactions.", "These include, for example, reward shaping (Ng et al., 1999; Konidaris & Barto, 2006) , curriculum learning (Bengio et al., 2009) , some meta-learning algorithms (Wang et al., 2016; Duan et al., 2016; Gupta et al., 2018; Houthooft et al., 2018; Xu et al., 2018) , and transfer learning (Caruana, 1997; Taylor & Stone, 2011; Bengio, 2012; Parisotto et al., 2015; Rusu et al., 2015; Teh et al., 2017) .", "One promising way to capture prior knowledge is to decompose policies into a hierarchy of subpolicies (or skills) that can be reused and combined in novel ways to solve new tasks (Dayan & Hinton, 1993; Thrun & Schwartz, 1995; Parr & Russell, 1998; Sutton et al., 1999; Barto & Mahadevan, 2003) .", "The idea of Hierarchical RL (HRL) is also supported by findings that humans appear to employ a hierarchical mental structure when solving tasks (Botvinick et al., 2009; Collins & Frank, 2016) .", "In such a hierarchical RL policy, lower-level, temporally extended skills yield directed behavior over multiple time steps.", "This has two advantages:", "i) it allows efficient exploration, as the target states of skills can be reached without having to explore much of the state space in between, and", "ii) directed behavior also reduces the variance of the future reward, which accelerates convergence of estimates thereof.", "On the other hand, while a hierarchical approach can therefore significantly speed up exploration and training, it can also severely limit the expressiveness of the final policy and lead to suboptimal performance when the temporally extended skills are not able to express the required policy for the task at hand (Mankowitz et al., 2014) .", "Many methods exist for constructing and/or learning skills for particular tasks (Dayan & Hinton, 1993; Sutton et al., 1999; McGovern & Barto, 2001; Menache et al., 2002; Ş imşek & Barto, 2009; Gregor et al., 2016; Kulkarni et al., 2016; Bacon et al., 2017; Nachum et al., 2018a) .", "Training on multiple tasks simultaneously is one promising approach to learn skills that are both relevant and generalise across tasks (Thrun & Schwartz, 1995; Pickett & Barto, 2002; Fox et al., 2016; Andreas et al., 2017; Frans et al., 2018) .", "Ideally, the entire hierarchy can be trained end-to-end on the obtained return, obviating the need to specify proxy rewards for skills (Frans et al., 2018) .", "However, learning hierarchical policies end-to-end in a multitask setting poses two major challenges:", "i) because skills optimize environmental rewards directly, correctly updating them relies on already (nearly) converged master policies that use them similarly across all tasks, requiring complex training schedules (Frans et al., 2018) , and", "ii) the end-to-end optimization is prone to local minima in which multiple skills have learned similar behavior.", "This second points is explained in more detail in Appendix A.", "In this paper, we propose Multitask Soft Option Learning (MSOL), a novel approach to learning hierarchical policies in a multi-task setting that extends Options (Sutton et al., 1999) , a common definition for skills, and casts the concept into the Planning as Inference (PAI) framework (see, e.g., Levine, 2018 , for a review).", "MSOL brings multiple advantages:", "i) it stabilizes end-to-end multitask training, removing the need for complex training schedules like in Frans et al. (2018) ,", "ii) it gives rise to coordination between master policies, avoiding local minima of the type described in Appendix A,", "iii) it allows fine-tuning of options, i.e. adapting them to new tasks at test-time without the risk of unlearning previously acquired useful behavior, thereby avoiding suboptimal performance due to restricted expressiveness,", "iv) and lastly, we show how the soft option framework gives rise to a natural solution to the challenging task of learning option-termination policies.", "MSOL differentiates between a prior policy for each option, shared across all tasks, and a flexible task-specific posterior policy.", "The option prior can be fixed once it is fully trained, preventing unlearning of useful behavior even when the posteriors are updated.", "On new tasks, the option posteriors are initialized to the priors and regularized towards them, but are still adaptable to the specific task.", "This allows the same accelerated training as with 'hard' options, but can solve more tasks due to the adjustable posteriors.", "Furthermore, during option learning, we can train prior and posterior policies simultaneously (Teh et al., 2017) , all without the need for complex training schedules (Frans et al., 2018) : training is stabilized because only the priors are shared across tasks.", "Our experiments demonstrate that MSOL outperforms previous hierarchical and transfer learning algorithms during transfer tasks in a multitask setting.", "MSOL only modifies the regularized reward and loss function, but does not require any specialized architecture.", "In particular, it also does not require artificial restrictions on the expressiveness of either the higher-level or intra-option policies.", "2 PRELIMINARIES An agent's task is formalized as a MDP (S, A, ρ, P, r), consisting of the state space S, the action space A, the initial state distribution ρ, the transition probability P (s t+1 |s t , a t ) of reaching state s t+1 by executing action a t in state s t , and the reward r(s t , a t ) an agent receives for this transition.", "Multitask Soft Option Learning (MSOL) proposes reformulating options using the perspective of prior and posterior distributions.", "This offers several key advantages.", "First, during transfer, it allows us to distinguish between fixed, and therefore knowledge-preserving option priors, and flexible option posteriors that can adjust to the reward structure of the task at hand.", "This effects a similar speed-up in learning as the original options framework, while avoiding sub-optimal performance when the available options are not perfectly aligned to the task.", "Second, utilizing this 'soft' version of options in a multitask learning setup increases optimization stability and removes the need for complex training schedules between master and lower level policies.", "Furthermore, this framework naturally allows master policies to coordinate across tasks and avoid local minima of insufficient option diversity.", "It also allows for autonomously learning option-termination policies, a very challenging task which is often avoided by fixing option durations manually.", "Lastly, using this formulation also allows inclusion of prior information in a principled manner without imposing too rigid a structure on the resulting hierarchy.", "We utilize this advantage to explicitly incorporate the bias that good options should be temporally extended.", "In future research, other types of information can be explored.", "As an example, one could investigate sets of tasks which would benefit from a learned master prior, like walking on different types of terrain.", "Tejas D Kulkarni, Karthik Narasimhan, Ardavan Saeedi, and Josh Tenenbaum.", "Hierarchical deep reinforcement learning: Integrating temporal abstraction and intrinsic motivation.", "In Advances in neural information processing systems, pp. 3675-3683, 2016.", "where all posteriors of z 1 are moving to A, but for z 2 , the posteriors on different tasks a and b move to different targets.", "Crucially, to maximize the regularized reward (6), the KL-divergences between priors and posteriors should be minimized along they trajectories, i.e. weighted by how likely they are to occur.", "Consequently, the higher D KL [z 1 is always used to reach A and z 2 (b) is always used to reach B, allowing bothz 1 andz 2 to also lead to A and B respectively." ]

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[ "In Hierarchical RL, we introduce the notion of a 'soft', i.e. adaptable, option and show that this helps learning in multitask settings." ]

[ "We propose an algorithm, guided variational autoencoder (Guided-VAE), that is able to learn a controllable generative model by performing latent representation disentanglement learning.", "The learning objective is achieved by providing signal to the latent encoding/embedding in VAE without changing its main backbone architecture, hence retaining the desirable properties of the VAE.", "We design an unsupervised and a supervised strategy in Guided-VAE and observe enhanced modeling and controlling capability over the vanilla VAE.", "In the unsupervised strategy, we guide the VAE learning by introducing a lightweight decoder that learns latent geometric transformation and principal components; in the supervised strategy, we use an adversarial excitation and inhibition mechanism to encourage the disentanglement of the latent variables.", "Guided-VAE enjoys its transparency and simplicity for the general representation learning task, as well as disentanglement learning.", "On a number of experiments for representation learning, improved synthesis/sampling, better disentanglement for classification, and reduced classification errors in meta learning have been observed.", "The resurgence of autoencoders (AE) (LeCun, 1987; Bourlard & Kamp, 1988; Hinton & Zemel, 1994) is an important component in the rapid development of modern deep learning .", "Autoencoders have been widely adopted for modeling signals and images (Poultney et al., 2007; Vincent et al., 2010) .", "Its statistical counterpart, the variational autoencoder (VAE) (Kingma & Welling, 2014) , has led to a recent wave of development in generative modeling due to its two-in-one capability, both representation and statistical learning in a single framework.", "Another exploding direction in generative modeling includes generative adversarial networks (GAN) Goodfellow et al. (2014) , but GANs focus on the generation process and are not aimed at representation learning (without an encoder at least in its vanilla version).", "Compared with classical dimensionality reduction methods like principal component analysis (PCA) (Hotelling, 1933; Jolliffe, 2011) and Laplacian eigenmaps (Belkin & Niyogi, 2003) , VAEs have demonstrated their unprecedented power in modeling high dimensional data of real-world complexity.", "However, there is still a large room to improve for VAEs to achieve a high quality reconstruction/synthesis.", "Additionally, it is desirable to make the VAE representation learning more transparent, interpretable, and controllable.", "In this paper, we attempt to learn a transparent representation by introducing guidance to the latent variables in a VAE.", "We design two strategies for our Guided-VAE, an unsupervised version ( Fig. 1 .a) and a supervised version ( Fig. 1.b) .", "The main motivation behind Guided-VAE is to encourage the latent representation to be semantically interpretable, while maintaining the integrity of the basic VAE architecture.", "Guided-VAE is learned in a multi-task learning fashion.", "The objective is achieved by taking advantage of the modeling flexibility and the large solution space of the VAE under a lightweight target.", "Thus the two tasks, learning a good VAE and making the latent variables controllable, become companions rather than conflicts.", "In unsupervised Guided-VAE, in addition to the standard VAE backbone, we also explicitly force the latent variables to go through a lightweight encoder that learns a deformable PCA.", "As seen in Fig. 1 .a", ", two decoders exist, both trying to reconstruct the input data x: Dec main .", "The main decoder, denoted as Dec main , functions regularly as in the standard VAE (Kingma & Welling, 2014) ; the secondary decoder, denoted as Dec sub , explicitly learns a geometric deformation together with a linear sub-space.", "In supervised Guided-VAE, we introduce a subtask for the VAE by forcing one latent variable to be discriminative (minimizing the classification error) while making the rest of the latent variable to be adversarially discriminative (maximizing the minimal classification error).", "This subtask is achieved using an adversarial excitation and inhibition formulation.", "Similar to the unsupervised Guided-VAE, the training process is carried out in an end-to-end multi-task learning manner.", "The result is a regular generative model that keeps the original VAE properties intact, while having the specified latent variable semantically meaningful and capable of controlling/synthesizing a specific attribute.", "We apply Guided-VAE to the data modeling and few-shot learning problems and show favorable results on the MNIST, CelebA, and Omniglot datasets.", "The contributions of our work can be summarized as follows:", "• We propose a new generative model disentanglement learning method by introducing latent variable guidance to variational autoencoders (VAE).", "Both unsupervised and supervised versions of Guided-VAE have been developed.", "• In unsupervised Guided-VAE, we introduce deformable PCA as a subtask to guide the general VAE learning process, making the latent variables interpretable and controllable.", "• In supervised Guided-VAE, we use an adversarial excitation and inhibition mechanism to encourage the disentanglement, informativeness, and controllability of the latent variables.", "Guided-VAE is able to keep the attractive properties of the VAE and it is easy to implement.", "It can be trained in an end-to-end fashion.", "It significantly improves the controllability of the vanilla VAE and is applicable to a range of problems for generative modeling and representation learning.", "In this paper we have presented a new representation learning method, guided variational autoencoder (Guided-VAE), for disentanglement learning.", "Both versions of Guided-VAE utilize lightweight guidance to the latent variables to achieve better controllability and transparency.", "Improvements on disentanglement, image traversal, and meta-learning over the competing methods are observed.", "Guided-VAE maintains the backbone of VAE and can be applied to other generative modeling applications." ]

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[ "Learning a controllable generative model by performing latent representation disentanglement learning." ]

[ "Neural language models (NLMs) are generative, and they model the distribution of grammatical sentences.", "Trained on huge corpus, NLMs are pushing the limit of modeling accuracy.", "Besides, they have also been applied to supervised learning tasks that decode text, e.g., automatic speech recognition (ASR).", "By re-scoring the n-best list, NLM can select grammatically more correct candidate among the list, and significantly reduce word/char error rate.", "However, the generative nature of NLM may not guarantee a discrimination between “good” and “bad” (in a task-specific sense) sentences, resulting in suboptimal performance.", "This work proposes an approach to adapt a generative NLM to a discriminative one.", "Different from the commonly used maximum likelihood objective, the proposed method aims at enlarging the margin between the “good” and “bad” sentences.", "It is trained end-to-end and can be widely applied to tasks that involve the re-scoring of the decoded text.", "Significant gains are observed in both ASR and statistical machine translation (SMT) tasks.", "Language models (LMs) estimate the likelihood of a symbol sequence {s i } n i=0 , based on the joint probability, p(s 0 , . . . , s n ) = p(s 0 ) n i=1 p(s i |s i−1 , s i−2 , . . . , s 0 ).(1", ") works, BID7 and BID25 , propose to predict the next symbol based on a fusion of the hidden states in the ASR/SMT and language model. A", "gating mechanism is jointly trained to determine how much the language model should contribute.The afore-discussed language models are generative in the sense that they merely model the joint distribution of a symbol sequence (Eq. (", "1) ).", "While the research community is mostly focused on pushing the limit of modeling accuracy (lower PPL) (e.g., BID12 , very limited attention has been paid to the discrimination ability of language models when they are applied to supervised learning tasks, such as ASR and SMT.", "Discriminative language modeling aims at enhancing the performance in supervised learning tasks.", "In specific, existing works BID23 BID10 BID21 often target at improving ASR accuracy.", "The key motivation underlying them is that the model should be able to discriminate between \"good\" and \"bad\" sentences in a task-specific sense, instead of just modeling grammatical ones.", "The common methodology is to build a binary classifier upon hand-crafted features extracted from the sentences.", "However, it is not obvious how these methods can utilize large unsupervised corpus, which is often easily available, and the hand-crafted features are also ad hoc and may result in suboptimal performance.In this work, we study how to improve the discrimination ability of a neural language model.", "The proposed method enlarges the difference between the log-likelihoods of \"good\" and \"bad\" sentences.", "In contrast to the existing works BID23 BID10 BID21 , our method does not rely on hand-crafted features.", "It is trained in end-to-end manner and able to take advantage of large external text corpus.", "We apply the proposed large margin language model to ASR and SMT tasks.", "It reduces word error rate (WER) and increases bilingual evaluation understudy (BLEU) scores significantly, showing notable advantage over several alternative methods that are well adopted.2", "RELATED WORK BID23 BID10 and BID21 proposed to train discriminative language models based on hand crafted features.", "They essentially build linear classifiers that give high scores on \"good\" sentences but low scores on \"bad\" ones.", "These methods all rely on ad hoc choice of features, e.g., counts of n-grams where n varies in a small range (e.g., 1 ∼ 3).", "Moreover, it is also not clear how these methods would take advantage of an existing language model (trained on large unsupervised corpus).", "BID28 tries to overcome the above issues by adapting an NLM on the transcriptions of a speech dataset.", "Although the setup is more similar to ours, their objective is not well-behaved and difficult to optimize when there are multiple beam candidates.", "An in-depth discussion will be given in Section 3.1.", "BID15 designed another approach to train a discriminative language model, which is based on bi-grams.", "Similar to our method, the objective there aims at increasing the difference between the scores of the best candidate and ground-truth.", "However, since the language model is not end-to-end, there are several issues complicating the training, e.g., handling back-off weight.Our proposed method is based on comparisons between pairs of sentences.", "Its implementation resembles siamese network architecture BID3 BID29 , first proposed for face verification tasks.", "Recently, siamese network has also been applied to learning similarities on sequences BID19 BID20 .", "In spite of solving different problems, the common methodology is to extract a pair of hidden representations for a pair of input samples (through a shared network).", "It then manipulates the distance between the hidden representations based on whether the two samples are considered similar or not.", "Our work also draws some inspirations from information retrieval (IR) BID16 .", "As a representative IR method, ranking SVM BID8 assumes a linear scoring function, and imposes a hinge loss on the difference between the scores of sample pairs.", "Conventional language models are guided by minimizing perplexity, and they are generative models.", "This work proposes an approach to enhance the discrimination ability of language models.", "It is trained end-to-end by maximizing the margin between \"good\" and \"bad\" (in a task-specific sense) sentences.", "The method is general and can be applied to various tasks that require re-scoring of text data.", "Experiments on ASR and SMT have shown a consistent gain over several baselines.", "These facts argue that min-perplexity is not necessarily an appropriate guideline when we want to apply language models in some supervised learning problems.", "A future direction is to apply the proposed method to conversation generation.", "The goal is to discriminate between boring (e.g., \"I don't know\") and informative replies, thus deprecating the former.", "Another interesting future work is to apply the LMLM/rank-LMLM to lattices during decoding." ]

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[ "Enhance the language model for supervised learning task " ]

[ "Conventionally, convolutional neural networks (CNNs) process different images with the same set of filters.", "However, the variations in images pose a challenge to this fashion.", "In this paper, we propose to generate sample-specific filters for convolutional layers in the forward pass.", "Since the filters are generated on-the-fly, the model becomes more flexible and can better fit the training data compared to traditional CNNs.", "In order to obtain sample-specific features, we extract the intermediate feature maps from an autoencoder.", "As filters are usually high dimensional, we propose to learn a set of coefficients instead of a set of filters.", "These coefficients are used to linearly combine the base filters from a filter repository to generate the final filters for a CNN.", "The proposed method is evaluated on MNIST, MTFL and CIFAR10 datasets.", "Experiment results demonstrate that the classification accuracy of the baseline model can be improved by using the proposed filter generation method.", "Variations exist widely in images.", "For example, in face images, faces present with different head poses and different illuminations which are challenges to most face recognition models.", "In the conventional training process of CNNs, filters are optimized to deal with different variations.", "The number of filters increases if more variations are added to the input data.", "However, for a test image, only a small number of the neurons in the network are activated which indicates inefficient computation BID13 ).Unlike", "CNNs with fixed filters, CNNs with dynamically generated sample-specific filters are more flexible since each input image is associated with a unique set of filters. Therefore", ", it provides possibility for the model to deal with variations without increasing model size.However, there are two challenges for training CNNs with dynamic filter generation. The first", "challenge is how to learn sample-specific features for filter generation. Intuitively", ", filter sets should correspond to variations in images. If the factors", "of variations are restricted to some known factors such as face pose or illumination, we can use the prior knowledge to train a network to represent the variation as a feature vector. The main difficulty", "is that besides the factors of variations that we have already known, there are also a number of them that we are not aware of. Therefore, it is difficult", "to enumerate all the factors of variations and learn the mapping in a supervised manner. The second challenge is that", "how to map a feature vector to a set of new filters. Due to the high dimension of", "the filters, a direct mapping needs a large number of parameters which can be infeasible in real applications.In response, we propose to use an autoencoder for variation representation leaning. Since the objective of an autoencoder", "is to reconstruct the input images from internal feature representations, each layer of the encoder contains sufficient information about the input image. Therefore, we extract features from each", "layer in the encoder as sample-specific features. For the generation of filters , given a", "sample-specific feature vector, we firstly construct a filter repository. Then we learn a matrix that maps the feature", "vector to a set of coefficients which will be used to linearly combine the base filters in the repository to generate new filters.Our model has several elements of interest. Firstly, our model bridges the gap between the", "autoencoder network and the prediction network by mapping the autoencoder features to the filters in the prediction network. Therefore, we embed the knowledge from unsupervised", "learning to supervised learning. Secondly, instead of generating new filters directly", "from a feature vector, we facilitate the generation with a filter repository which stores a small number of base filters. Thirdly, we use linear combination of the base filters", "in the repository to generate new filters. It can be easily implemented as a convolution operation", "so that the whole pipeline is differentiable with respect to the model parameters.", "In this paper, we propose to learn to generate filters for convolutional neural networks.", "The filter generation module transforms features from an autoencoder network to sets of coefficients which are then used to linearly combine base filters in filter repositories.", "Dynamic filters increase model capacity so that a small model with dynamic filters can also be competitive to a deep model.", "Evaluation on three tasks show the accuracy improvement brought by our filter generation.", "In this section, we show the details of the network structures used in our experiments.When we extract sample-specific features, we directly take the convolution feature maps (before LReLU layer) from the autoencoder network as input and feed them to the dimension reduction network.", "The entire process of sample-specific feature extraction is split into the autoencoder network and the dimension reduction network for the purpose of plain and straightforward illustration." ]

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[ "dynamically generate filters conditioned on the input image for CNNs in each forward pass " ]

[ "We propose a new anytime neural network which allows partial evaluation by subnetworks with different widths as well as depths.", "Compared to conventional anytime networks only with the depth controllability, the increased architectural diversity leads to higher resource utilization and consequent performance improvement under various and dynamic resource budgets.", "We highlight architectural features to make our scheme feasible as well as efficient, and show its effectiveness in image classification tasks.", "When we deploy deep neural network models on resource-constrained mobile devices or autonomous vehicles with a strict real-time latency requirement, it is essential to develop a model which makes the best of available resources.", "Although many network compaction techniques including distillation, pruning and quantization have been proposed BID7 BID12 BID4 BID3 BID9 BID6 BID13 , this goal is still challenging because (1) the resource availabilities are continuously changing over time while these resources are being shared with other program instances BID1 , and (2) multiple resources with different characteristics (e.g. computational capacity, memory usage) should be considered together.Anytime machine learning algorithms have addressed the first issue, how to get the optimal performance under dynamic resource budgets, by allowing us to activate only a part of the model with graceful output quality degradation BID14 BID2 .", "Most anytime algorithms based on deep neural networks appear in the form of early termination of forward processing according to the current resource budget or the difficulty of the given task BID8 BID0 BID10 .", "In other words, the conventional anytime networks are trained to embed many potential sub-networks with different effective depths so that the best one can be chosen according to the current budget.In this work, we propose a new type of the anytime neural network, doubly nested network, to solve the other issue, more efficient utilization of multiple heterogeneous resources.", "The proposed network can be sliced along the width as well as the depth to generate more diverse sub-networks than the conventional anytime networks allowing the sub-network extraction only along the depth-wise direction.", "As depicted in FIG0 , the increased degree of freedom enables us to get higher resource utilization in the devices constrained by dynamically changing resource budget with multiple criteria.", "Causal convolution It is straightforward to form a sub-network along the depth by appending a separate output generation stage to the final convolution layer of the sub-network.", "Since one specific layer's output does not depend on the following (upper) layers' outputs, the jointly trained subnetwork does not suffer from the performance degradation even after the extraction.", "However, this approach does not work along the width because of the interdependence between two nodes at different horizontal locations (e.g. different channels).", "To address this issue, we propose a channelcausal convolution where i-th channel group in one layer is calculated only with activation values from the channel groups from the first to i-th channel group in the previous layer as shown in the right of FIG1 .", "The circle indicates the feature map while the square indicates the classifier.", "Color refers each channel.", "Our network based on the causal convolution allows us to extract the sub-network easily along any directions by making both horizontal and vertical data flow unidirectionally.Output generation stage sharing fully-connected layers Rather than having a separate fullyconnected (FC) layer for one sub-network to generate the final output (e.g. a predicted class given image input), our network is designed to have the FC layers each of which takes only a part of activations from the preceding convolution layers and produce the final output for one sub-network by averaging multiple FC layers' outputs as depicted in FIG1 .", "Sharing the FC layers between the sub-networks at the same depth helps us to have similar computational and memory costs of the FC layers in the depth-controllable anytime network BID8 even with much more possible output locations.", "We revealed that resource-constrained devices could benefit from the architectural diversity enriched by our anytime prediction scheme.", "Our future works include adding adaptive conditioning BID11 which modulates intermediate activations or weight parameters depending on the current sub-network configuration to improve the performance only with a small increase of conditioning parameters." ]

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[ "We propose a new anytime neural network which allows partial evaluation by subnetworks with different widths as well as depths." ]

[ "We propose a new model for making generalizable and diverse retrosynthetic reaction predictions.", "Given a target compound, the task is to predict the likely chemical reactants to produce the target.", "This generative task can be framed as a sequence-to-sequence problem by using the SMILES representations of the molecules.", "Building on top of the popular Transformer architecture, we propose two novel pre-training methods that construct relevant auxiliary tasks (plausible reactions) for our problem.", "Furthermore, we incorporate a discrete latent variable model into the architecture to encourage the model to produce a diverse set of alternative predictions.", "On the 50k subset of reaction examples from the United States patent literature (USPTO-50k) benchmark dataset, our model greatly improves performance over the baseline, while also generating predictions that are more diverse.", "This paper proposes a novel approach for one-step retrosynthesis.", "This task is crucial for material and drug manufacturing (Corey & Wipke, 1969; Corey, 1991) and aims to predict which reactants are needed to generate a given target molecule as the main product.", "For instance, Figure 1 demonstrates that the input molecule \"[N-]=[N+]=NCc1ccc(SCCl)cc1\", expressed here as a SMILES string (Weininger, 1988) , can be generated using reactants \"CSc1ccc(CN= [N+] =[N-])cc1\" and \"ClCCl\".", "For decades, this task has been solved using template-based approaches (Gelernter et al., 1990; Satoh & Funatsu, 1999) .", "Templates encode transformation rules as regular expressions operating on SMILES strings and are typically extracted directly from the available training reactions.", "The primary limitation of such templates is coverage, i.e., it is possible that none of the templates applies to a test molecule.", "In order to better generalize to newer or broader chemical spaces, recently developed template-free approaches cast the problem as a sequence-to-sequence prediction task.", "These approaches were first explored by Liu et al. (2017) using LSTM models; the current state-of-the-art performance on this task uses Transformer models (Lin et al., 2019; Karpov et al., 2019) .", "Out-of-the-box Transformers nevertheless do not effectively generalize to rare reactions.", "For instance, model accuracy drops by 25% on reactions with 10 or fewer representative instances in the Figure 1: An example prediction task: on the left is the input target SMILES, and on the right are the output reactants SMILES.", "The input is a single molecule, while the output is a set of molecules separated by a period (\".\").", "training set.", "1 Another key issue is diversity.", "Manufacturing processes involve a number of additional criteria -such as green chemistry (having low detrimental effects on the environment).", "It is therefore helpful to generate a diverse collection of alternative ways of synthesizing the given target molecule.", "However, predicted reactions are unlikely to encompass multiple reaction classes (see Figure 2 ) without additional guidance.", "This is because the training data only provides a single reactant set for each input target, even if this is not the only valid reaction to synthesize the target.", "Figure 2: For the input target compound shown on the left, three possible reactant predictions are shown on the right.", "Prediction 1 suggestions a heterocycle formation reaction, while Predictions 2 and 3 both suggest substitution reactions.", "The only difference between the latter two is the halide functional group (Cl vs Br) highlighted in red.", "They share similar chemical properties and thus provide no additional insights for chemists.", "We extend molecular Transformers to address both of these challenges.", "First, we propose a novel pre-training approach to drive molecular representations to better retain alternative reaction possibilities.", "Our approach is reminiscent of successful pre-training schemes in natural language processing (NLP) applications (Devlin et al., 2018) .", "However, rather than using conventional token masking methods, we adopt chemically-relevant auxiliary tasks.", "Each training instance presents a single way to decompose a target molecule into its reactants.", "Here, we add alternative proxy decompositions for each target molecule by either", "1) randomly removing bond types that can possibly break during reactions, or", "2) transforming the target based on templates.", "While neither of these two auxiliary tasks are guaranteed to construct valid chemical reactions, they are closely related to the task of interest.", "Indeed, representations trained in this manner provide useful initializations for the actual retrosynthesis problem.", "To improve the diversity of predicted reactions, we incorporate latent variables into the generation process.", "Specifically, we merge the Transformer architecture with a discrete mixture over reactions.", "The role of the latent variable is to encode distinct modes that can be related to underlying reaction classes.", "Even though the training data only presents one reaction for each target molecule, our model learns to associate each reaction with a latent class, and in the process covers multiple reaction classes across the training set.", "At test time, a diverse collection of reactions is then obtained by collecting together predictions resulting from conditioning on each latent class.", "Analogous mixture models have shown promise in generating diverse predictions in natural language translation tasks (He et al., 2018; Shen et al., 2019) .", "We demonstrate similar gains in the chemical context.", "We evaluate our model on the benchmark USPTO-50k dataset, and compare it against state-ofthe-art template-free baselines using the Transformer model.", "We focus our evaluation on top-10 accuracy, because there are many equally valuable reaction transformations for each input target, though only one is presented in the data.", "Compared to the baseline, we achieve better performance overall, with over 13% increase in top-10 accuracy for our best model.", "When we create a split of the data based on different reaction templates (a task that any template-based model would fail on), we similarly observe a performance increase for our model.", "Additionally, we demonstrate that our model outputs exhibit significant diversity through both quantitative and human evaluations.", "We explored the problem of making one-step retrosynthesis reaction predictions, dealing with the issues of generalizability and making diverse predictions.", "Through pre-training and use of mixture models, we show that our model beats state-of-the-art methods in terms of accuracy and generates more diverse predictions.", "Even on a challenging task, for which any template-based models would fail, our model still is able to generalize to the test set." ]

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[ "We propose a new model for making generalizable and diverse retrosynthetic reaction predictions." ]

[ "Unsupervised learning of disentangled representations is an open problem in machine learning.", "The Disentanglement-PyTorch library is developed to facilitate research, implementation, and testing of new variational algorithms.", "In this modular library, neural architectures, dimensionality of the latent space, and the training algorithms are fully decoupled, allowing for independent and consistent experiments across variational methods.", "The library handles the training scheduling, logging, and visualizations of reconstructions and latent space traversals.", "It also evaluates the encodings based on various disentanglement metrics.", "The library, so far, includes implementations of the following unsupervised algorithms VAE, Beta-VAE, Factor-VAE, DIP-I-VAE, DIP-II-VAE, Info-VAE, and Beta-TCVAE, as well as conditional approaches such as CVAE and IFCVAE.", "The library is compatible with the Disentanglement Challenge of NeurIPS 2019, hosted on AICrowd and was used to compete in the first and second stages of the challenge, where it was ranked among the best few participants.", "There are two overlapping avenues in representation learning.", "One focuses on learning task-specific transformations often optimized towards specific domains and applications.", "The other approach learns the intrinsic factors of variation, in a disentangled and taskinvariant fashion.", "The unsupervised disentanglement of latent factors, where changes in a single factor of variation shifts the latent encoding in a single direction, is an open problem of representation learning (Bengio et al., 2013; Lake et al., 2016) .", "Disentangled representations are valuable in few-shot learning, reinforcement learning, transfer learning, as well as semisupervised learning (Bengio et al., 2013; Peters et al., 2017; .", "In this work, we developed a library based on the functionalities of the PyTorch framework, which facilitates research, implementation, and testing of new variational algorithms focusing on representation learning and disentanglement.", "The library branches from the Disentanglement Challenge of NeurIPS 2019, hosted on AICrowd (aicrowd.com), and was used to compete in the first and second stages of the challenge where it was highly ranked.", "The Disentanglement-PyTorch library is released under the GNU General Public License at https://github.com/amir-abdi/disentanglement-pytorch." ]

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[ "Disentanglement-PyTorch is a library for variational representation learning" ]

[ "Trust region methods, such as TRPO, are often used to stabilize policy optimization algorithms in reinforcement learning (RL).", "While current trust region strategies are effective for continuous control, they typically require a large amount of on-policy interaction with the environment.", "To address this problem, we propose an off-policy trust region method, Trust-PCL, which exploits an observation that the optimal policy and state values of a maximum reward objective with a relative-entropy regularizer satisfy a set of multi-step pathwise consistencies along any path.", "The introduction of relative entropy regularization allows Trust-PCL to maintain optimization stability while exploiting off-policy data to improve sample efficiency.", "When evaluated on a number of continuous control tasks, Trust-PCL significantly improves the solution quality and sample efficiency of TRPO.", "The goal of model-free reinforcement learning (RL) is to optimize an agent's behavior policy through trial and error interaction with a black box environment.", "Value-based RL algorithms such as Q-learning BID36 and policy-based algorithms such as actor-critic BID15 have achieved well-known successes in environments with enumerable action spaces and predictable but possibly complex dynamics, e.g., as in Atari games BID19 BID34 .", "However, when applied to environments with more sophisticated action spaces and dynamics (e.g., continuous control and robotics), success has been far more limited.In an attempt to improve the applicability of Q-learning to continuous control, BID32 and BID16 developed an off-policy algorithm DDPG, leading to promising results on continuous control environments.", "That said, current off-policy methods including DDPG often improve data efficiency at the cost of optimization stability.", "The behaviour of DDPG is known to be highly dependent on hyperparameter selection and initialization BID18 ; even when using optimal hyperparameters, individual training runs can display highly varying outcomes.On the other hand, in an attempt to improve the stability and convergence speed of policy-based RL methods, BID13 developed a natural policy gradient algorithm based on Amari (1998), which subsequently led to the development of trust region policy optimization (TRPO) BID28 .", "TRPO has shown strong empirical performance on difficult continuous control tasks often outperforming value-based methods like DDPG.", "However, a major drawback is that such methods are not able to exploit off-policy data and thus require a large amount of on-policy interaction with the environment, making them impractical for solving challenging real-world problems.Efforts at combining the stability of trust region policy-based methods with the sample efficiency of value-based methods have focused on using off-policy data to better train a value estimate, which can be used as a control variate for variance reduction BID8 b) .In", "this paper, we investigate an alternative approach to improving the sample efficiency of trust region policy-based RL methods. We", "exploit the key fact that, under entropy regularization, the optimal policy and value function satisfy a set of pathwise consistency properties along any sampled path BID21 , which allows both on and off-policy data to be incorporated in an actor-critic algorithm, PCL. The", "original PCL algorithm optimized an entropy regularized maximum reward objective and was evaluated on relatively simple tasks. Here", "we extend the ideas of PCL to achieve strong results on standard, challenging continuous control benchmarks. The", "main observation is that by alternatively augmenting the maximum reward objective with a relative entropy regularizer, the optimal policy and values still satisfy a certain set of pathwise consistencies along any sampled trajectory. The", "resulting objective is equivalent to maximizing expected reward subject to a penalty-based constraint on divergence from a reference (i.e., previous) policy.We exploit this observation to propose a new off-policy trust region algorithm, Trust-PCL, that is able to exploit off-policy data to train policy and value estimates. Moreover", ", we present a simple method for determining the coefficient on the relative entropy regularizer to remain agnostic to reward scale, hence ameliorating the task of hyperparameter tuning. We find", "that the incorporation of a relative entropy regularizer is crucial for good and stable performance. We evaluate", "Trust-PCL against TRPO, and observe that Trust-PCL is able to solve difficult continuous control tasks, while improving the performance of TRPO both in terms of the final reward achieved as well as sample-efficiency.", "We have presented Trust-PCL, an off-policy algorithm employing a relative-entropy penalty to impose a trust region on a maximum reward objective.", "We found that Trust-PCL can perform well on a set of standard control tasks, improving upon TRPO both in terms of average reward and sample efficiency.", "Our best results on Trust-PCL are able to maintain the stability and solution quality of TRPO while approaching the sample-efficiency of value-based methods (see e.g., BID18 ).", "This gives hope that the goal of achieving both stability and sample-efficiency without trading-off one for the other is attainable in a single unifying RL algorithm." ]

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[ "We extend recent insights related to softmax consistency to achieve state-of-the-art results in continuous control." ]

[ "Deep reinforcement learning has achieved many recent successes, but our understanding of its strengths and limitations is hampered by the lack of rich environments in which we can fully characterize optimal behavior, and correspondingly diagnose individual actions against such a characterization. \n\n", "Here we consider a family of combinatorial games, arising from work of Erdos, Selfridge, and Spencer, and we propose their use as environments for evaluating and comparing different approaches to reinforcement learning.", "These games have a number of appealing features: they are challenging for current learning approaches, but they form", "(i) a low-dimensional, simply parametrized environment where", "(ii) there is a linear closed form solution for optimal behavior from any state, and", "(iii) the difficulty of the game can be tuned by changing environment parameters in an interpretable way.", "We use these Erdos-Selfridge-Spencer games not only to compare different algorithms, but also to compare approaches based on supervised and reinforcement learning, to analyze the power of multi-agent approaches in improving performance, and to evaluate generalization to environments outside the training set.", "Deep reinforcement learning has seen many remarkable successes over the past few years BID5 BID9 .", "But developing learning algorithms that are robust across tasks and policy representations remains a challenge.", "Standard benchmarks like MuJoCo and Atari provide rich settings for experimentation, but the specifics of the underlying environments differ from each other in many different ways, and hence determining the principles underlying any particular form of sub-optimal behavior is difficult.", "Optimal behavior in these environments is generally complex and not fully characterized, so algorithmic success is generally associated with high scores, making it hard to analyze where errors are occurring in any sort of fine-grained sense.An ideal setting for studying the strengths and limitations of reinforcement learning algorithms would be", "(i) a simply parametrized family of environments where", "(ii) optimal behavior can be completely characterized,", "(iii) the inherent difficulty of computing optimal behavior is tightly controlled by the underlying parameters, and", "(iv) at least some portions of the parameter space produce environments that are hard for current algorithms.", "To produce such a family of environments, we look in a novel direction -to a set of two-player combinatorial games with their roots in work of Erdos and Selfridge BID3 , and placed on a general footing by BID10 .", "Roughly speaking, these Erdos-Selfridge-Spencer (ESS) games are games in which two players take turns selecting objects from some combinatorial structure, with the feature that optimal strategies can be defined by potential functions derived from conditional expectations over random future play.These ESS games thus provide an opportunity to capture the general desiderata noted above, with a clean characterization of optimal behavior and a set of instances that range from easy to very hard as we sweep over a simple set of tunable parameters.", "We focus in particular on one of the best-known games in this genre, Spencer's attacker-defender game (also known as the \"tenure game\"; BID10 , in which -roughly speaking -an attacker advances a set of pieces up the levels of a board, while a defender destroys subsets of these pieces to try prevent any of them from reaching the final level ( FIG0 ).", "An instance of the game can be parametrized by two key quantities.", "The first is the number of levels K, which determines both the size of the state space and the approximate length of the game; the latter is directly related to the sparsity of win/loss signals as rewards.", "The second quantity is a potential function φ, whose magnitude characterizes whether the instance favors the defender or attacker, and how much \"margin of error\" there is in optimal play.The environment therefore allows us to study learning by the defender, or by the attacker, or in a multi-agent formulation where the defender and attacker are learning concurrently.", "Because we have a move-by-move characterization of optimal play, we can go beyond simple measures of reward based purely on win/loss outcomes and use supervised learning techniques to pinpoint the exact location of the errors in a trajectory of play.", "In the process, we are able to develop insights about the robustness of solutions to changes in the environment.", "These types of analyses have been long-standing goals, but they have generally been approached much more abstractly, given the difficulty in characterizing step-by-step optimally in non-trivial environments such as this one.The main contributions of this work are thus the following:1.", "The development of these combinatorial games as environments for studying the behavior of reinforcement learning algorithms, with sensitive control over the difficulty of individual instances using a small set of natural parameters.2.", "A comparison of the performance of an agent trained using deep RL to the performance of an agent trained using supervised learning on move-by-move decisions.", "Exploiting the fact that we can characterize optimal play at the level of individual moves, we find an intriguing phenomenon: while the supervised learning agent is, not surprisingly, more accurate on individual move decisions than the deep RL agent, the deep RL agent is better at playing the game!", "We further interpret this result by studying fatal mistakes.3.", "An investigation of the way in which the success of one of the two players (defender or attacker) in training turns out to depend crucially on the algorithm being used to implement the other player.", "We explore properties of this other player's algorithm, and also properties of mulitagent learning, that lead to more robust policies with better generalization.", "This is a largely empirical paper, building on a theoretically grounded environment derived from a combinatorial game.", "We present learning and generalization experiments for a variety of commonly used model architectures and learning algorithms.", "We aim to show that despite the simple structure of the game, it provides both significant challenges for standard reinforcement learning approaches and a number of tools for precisely understanding those challenges.", "In this paper, we have proposed Erdos-Selfridge-Spencer games as rich environments for investigating reinforcement learning, exhibiting continuously tunable difficulty and an exact combinatorial characterization of optimal behavior.", "We have demonstrated that algorithms can exhibit wide variation in performance as we tune the game's difficulty, and we use the characterization of optimal behavior to expose intriguing contrasts between performance in supervised learning and reinforcement learning approaches.", "Having reformulated the results to enable a trainable attacker, we have also been able to explore insights on overfitting, generalization, and multiagent learning.", "We also develop further results in the Appendix, including an analysis of catastrophic forgetting, generalization across different values of the game's parameters, and a method for investigating measures of the model's confidence.", "We believe that this family of combinatorial games can be used as a rich environment for gaining further insights into deep reinforcement learning.", "On the left we train on different potentials and test on potential 0.99.", "We find that training on harder games leads to better performance, with the agent trained on the easiest potential generalizing worst and the agent trained on a harder potential generalizing best.", "This result is consistent across different choices of test potentials.", "The right pane shows the effect of training on a larger K and testing on smaller K. We see that performance appears to be inversely proportional to the difference between the train K and test K." ]

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[ "We adapt a family of combinatorial games with tunable difficulty and an optimal policy expressible as linear network, developing it as a rich environment for reinforcement learning, showing contrasts in performance with supervised learning, and analyzing multiagent learning and generalization. " ]

[ "Adoption of deep learning in safety-critical systems raise the need for understanding what deep neural networks do not understand.", "Several methodologies to estimate model uncertainty have been proposed, but these methodologies constrain either how the neural network is trained or constructed.", "We present Outlier Detection In Neural networks (ODIN), an assumption-free method for detecting outlier observations during prediction, based on principles widely used in manufacturing process monitoring.", "By using a linear approximation of the hidden layer manifold, we add prediction-time outlier detection to models after training without altering architecture or training.", "We demonstrate that ODIN efficiently detect outliers during prediction on Fashion-MNIST, ImageNet-synsets and speech command recognition.", "Thanks to the powerful transformations learned by deep neural networks, deep learning is applied in an increasing number of applications.", "But deep neural networks, as all data-driven models, tend to fail when input data differs from training data.", "Adopting deep learning in increasingly complex and possibly safety-critical systems makes it crucial to know not only whether the model's predictions are accurate, but also whether the model should predict at all.", "If the model is able to detect outlier observations post-training directly, the system can fall back to safe behaviour minimizing negative consequences of faulty predictions.", "By understanding the limits of models' learned representations and detecting when observations are not recognized, autonomous decision making based on deep learning can be improved.In manufacturing process control, predictive models have long been used to predict process outcomes as well as detecting outlier input for decades BID8 BID17 BID9 .", "A widely used model for this purpose is Partial Least Squares regression (PLS) BID33 , which project input data onto a set of linear latent variables prior to prediction.", "In the latent variable space, the distance from new observations to the training data distribution is used to detect outlier observations.", "The latent variables can also be used to approximate input observations, meaning that outliers can also be detected by measuring the distance to the latent variable subspace itself.", "However, the layers of a neural network learn a non-linear mapping from input to output data spaces rather than a single linear subspace.", "This makes it difficult to directly determine the limits of a neural network model's knowledge in the same manner as for a PLS model.In this paper we present Outlier Detection In Neural networks (ODIN), a method for detecting outliers during prediction in deep neural networks.", "Based on principles long used in manufacturing process control, we propose using a linear approximation of intermediate activations to provide a fixed representation of the training data.", "By comparing new data to this fixed representation we are able to detect outliers during prediction without imposing constraints on architecture or training.", "This allows us to use ODIN as a plug-in method allowing reliable and safe autonomous decision making based on deep learning.", "Deep neural networks are powerful transformers that have shown great success in many applications.", "But, in order to adopt deep learning in safety-critical applications it is crucial to understand when new observations do not match the data used during training.", "To imitate linear latent variable models used in manufacturing process monitoring, we use a linear approximation of the hidden layer manifolds to measure distance to and within the manifold.", "We compare our results to MC-dropout, a well established Bayesian approach, and consistently detect outliers post-training without imposing any constraints on either architecture or training procedure.", "We demonstrate our method in two image classification experiments, with and without a pre-trained network, and a speech recognition example using a recurrent neural network.", "By defining the limits of our neural networks' knowledge, ODIN contribute to safer use of deep learning.APPENDIX A APPENDIX" ]

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[ "An add-on method for deep learning to detect outliers during prediction-time" ]

[ "This work introduces a simple network for producing character aware word embeddings.", "Position agnostic and position aware character embeddings are combined to produce an embedding vector for each word.", "The learned word representations are shown to be very sparse and facilitate improved results on language modeling tasks, despite using markedly fewer parameters, and without the need to apply dropout.", "A final experiment suggests that weight sharing contributes to sparsity, increases performance, and prevents overfitting.", "When processing text for Natural Language Processing (NLP), one important decision to make is how to represent the words for a given model or system.", "For many tasks tackled by deep learning such as language modeling, language understanding, and translation, the use of word embeddings has become the standard approach.", "BID20 BID4 BID0 This is in part due to their ability to represent complex syntactic and semantic relationships between words as spatial relationships within the embedding dimensions BID13 .Embeddings", "are generally implemented as a lookup table for computational efficiency. However for", "those unfamiliar with their use it may be beneficial to formulate them as the output of the first layer in a neural network. This is true", "for a layer that has one-hot feature vectors as inputs, no bias, and no activation function.For a given one-hot feature vector x, the activations of such a layer can be computed by xW , which is equivalent to selecting the row W i of the weight matrix, where x i == 1. The weight matrix", "or embedding lookup matrix can then be optimized via typical techniques such as gradient descent, including from subsequent layers of a DNN through back propagation. BID15 For word embeddings", ", the basic approach is to assign a unique vector of trainable parameters to each word in a vocabulary. These vectors are referred", "to in this paper as token embeddings. Token embeddings present a", "number of limitations. For example, any out-of-vocabulary", "word cannot be represented except as a pre-defined < U N K > token. A corollary of this is that the number", "of embeddings (and therefore trainable parameters) grows linearly with the size of the vocabulary. Furthermore, characters are ignored, meaning", "that potentially useful morphological information is thrown out.To get around these limitations, researchers have explored building word embeddings from lower level character representations. A variety of techniques have been presented,", "including the use of feedforward multi layer perceptrons (MLPs) BID3 , convolutional neural networks (CNNs) BID9 BID10 , and recurrent neural networks (RNNs) BID12 . These character level representations of words", "have the advantage over token embeddings of allowing an open vocabulary, usually having fewer parameters, and improving performance by making use of information available in sub-word level features.The most successful approaches for building word embeddings from characters use CNNs. BID9 However, the architecture of CNNs is designed", "to identify positioninvariant features, not the specific ordering of characters that make up a word's spelling. Here we ask whether such ordering is a valuable source", "of information.A number of convolutional features of varying size can be used to capture some ordering, for example within each feature independently. However as the vocabulary is expanded, the number convolutional", "features must be increased to compensate BID9 . Once convolution is performed, the used of a deep highway network", ", as introduced by BID18 , is then needed to produce the final word embedding.The current study presents a simple fully connected architecture for combining characters. In this framework, each character is represented both by position-agnostic", "character embeddings and position-aware character embeddings, which we call spelling embeddings. The combination of the two allows the model to learn both position invariant", "features and positional features. A word embedding is then constructed by combining both the character and spelling", "embeddings of the word, for example by summing or by averaging them together. The resulting vector is then passed through a nonlinear MLP that combines the character", "and spelling information to produce the final word embedding.This MLP, along with the spelling and character embeddings, were trained via gradient descent as inputs to a Recurrent Neural Network (RNN) being trained for a language modeling task. Results show that including the spelling information facilitates improvement over token", "embeddings despite requiring far fewer parameters. Without the position information, character embeddings alone are not sufficient in this", "fully connected architecture.An analysis of the learned representations at the word embedding level shows much greater sparsity for spelling embeddings than for token embeddings, and demonstrates some of the negative impacts of dropout on the representations. Finally, we compare token based models with a fully connected layer of shared weights to", "raw token embeddings with no weight sharing. Passing the token embeddings through a layer of shared weights is shown to drastically increase", "representation sparsity and prevent overfitting. Given that the character and spelling weights are heavily shared among word embeddings, this is", "presented as possible explanation for the spelling aware model's robustness against overfitting.", "This work shows that a simple fully connected network is able to produce character aware word embeddings that outperform traditional token embeddings.", "The architecture is relatively simple compared to previous approaches that use CNNs or RNNs to combine character information.", "This work lacks a direct comparison to these other character aware methods, which is an obvious direction for future work.Investigation into the word embeddings produced by the presented architectures reveal a number of interesting properties.", "Spelling embeddings are especially resistant to overfitting compared to token embeddings, and are also significantly more sparse in their activations.", "Furthermore, dropout is shown to have some negative impacts on the word representations, and weight sharing is presented as a better way to regularize word embeddings.Spelling embeddings exhibit the most weight sharing, because each character embedding is shared across many words in the vocabulary.", "This may be a contributing factor to their increased sparsity and resistance to overfitting.", "Additional evidence for this is provided in the comparison of raw token embeddings to those passed through a fully connected layer.Whereas raw token embeddings share none of their weights with other words in the vocabulary, token embeddings passed through a fully connected layer share all the weights in that layer across the entire vocabulary.", "Not only do token embeddings enjoy increased resistance to overfitting when passed though a shared weight layer, they also become drastically more sparse.", "Whereas dropout is a popular technique for regularization in NLP, it can have a negative impact on the word embeddings, causing some of them to gain a Gini coefficient of 0.", "This suggests that these particular words have completely homogeneous representations and are indistinguishable from each other.On the smaller dataset the number of shared parameters in the fully connected layer of the token embeddings is large compared to the vocabulary size.", "In this case, dropout is needed to prevent overfitting.", "On the larger dataset, the number of shared parameters is much smaller relative to the vocabulary size.", "In this case dropout is not needed for the token embeddings and actually hinders them.", "The spelling embeddings perform worse with dropout on both datasets.The architecture presented here should be compared to the state of the art character CNN results obtained on the One Billion Word benchmark.", "BID9 ) Also, whereas a number hyper-parameters governing the number and size of the layers were tried before the ones presented in this paper were found, other techniques such as highway networks BID18 have not yet been investigated.Furthermore, extending the concept of character aware word embeddings to the output softmax layer is another open area of research that has been tried with character CNNs BID9 , but not to our knowledge with a spelling network as presented in this work." ]

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[ "A fully connected architecture is used to produce word embeddings from character representations, outperforms traditional embeddings and provides insight into sparsity and dropout." ]

[ "Neural networks with low-precision weights and activations offer compelling\n", "efficiency advantages over their full-precision equivalents.", "The two most\n", "frequently discussed benefits of quantization are reduced memory consumption,\n", "and a faster forward pass when implemented with efficient bitwise\n", "operations.", "We propose a third benefit of very low-precision neural networks:\n", "improved robustness against some adversarial attacks, and in the worst case,\n", "performance that is on par with full-precision models.", "We focus on the very\n", "low-precision case where weights and activations are both quantized to $\\pm$1,\n", "and note that stochastically quantizing weights in just one layer can sharply\n", "reduce the impact of iterative attacks.", "We observe that non-scaled binary neural\n", "networks exhibit a similar effect to the original \\emph{defensive distillation}\n", "procedure that led to \\emph{gradient masking}, and a false notion of security.\n", "We address this by conducting both black-box and white-box experiments with\n", "binary models that do not artificially mask gradients.", "The ability to fool machine learning models by making small changes to their input severely limits their potential for safe use in many real-world scenarios.", "Example vulnerabilities include a seemingly innocuous audio broadcast that is interpreted by a speech recognition model in a smartphone, with the intent to trigger an e-transfer, as well as pictures or identity documents that are automatically tagged as someone other than the real individual.The two most common threat models when evaluating the security of a system are the black-box and white-box assumptions, which represent varying degrees of information that an adversary may possess.", "In a black-box threat model, an adversary has similar abilities to a normal user that interacts with a system by providing inputs and observing the corresponding outputs.", "Under this threat model, an adversary generally does not know details of the model architecture or dataset used to train the model.", "Of course, an adversary is free to assume that a convolutional architecture was likely used if the input domain is images, or a recurrent model for speech or text.In a white-box threat model, an adversary has complete access to the model architecture and parameters.", "In the case of neural networks, white-box attacks frequently rely on gradient information to craft especially strong adversarial examples, where strong means that the example is very close to the original input as defined by some distance norm (e.g. L 0 -number of features modified, L 2 -mean squared distance), yet is very likely to cause the model to yield the incorrect output.", "For both threat types, targeted attacks where a model is made to fail in a specific way (e.g. causing a handwritten '7' look like a '3') represents a stronger attack than simple misclassification.The problem with deploying machine learning systems that are secured in a traditional sense, is that adversarial examples have been shown to generalize well between models with different source and target architectures BID19 BID16 Tramèr et al., 2017) .", "This means that a secured model can be compromised in an approximately white-box setting by training and attacking a substitute model that approximates the decision boundary of the model under attack BID16 .", "Thus, to make strong conclusions about the robustness of a machine learning model to adversarial attacks, both threat models should be considered.Tangent to research on defences against adversarial attacks, significant progress has been made towards training very low-precision deep neural networks to accuracy levels that are competitive with full-precision models BID4 BID22 BID20 .", "The current motivation for extreme quantization is the ability to deploy these models under hardware resource constraints, acceleration, or reduced power consumption.", "Ideally, 32× compression is possible by using 1-bit to represent single-precision floating point parameters.", "By similarly quantizing activations, we can reduce run-time memory consumption as well.", "These savings enable large scale deployment of neural networks on the billions of existing embedded devices.", "Very low-precision models were designed with deployment in mind, and may be responsible for making critical decisions in embedded systems, all subject to reverse engineering and a diverse set of real world attacks.", "With much at stake in applications like autonomous navigation, robotics, and network infrastructure, understanding how very low-precision neural networks behave in adversarial settings is essential.", "To that end, we make the following contributions:• To the best of our knowledge, we are the first to formally evaluate and interpret the robustness of binary neural networks (BNNs) to adversarial attacks on the MNIST BID10 Cortes, 1998) and CIFAR-10 (Krizhevsky, 2009 ) datasets.•", "We compare and contrast the properties of low-precision neural networks that confer adversarial robustness to previously proposed defense strategies. We", "then combine these properties to propose an optimal defense strategy.• We", "attempt to generalize and make recommendations regarding the suitability of lowprecision neural networks against various classes of attacks (e.g. single step vs. iterative).", "We suspect that plain BNNs implement two different kinds of gradient masking.", "We discovered the first by tracking the L1 norm of the hidden layer activations and unscaled logits.", "BNNs operate with larger range and variance than 'normal' networks, which can be explained by virtue of convolving inputs with greater magnitude (±1) compared with the typically small values taken by weights and activations.", "For our 64 kernel CNN, the logits were about 4× larger than the scaled or full-precision networks.", "This is analogous to the more complex defensive distillation procedure in which the model to be secured is trained with soft-labels generated by a teacher model.", "When training the teacher, a softmax temperature, T 1 is used.", "The distilled model is trained on the labels assigned by the teacher and using the same T .", "At test time, the model is deployed with T = 1, which causes the logits to explode with respect to their learned values.", "The logits saturate the softmax function and cause gradients to vanish, leading FGSM and JSMA to fail at a higher rate.", "However, this defense is defeated with a close enough guess for T , or via a black box attack BID3 .The", "second type of gradient masking is less easily overcome, and has to do with gradients being inherently discontinuous and non-smooth, as seen in FIG1 of Appendix B. We believe that this effect is what gives scaled BNNs an advantage over full-precision with respect to targeted attacks. Even", "more importantly, through a regularization effect, the decision boundary for the MLP with binary units FIG1 ) better represents the actual function to be learned, and is less susceptible to adversarial examples. But", "why does gradient masking have a disproportionate effect when attacking compared with training on clean inputs? Models", "'A' and 'B' were trained to within 1.2% test accuracy, while 'B' had improvements of 9.0% and 29.5% on JSMA and CWL2 attacks respectively, corresponding to 8× and 25× difference in accuracy, respectively, for adversarial vs. clean inputs. For JSMA", ", the performance gap can be attributed to the sub-optimality of the attack as it uses logits rather than softmax probabilities. Furthermore", ", to achieve its L0 goal, pairs of individual pixels are manipulated which is noisy process in a binarized model. The success", "of model 'S' with stochastically quantized weights in its third convolutional layer against iterative attacks is more easily explained. Adversarial", "examples are not random noise, and do not occur in random directions. In fact, neural", "networks are extremely robust to large amounts of benign noise. An iterative attack", "that attempts to fool our stochastically quantized model faces a unique model at every step, with unique gradients. Thus, the direction", "that minimizes the probability of the true class in the first iteration is unlikely to be the same in the second. An iterative attack", "making n steps is essentially attacking an ensemble of n models. By making a series", "of small random steps, the adversary is sent on the equivalent of a wild goose chase and has a difficult time making progress in any particularly relevant direction to cause an adversarial example.", "We have shown that for binarized neural networks, difficulty in training leads to difficulty when attacking.", "Although we did not observe a substantial improvement in robustness to single step attacks through binarization, by introducing stochasticity we have reduced the impact of the strongest attacks.", "Stochastic quantization is clearly far more computationally and memory efficient than a traditional ensemble of neural networks, and could be run entirely on a micro-controller with a pseudo random number generator.", "Our adversarial accuracy on MNIST against the best white-box attack (CWL2) is 71±2% (S64+) compared with the best full-precision model 1.8±0.9% (A256+).", "Blackbox results were competitive between binary and full-precision on MNIST, and binary models were slightly more robust for CIFAR-10, which we attribute to their improved regularization.", "Beyond their favourable speed and resource usage, we have demonstrated another benefit of deploying binary neural networks in industrial settings.", "Future work will consider other types of low-precision models as well as other adversarial attack methods.", "Table 6 : Error on clean MNIST test set for models with varying capacity and precision.", "A is fullprecision, B is binary, and C is binary with a learned scalar applied to the ReLU in hidden layers.", "All models were trained with Adam for 15 epochs with a batch size of 128 and a learning rate of 1e-3." ]

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[ "We conduct adversarial attacks against binarized neural networks and show that we reduce the impact of the strongest attacks, while maintaining comparable accuracy in a black-box setting" ]

[ "Unsupervised bilingual dictionary induction (UBDI) is useful for unsupervised machine translation and for cross-lingual transfer of models into low-resource languages.", "One approach to UBDI is to align word vector spaces in different languages using Generative adversarial networks (GANs) with linear generators, achieving state-of-the-art performance for several language pairs.", "For some pairs, however, GAN-based induction is unstable or completely fails to align the vector spaces.", "We focus on cases where linear transformations provably exist, but the performance of GAN-based UBDI depends heavily on the model initialization.", "We show that the instability depends on the shape and density of the vector sets, but not on noise; it is the result of local optima, but neither over-parameterization nor changing the batch size or the learning rate consistently reduces instability.", "Nevertheless, we can stabilize GAN-based UBDI through best-of-N model selection, based on an unsupervised stopping criterion.", "A word vector space -also sometimes referred to as a word embedding -associates similar words in a vocabulary with similar vectors.", "Learning a projection of one word vector space into another, such that similar words -across the two word embeddings -are associated with similar vectors, is useful in many contexts, with the most prominent example being the alignment of vocabularies of different languages.", "This is a key step in machine translation of low-resource languages ).", "An embedding of English words may associate thoughtful, considerate, and gracious with similar vectors, for example, but for English-Icelandic translation, it would be useful to have access to a cross-lingual word embedding space in which hugulsamur (lit.: 'thoughtful') was also associated with a similar vector.", "Such joint embeddings of words across languages can also be used to extract bilingual dictionaries.Projections between word vector spaces have typically been learned from dictionary seeds.", "In seminal papers such as BID22 and BID11 , these seeds would comprise thousands of words, but BID31 showed that we can learn reliable projections from as little as 50 words.", "and BID15 subsequently showed that the seed can be replaced with just words that are identical across languages; and BID1 showed that numerals can also do the job, in some cases; both proposals removing the need for an actual dictionary.", "Even more recently, a handful of papers have proposed an entirely unsupervised approach to projecting word vector spaces onto each other, based on Generative Adversarial Networks (GANs) BID12 .", "We present the core idea behind such approaches in §3, but briefly put, GANs are used to learn a linear transformation to minimize the divergence between a target distribution (say the Icelandic embeddings) and a source distribution (the English embeddings projected into the Icelandic space).The", "possibility of unsupervised bilingual dictionary induction (UBDI) has seemingly removed the data bottleneck in machine translation, evoking the idea that we can now learn to translate without human supervision ). Yet", ", it remains an open question whether the initial, positive results extrapolate to real-world scenarios of learning translations between low-resource language pairs. recently", "presented results suggesting that UBDI is challenged by some language pairs exhibiting very different morphosyntactic properties, as well as when the monolingual corpora are very different. In this", "paper, we identify easy, hard, and impossible instances of GAN-based UBDI, and apply a simple test for discriminating between them. The hard", "cases exhibit instability, i.e. their success depends heavily on initialization. We set up", "a series of experiments to investigate these hard cases.Our contributions We introduce a distinction between easy, hard, and impossible alignment problems over pairs of word vector spaces and show that a simple linearity test can be used to tell these cases apart. We show that", "the impossible cases are caused not necessarily by linguistic differences, but rather by properties of the corpora and the embedding algorithms. We also show", "that in the hard cases, the likelihood of being trapped in local minima depends heavily on the shape and density of the vector sets, but not on noise. Changes in the", "number of parameters, batch size, and learning rate do not alleviate the instability. Yet, using an", "unsupervised model selection method over N different initializations to select the best generators, leads to a 6.74% average error reduction over standard MUSE.Structure of the paper §2 presents MUSE BID6 , an approach to GAN-based UBDI. Here we also", "discuss theoretical results from the GAN literature, relevant to our case, and show a relation to a common point set registration method. In §3, we use", "a test based on Procrustes Analysis to discriminate between easy, hard, and impossible cases, discussing its relation with tests of isomorphism and isospectrality. We then focus", "on the hard cases, where linear transformations provably exist, but GANs exhibit considerable instability. Through a series", "of experiments, we analyze what affects the instability of GAN-based UBDI. §4 presents our", "unsupervised best-of-N model selection method for stabilizing GAN-based UBDI.", "Some pairs of word vector spaces are not alignable based on distributional information alone.", "For other pairs, GANs can be used to induce such an alignment, but the degree of instability is very susceptible to the shape and density of the word vector spaces, albeit not to noise.", "Instability is caused by local optima, but not remedied by standard techniques such as over-parameterization, increasing the batch size or decreasing the learning rate.", "We propose an unsupervised model selection criterion that enables stable learning, leading to a~7% error reduction over MUSE, and present further observations about the alignability of word vector distributions." ]

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[ "An empirical investigation of GAN-based alignment of word vector spaces, focusing on cases, where linear transformations provably exist, but training is unstable." ]

[ "Owing to the ubiquity of computer software, software vulnerability detection (SVD) has become an important problem in the software industry and in the field of computer security.", "One of the most crucial issues in SVD is coping with the scarcity of labeled vulnerabilities in projects that require the laborious manual labeling of code by software security experts.", "One possible way to address is to employ deep domain adaptation which has recently witnessed enormous success in transferring learning from structural labeled to unlabeled data sources.", "The general idea is to map both source and target data into a joint feature space and close the discrepancy gap of those data in this joint feature space.", "Generative adversarial network (GAN) is a technique that attempts to bridge the discrepancy gap and also emerges as a building block to develop deep domain adaptation approaches with state-of-the-art performance.", "However, deep domain adaptation approaches using the GAN principle to close the discrepancy gap are subject to the mode collapsing problem that negatively impacts the predictive performance.", "Our aim in this paper is to propose Dual Generator-Discriminator Deep Code Domain Adaptation Network (Dual-GD-DDAN) for tackling the problem of transfer learning from labeled to unlabeled software projects in the context of SVD in order to resolve the mode collapsing problem faced in previous approaches.", "The experimental results on real-world software projects show that our proposed method outperforms state-of-the-art baselines by a wide margin.", "In the software industry, software vulnerabilities relate to specific flaws or oversights in software programs which allow attackers to expose or alter sensitive information, disrupt or destroy a system, or take control of a program or computer system (Dowd et al., 2006) .", "The software vulnerability detection problem has become an important issue in the software industry and in the field of computer security.", "Computer software development employs of a vast variety of technologies and different software development methodologies, and much computer software contains vulnerabilities.", "This has necessitated the development of automated advanced techniques and tools that can efficiently and effectively detect software vulnerabilities with a minimal level of human intervention.", "To respond to this demand, many vulnerability detection systems and methods, ranging from open source to commercial tools, and from manual to automatic methods have been proposed and implemented.", "Most of the previous works in software vulnerability detection (SVD) (Neuhaus et al., 2007; Shin et al., 2011; Yamaguchi et al., 2011; Almorsy et al., 2012; Li et al., 2016; Grieco et al., 2016; Kim et al., 2017) have been developed based on handcrafted features which are manually chosen by knowledgeable domain experts who may have outdated experience and underlying biases.", "In many situations, handcrafted features normally do not generalize well.", "For example, features that work well in a certain software project may not perform well in other projects (Zimmermann et al., 2009) .", "To alleviate the dependency on handcrafted features, the use of automatic features in SVD has been studied recently (Li et al., 2018; Lin et al., 2018; Dam et al., 2018) .", "These works have shown the advantages of automatic features over handcrafted features in the context of software vulnerability detection.", "However, most of these approaches lead to another crucial issue in SVD research, namely the scarcity of labeled projects.", "Labelled vulnerable code is needed to train these models, and the process of labeling vulnerable source code is very tedious, time-consuming, error-prone, and challenging even for domain experts.", "This has led to few labeled projects compared with the vast volume of unlabeled ones.", "A viable solution is to apply transfer learning or domain adaptation which aims to devise automated methods that make it possible to transfer a learned model from the source domain with labels to the target domains without labels.", "Studies in domain adaptation can be broadly categorized into two themes: shallow (Borgwardt et al., 2006; Gopalan et al., 2011) and deep domain adaptations (Ganin & Lempitsky, 2015; Shu et al., 2018; .", "These recent studies have shown the advantages of deep over shallow domain adaptation (i.e., higher predictive performance and capacity to tackle structural data).", "Deep domain adaptation encourages the learning of new representations for both source and target data in order to minimize the divergence between them (Ganin & Lempitsky, 2015; Shu et al., 2018; .", "The general idea is to map source and target data to a joint feature space via a generator, where the discrepancy between the source and target distributions is reduced.", "Notably, the work of (Ganin & Lempitsky, 2015; Shu et al., 2018) employed generative adversarial networks (GANs) to close the discrepancy gap between source and target data in the joint space.", "However, most of aforementioned works mainly focus on transfer learning in the computer vision domain.", "The work of is the first work which applies deep domain adaptation to SVD with promising predictive performance on real-world source code projects.", "The underlying idea is to employ the GAN to close the gap between source and target domain in the joint space and enforce the clustering assumption (Chapelle & Zien, 2005) to utilize the information carried in the unlabeled target samples in a semi-supervised context.", "GANs are known to be affected by the mode collapsing problem (Goodfellow, 2016; Santurkar et al., 2018) .", "In particular, (Santurkar et al., 2018) recently studied the mode collapsing problem and further classified this into the missing mode problem i.e., the generated samples miss some modes in the true data, and the boundary distortion problem i.e., the generated samples can only partly recover some modes in the true data.", "It is certain that deep domain adaptation approaches that use the GAN principle will inherently encounter both the missing mode and boundary distortion problems.", "Last but not least, deep domain adaptation approaches using the GAN principle also face the data distortion problem.", "The representations of source and target examples in the joint feature space degenerate to very small regions that cannot preserve the manifold/clustering structure in the original space.", "Our aim in this paper is to address not only deep domain adaptation mode collapsing problems but also boundary distortion problems when employing the GAN as a principle in order to close the discrepancy gap between source and target data in the joint feature space.", "Our two approaches are:", "i) apply manifold regularization for enabling the preservation of manifold/clustering structures in the joint feature space, hence avoiding the degeneration of source and target data in this space; and", "ii) invoke dual discriminators in an elegant way to reduce the negative impacts of the missing mode and boundary distortion problems in deep domain adaptation using the GAN principle as mentioned before.", "We name our mechanism when applied to SVD as Dual Generator-Discriminator Deep Code Domain Adaptation Network (Dual-GD-DDAN).", "We empirically demonstrate that our Dual-GD-DDAN can overcome the missing mode and boundary distortion problems which is likely to happen as in Deep Code Domain Adaptation (DDAN) in which the GAN was solely applied to close the gap between the source and target domain in the joint space (see the discussion in Sections 2.4 and 3.3, and the visualization in Figure 3 ).", "In addition, we incorporate the relevant approaches -minimizing the conditional entropy and manifold regularization with spectral graph -proposed in to enforce the clustering assumption (Chapelle & Zien, 2005) and arrive at a new model named Dual Generator-Discriminator Semi-supervised Deep Code Domain Adaptation Network (Dual-GD-SDDAN).", "We further demonstrate that our Dual-GD-SDDAN can overcome the mode collapsing problem better than SCDAN in , hence obtaining better predictive performance.", "We conducted experiments using the data sets collected by (Lin et al., 2018) , that consist of five real-world software projects: FFmpeg, LibTIFF, LibPNG, VLC and Pidgin to compare our proposed Dual-GD-DDAN and Dual-GD-SDDAN with the baselines.", "The baselines consider to include VULD (i.e., the model proposed in (Li et al., 2018) without domain adaptation), MMD, DIRT-T, DDAN and SCDAN as mentioned and D2GAN (Nguyen et al., 2017 ) (a variant of the GAN using dual-discriminator to reduce the mode collapse for which we apply this mechanism in the joint feature space).", "Our experimental results show that our proposed methods are able to overcome the negative impact of the missing mode and boundary distortion problems inherent in deep domain adaptation approaches when solely using the GAN principle as in DDAN and SCDAN .", "In addition, our method outperforms the rival baselines in terms of predictive performance by a wide margin.", "is also a sequence of L embedding vectors.", "We wish to bridge the gap between the source and target domains in the joint feature space.", "This allows us to transfer a classifier trained on the source domain to predict well on the target domain.", "Software vulnerability detection (SVD) is an important problem in the software industry and in the field of computer security.", "One of the most crucial issues in SVD is to cope with the scarcity of labeled vulnerabilities in projects that require the laborious labeling of code by software security experts.", "In this paper, we propose the Dual Generator-Discriminator Deep Code Domain Adaptation Network (Dual-GD-DDAN) method to deal with the missing mode and boundary distortion problems which arise from the use of the GAN principle when reducing the discrepancy between source and target data in the joint space.", "We conducted experiments to compare our Dual-GD-DDAN method with the state-of-the-art baselines.", "The experimental results show that our proposed method outperforms these rival baselines by a wide margin in term of predictive performances." ]

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[ "Our aim in this paper is to propose a new approach for tackling the problem of transfer learning from labeled to unlabeled software projects in the context of SVD in order to resolve the mode collapsing problem faced in previous approaches." ]

[ "Representation learning is one of the foundations of Deep Learning and allowed important improvements on several Machine Learning tasks, such as Neural Machine Translation, Question Answering and Speech Recognition.", "Recent works have proposed new methods for learning representations for nodes and edges in graphs.", "Several of these methods are based on the SkipGram algorithm, and they usually process a large number of multi-hop neighbors in order to produce the context from which node representations are learned.", "In this paper, we propose an effective and also efficient method for generating node embeddings in graphs that employs a restricted number of permutations over the immediate neighborhood of a node as context to generate its representation, thus ego-centric representations.", "We present a thorough evaluation showing that our method outperforms state-of-the-art methods in six different datasets related to the problems of link prediction and node classification, being one to three orders of magnitude faster than baselines when generating node embeddings for very large graphs.", "Many important problems involving graphs require the use of learning algorithms to make predictions about nodes and edges.", "These predictions and inferences on nodes and edges from a graph are typically done using classifiers with carefully engineered features BID13 .", "These features, besides taking time and manual labor to be developed and acquired, usually do not generalize well to other problems or contexts.The field of Natural Language Processing (NLP) has had many advances due to the use of algorithms that learn word representations, instead of manually extracted features.", "Originally proposed by BID5 and commonly used with Word2Vec algorithms like CBOW and SkipGram (Mikolov et al., 2013a) , word embeddings are used in many state-of-the-art solutions for neural machine translation (Luong & Manning, 2016; BID12 , question answering BID2 and natural language generation (Wen et al., 2015) .", "Recent works have proposed new methods for learning representations for nodes and edges in graphs, based on random walks (Perozzi et al., 2014; BID13 or auto-encoding adjacency vectors (Wang et al., 2016) .In", "this paper, we propose a new general purpose method for generating node embeddings in very large graphs, which we call Neighborhood Based Node Embeddings (or simply NBNE). NBNE", "is based on the SkipGram algorithm and uses nodes neighborhoods as contexts. NBNE", "outperforms state-of-the-art DeepWalk (Perozzi et al., 2014) and Node2Vec BID13 for the tasks of link prediction and node classification on six collections, being one to three orders of magnitude faster. In this", "work, we considered DeepWalk and Node2Vec as baselines.The main reason for this improvement on effectiveness and efficiency is that we concentrate learning on the \"predictable\" parts of the graph. A study", "by Facebook research BID8 found that each person in the world (at least among the people active on Facebook) is connected to every other person by an average 3.57 other people. In a graph", "of this magnitude and connectedness, learning node embeddings by maximizing the log-probability of predicting nearby nodes in a random walk (with a window size of 5) can be highly inefficient and make it 'harder' for the embeddings to be constructed, even if these random walks are biased like in Node2Vec. We suspect", "this can also make them more unstable, which would explain why they need more iterations before embedding convergence.", "The proposed node embedding method NBNE shows results similar or better than the state-of-theart algorithms Node2Vec and DeepWalk on several different datasets.", "It shows promising results in two application scenarios: link prediction and node classification, while being efficient and easy to compute for large graphs, differently from other node embedding algorithms, such as LINE (Tang et al., 2015) or SDNE (Wang et al., 2016) .", "NBNE focuses learning on node's immediate neighbors, creating more ego-centric representations, which we suspect makes them more stable and faster to learn.", "Empirical results show that, although it has a similar time complexity, NBNE can be trained in a fraction of the time taken by DeepWalk (10 to 190 times faster) or Node2Vec (200 to 6,000 times faster), giving fairly robust results.", "Since embeddings are learned using only a node's immediate neighbors, we suspect it should also be easier to implement more stable asynchronous distributed algorithms to train them, and we leave this as future work." ]

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[ "A faster method for generating node embeddings that employs a number of permutations over a node's immediate neighborhood as context to generate its representation." ]

[ "Orthogonal recurrent neural networks address the vanishing gradient problem by parameterizing the recurrent connections using an orthogonal matrix.", "This class of models is particularly effective to solve tasks that require the memorization of long sequences.", "We propose an alternative solution based on explicit memorization using linear autoencoders for sequences.", "We show how a recently proposed recurrent architecture, the Linear Memory Network, composed of a nonlinear feedforward layer and a separate linear recurrence, can be used to solve hard memorization tasks.", "We propose an initialization schema that sets the weights of a recurrent architecture to approximate a linear autoencoder of the input sequences, which can be found with a closed-form solution.", "The initialization schema can be easily adapted to any recurrent architecture.\n ", "We argue that this approach is superior to a random orthogonal initialization due to the autoencoder, which allows the memorization of long sequences even before training.", "The empirical analysis show that our approach achieves competitive results against alternative orthogonal models, and the LSTM, on sequential MNIST, permuted MNIST and TIMIT.", "Several sequential problems require the memorization of long sequences of patterns.", "As an example, a generative model for music should be able to memorize long sequences of notes and be able to repeat them, as it is typically done in musical pieces.", "RNNs and LSTMs struggle to solve even simple memorization tasks (Arjovsky et al., 2015; Graves et al., 2014) .", "Therefore, it is important to study alternative solutions to this problem.", "Orthogonal RNNs are a class of recurrent architectures that solve the vanishing gradient problem by constraining the recurrent connections to be an orthogonal or unitary matrix (Arjovsky et al., 2015) .", "They are particularly effective to solve long memorization tasks Henaff et al. (2016) .", "In this paper, we address the problem of memorization with orthogonal RNNs and linear autoencoders.", "Our objective is to find a solution to the problem of memorization of long sequences.", "The memorization of long sequences with orthogonal models can require a large number of hidden units, increasing the hidden state size and the cost in time and space.", "If we assume that the input sequences in the training data lay in a low-dimensional manifold, as is typically believed for real-world data, then we can train an autoencoder with a small number of hidden units, sufficient to encode the entire sequence.", "If we restrict ourselves to the linear case, we can compute the optimal autoencoder with a closedform solution (Sperduti, 2013) .", "This result can be exploited to initialize recurrent architectures to approximate the linear autoencoder for the input sequences.", "In our experiments we use the RNN (Elman, 1990 ) and the Linear Memory Network (LMN) (Bacciu et al., 2019) .", "The LMN with the autoencoder initialization is a recurrent architecture equivalent to the Elman RNN but able to solve the vanishing gradient problem and memorize input sequences with a minimal hidden state.", "We test our approach on classic benchmarks for orthogonal RNNs, showing that our proposed approach behaves similarly to orthogonal architectures on pure memorization tasks, and even improving the performance on real-world datasets.", "Finally, we show that the model can also be used in situations where a strict orthogonal parameterization struggles (Vorontsov et al., 2017) , like the TIMIT benchmark (Garofolo et al., 1993) .", "Work on orthogonal models typically focuses on the properties of an orthogonal parameterization at the backward step, to address the vanishing gradient.", "In our work instead, we focus on the forward step, by investigating the effect of an orthogonal parameterization against an autoencoder-based solution.", "For these reasons, we are not particularly interested in enforcing exact orthogonality constraints, but in the study of the effectiveness of an autoencoder-based memorization mechanism.", "Our proposed approach requires the memorization of the entire sequence within the hidden state activations.", "It is necessary to note that this approach can be quite inefficient whenever the underlying task does not require complete memorization of the input sequences.", "In this situation, the hidden state size necessary to encode the entire sequence could be much larger than the minimal hidden state size necessary to solve the problem.", "Therefore, it is fundamental to allow the model to diverge from the orthogonality or the autoencoder solution by only imposing soft orthogonality constraints.", "Nonetheless, we believe that even when complete full memorization is not necessary, the autoencoder initialization can help to speed up training convergence by allowing the model to remember long sequences, which can then be gradually forgotten during training if deemed uninformative.", "In summary, the main contributions of the paper are:", "• the proposal of a novel initialization schema designed for the explicit memorization of long sequences;", "• highlighting the connection between orthogonal models and linear autoencoders for sequences;", "• an empirical analysis that shows the effectiveness of our proposed initialization schema to solve tasks that require long memorization.", "In this work, we studied the problem of building an autoencoder-based memorization mechanism.", "This system has the ability to encode and decode the input sequences to compute the desired target.", "Using results for the linear autoencoder for sequences, we showed how to initialize a recurrent neural network by approximating a linear autoencoder of the input sequences.", "The architecture exploits a linear recurrence to obtain a better approximation of the autoencoder.", "The results show that an autoencoder-based initialization can be effective for learning memorization tasks.", "In the future, we plan to extend this work by studying the effect of the autoencoder during training, possibly by enforcing the encoding of the input sequence even during the learning phase.", "Another possible avenue of research is the study of better optimization algorithms for the parameters of the linear component, where the linearity could be exploited to speed up the training process through dedicated learning algorithms." ]

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[ "We show how to initialize recurrent architectures with the closed-form solution of a linear autoencoder for sequences. We show the advantages of this approach compared to orthogonal RNNs." ]

[ "This paper improves upon the line of research that formulates named entity recognition (NER) as a sequence-labeling problem.", "We use so-called black-box long short-term memory (LSTM) encoders to achieve state-of-the-art results while providing insightful understanding of what the auto-regressive model learns with a parallel self-attention mechanism.", "Specifically, we decouple the sequence-labeling problem of NER into entity chunking, e.g., Barack_B Obama_E was_O elected_O, and entity typing, e.g., Barack_PERSON Obama_PERSON was_NONE elected_NONE, and analyze how the model learns to, or has difficulties in, capturing text patterns for each of the subtasks.", "The insights we gain then lead us to explore a more sophisticated deep cross-Bi-LSTM encoder, which proves better at capturing global interactions given both empirical results and a theoretical justification.", "Named entity recognition is an important task in information extraction in which we seek to locate entity chunks in text and classify their entity types.", "Originally a structured prediction task, NER has since been formulated as a task of sequential token labeling, much like text chunking and part-ofspeech tagging.", "With the ability to compute representations of past and future context respectively for each token, bidirectional LSTM (Bi-LSTM) has proved a robust building block for sequencelabeling NER BID7 BID13 BID0 .", "However, it has been predominantly used as a black box; research directed to understanding how the model learns to tackle the task is minimal.In this work, we decouple sequence-labeling NER into the entity chunking and entity typing subtasks, and seek insight into what patterns LSTM learns to capture or has difficulties capturing.", "We propose the use of a fast and effective parallel self-attention mechanism alongside Bi-LSTM.", "Unlike traditional attention mechanisms used for tasks such as machine translation BID12 and sentence classification BID2 BID11 , our self-attentive Bi-LSTM uses the hidden state of each token as its own query vector and computes context vectors for all tokens in parallel.", "For both subtasks, we then find important global patterns that cross past and future context, and in particular discover the way multi-chunk entities are handled.", "Furthermore, we discover that the theoretical limitations of traditional Bi-LSTMs harms performance on the task, and hence propose using a cross construction of deep Bi-LSTMs.", "As a result, with these cross structures, both selfattentive Bi-LSTM and cross-Bi-LSTM achieve new state-of-the-art results on sequence-labeling NER.In Section 3, the normal Bi-LSTM-CNN model is formulated.", "Section 4 details the computation of the parallel self-attention mechanism.", "Section 5 presents the empirical results and detailed analyses of the models, with a particular focus on patterns captured for {B, I, E} labels.", "Finally in Section 6, cross-Bi-LSTM-CNN is formulated and evaluated on a theoretical basis.", "Our contribution is threefold:• We provide insightful understanding of how a sequence-labeling model tackles NER and the difficulties it faces;• We propose using cross-Bi-LSTM-CNN for sequence-labeling NER with theoreticallygrounded improvements.", "In this paper, we have decoupled named entity recognition into entity chunking and entity typing and demonstrated how sequence-labeling models can learn to handle each of these two subtasks.", "By using a fast parallel self-attention mechanism, we have discovered how the beginning and ending of a multi-token entity is determined and how they are jointly correlated to locate the inside tokens.Further, through our quantitative and qualitative analyses for both chunking and typing, we have shown that it is crucial to capture global patterns that cross both sides of a token.", "We demonstrate the theoretical limitation of the conventional deep Bi-LSTM-CNN used in sequence labeling tasks.", "In addition to the interpretability of the proposed parallel self-attention, it is shown that it constitutes a way to correlate past and future contexts.", "We have also provided deep cross-Bi-LSTM-CNN as another way to extract global context features.", "With their respective cross structures, both selfattentive Bi-LSTM and cross-Bi-LSTM achieve new state-of-the-art results on sequence-labeling NER." ]

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[ "We provide insightful understanding of sequence-labeling NER and propose to use two types of cross structures, both of which bring theoretical and empirical improvements." ]

[ "Knowledge Graph Embedding (KGE) is the task of jointly learning entity and relation embeddings for a given knowledge graph.", "Existing methods for learning KGEs can be seen as a two-stage process where", "(a) entities and relations in the knowledge graph are represented using some linear algebraic structures (embeddings), and", "(b) a scoring function is defined that evaluates the strength of a relation that holds between two entities using the corresponding relation and entity embeddings.", "Unfortunately, prior proposals for the scoring functions in the first step have been heuristically motivated, and it is unclear as to how the scoring functions in KGEs relate to the generation process of the underlying knowledge graph.", "To address this issue, we propose a generative account of the KGE learning task.", "Specifically, given a knowledge graph represented by a set of relational triples (h, R, t), where the semantic relation R holds between the two entities h (head) and t (tail), we extend the random walk model (Arora et al., 2016a) of word embeddings to KGE.", "We derive a theoretical relationship between the joint probability p(h, R, t) and the embeddings of h, R and t.", "Moreover, we show that marginal loss minimisation, a popular objective used by much prior work in KGE, follows naturally from the log-likelihood ratio maximisation under the probabilities estimated from the KGEs according to our theoretical relationship.", "We propose a learning objective motivated by the theoretical analysis to learn KGEs from a given knowledge graph.", "The KGEs learnt by our proposed method obtain state-of-the-art performance on FB15K237 and WN18RR benchmark datasets, providing empirical evidence in support of the theory.\n", "Knowledge graphs such as Freebase BID2 organise information in the form of graphs, where entities are represented by vertices in the graph and the relation between two entities is represented by the edge that connects the corresponding two vertices.", "By embedding entities and relations that exist in a knowledge graph in some (possibly lower-dimensional and latent) space we can infer previously unseen relations between entities, thereby expanding a given knowledge graph BID11 BID20 Lin et al., 2015; BID9 BID16 BID17 BID4 .Existing", "KGE methods can be seen as involving two main steps. First, given", "a knowledge graph represented by a set of relational triples (h, R, t), where a semantic relation R holds between a head entity h and a tail entity t, entities and relations are represented using some mathematical structures such as vectors, matrices or tensors. Second, a scoring", "function is proposed that evaluates the relational strength of a triple (h, R, t) and entity and relation embeddings that optimise the defined scoring function are learnt using some optimisation method. Table 1 shows some", "of the scoring functions proposed in prior work in KGE learning.Despite the wide applications of entity and relation embeddings created via KGE methods, the existing scoring functions are motivated heuristically to capture some geometric requirements of the embedding space. For example, TransE", "BID4 assumes that the entity and relation embeddings co-exist in the same (possibly lower dimensional) vector space and translating (shifting) the head entity embedding by the relation embedding must make it closer to the tail entity embedding, whereas ComplEx BID16 ) models the asymmetry in relations using", "We proposed RelWalk, a generative model of KGE and derived a theoretical relationship between the probability of a triple and entity, relation embeddings.", "We then proposed a learning objective based on the theoretical relationship we derived.", "Experimental results on a link prediction and a triple classification tasks show that RelWalk obtains strong performances in multiple benchmark datasets." ]

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[ "We present a theoretically proven generative model of knowledge graph embedding. " ]

[ "Currently the only techniques for sharing governance of a deep learning model are homomorphic encryption and secure multiparty computation.", "Unfortunately, neither of these techniques is applicable to the training of large neural networks due to their large computational and communication overheads.", "As a scalable technique for shared model governance, we propose splitting deep learning model between multiple parties.", "This paper empirically investigates the security guarantee of this technique, which is introduced as the problem of model completion: Given the entire training data set or an environment simulator, and a subset of the parameters of a trained deep learning model, how much training is required to recover the model’s original performance? ", "We define a metric for evaluating the hardness of the model completion problem and study it empirically in both supervised learning on ImageNet and reinforcement learning on Atari and DeepMind Lab.", "Our experiments show that (1) the model completion problem is harder in reinforcement learning than in supervised learning because of the unavailability of the trained agent’s trajectories, and (2) its hardness depends not primarily on the number of parameters of the missing part, but more so on their type and location. ", "Our results suggest that model splitting might be a feasible technique for shared model governance in some settings where training is very expensive.", "With an increasing number of deep learning models being deployed in production, questions regarding data privacy and misuse are being raised BID4 .", "The trend of training larger models on more data BID28 , training models becomes increasingly expensive.", "Especially in a continual learning setting where models get trained over many months or years, they accrue a lot of value and are thus increasingly susceptible to theft.", "This prompts for technical solutions to monitor and enforce control over these models BID41 .", "We are interested in the special case of shared model governance: Can two or more parties jointly train a model such that each party has to consent to every forward (inference) and backward pass (training) through the model?Two", "popular methods for sharing model governance are homomorphic encryption (HE; BID36 and secure multi-party computation (MPC; BID48 . The", "major downside of both techniques is the large overhead incurred by every multiplication, both computationally, >1000x for HE BID29 BID14 , >24x for MPC BID25 BID7 , in addition to space (>1000x in case of HE) and communication (>16 bytes per 16 bit floating point multiplication in case of MPC). Unfortunately", ", this makes HE and MPC inapplicable to the training of large neural networks. As scalable", "alternative for sharing model governance with minimal overhead, we propose the method of model splitting: distributing a deep learning model between multiple parties such that each party holds a disjoint subset of the model's parameters.Concretely, imagine the following scenario for sharing model governance between two parties, called Alice and Bob. Alice holds", "the model's first layer and Bob holds the model's remaining layers. In each training", "step (1) Alice does a forward pass through the first layer, (2) sends the resulting activations to Bob, (3) Bob completes the forward pass, computes the loss from the labels, and does a backward pass to the first layer, (4) sends the resulting gradients to Alice, and (5) Alice finishes the backward pass. How much security", "would Alice and Bob enjoy in this setting? To answer this question", ", we have to consider the strongest realistic attack vector. In this work we assume", "that the adversary has access to everything but the missing parameters held by the other party. How easy would it be for", "this adversary to recover the missing part of the model? We introduce this as the", "problem of model completion:Given the entire training data set or an environment simulator, and a subset of the parameters of a trained model, how much training is required to recover the model's original performance?In this paper, we define", "the problem of model completion formally (Section 3.1), propose a metric to measure the hardness of model completion (Section 3.2), and provide empirical results (Section 4 and Section 5) in both the supervised", "learning (SL) and in reinforcement learning (RL). For our SL experiments we", "use the AlexNet convolutional network BID26 and the ResNet50 residual network BID17 on ImageNet BID9 ); for RL we use A3C and Rainbow BID19 in the Atari domain BID1 and IMPALA BID11 on DeepMind Lab BID0 . After training the model,", "we reinitialize one of the model's layers and measure how much training is required to complete it (see FIG1 ).Our key findings are: (1)", "Residual networks are easier to complete than nonresidual networks (", "Our results shed some initial glimpse on the model completion problem and its hardness.", "Our findings include: residual networks are easier to complete than non-residual networks, lower layers are often harder to complete than higher layers, and RL models are harder to complete than SL models.", "Nevertheless several question remain unanswered: Why is the difference in MC-hardness less pronounced between lower and higher layers in Rainbow and AlexNet than in A3C?", "Why is the absolute number of parameters insubstantial?", "Are there retraining procedures that are faster than T 1 ?", "Furthermore, our definition of hardness of the model completion problem creates an opportunity to modulate the hardness of model completion.", "For example, we could devise model architectures with the explicit objective that model completion be easy (to encourage robustness) or hard (to increase security when sharing governance through model splitting).", "Importantly, since Equation 1 can be evaluated automatically, we can readily combine this with architecture search BID50 .Our", "experiments show that when we want to recover 100% of the original performance, model completion may be quite costly: ∼ 40% of the original training costs in many settings; lower performance levels often retrain significantly faster. In", "scenarios where a model gets trained over many months or years, 40% of the cost may be prohibitively expensive. However", ", this number also has to be taken with a grain of salt because there are many possible retraining procedures that we did not try. The security", "properties of model splitting as a method for shared governance require further investigation: in addition to more effective retraining procedures, an attacker may also have access to previous activations or be able to inject their own training data. Yet our experiments", "suggest that model splitting could be a promising method for shared governance. In contrast to MPC", "and HE it has a substantial advantage because it is cost-competitiveness with normal training and inference.Learning rate Training batches Retraining batches 5e − 2 0 0 5e − 3 60e3 30e3 5e − 4 90e3 45e3 5e − 5 105e3 72.5e3 Table 1 : AlexNet: Learning schedule for training and retraining procedures." ]

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[ "We study empirically how hard it is to recover missing parts of trained models" ]

[ "This paper proposes variational domain adaptation, a unified, scalable, simple framework for learning multiple distributions through variational inference.", "Unlike the existing methods on domain transfer through deep generative models, such as StarGAN (Choi et al., 2017) and UFDN (Liu et al., 2018), the variational domain adaptation has three advantages.", "Firstly, the samples from the target are not required.", "Instead, the framework requires one known source as a prior $p(x)$ and binary discriminators, $p(\\mathcal{D}_i|x)$, discriminating the target domain $\\mathcal{D}_i$ from others.", "Consequently, the framework regards a target as a posterior that can be explicitly formulated through the Bayesian inference, $p(x|\\mathcal{D}_i) \\propto p(\\mathcal{D}_i|x)p(x)$, as exhibited by a further proposed model of dual variational autoencoder (DualVAE).", "Secondly, the framework is scablable to large-scale domains.", "As well as VAE encodes a sample $x$ as a mode on a latent space: $\\mu(x) \\in \\mathcal{Z}$, DualVAE encodes a domain $\\mathcal{D}_i$ as a mode on the dual latent space $\\mu^*(\\mathcal{D}_i) \\in \\mathcal{Z}^*$, named domain embedding.", "It reformulates the posterior with a natural paring $\\langle, \\rangle: \\mathcal{Z} \\times \\mathcal{Z}^* \\rightarrow \\Real$, which can be expanded to uncountable infinite domains such as continuous domains as well as interpolation.", "Thirdly, DualVAE fastly converges without sophisticated automatic/manual hyperparameter search in comparison to GANs as it requires only one additional parameter to VAE.", "Through the numerical experiment, we demonstrate the three benefits with multi-domain image generation task on CelebA with up to 60 domains, and exhibits that DualVAE records the state-of-the-art performance outperforming StarGAN and UFDN.", "\"...we hold that all the loveliness of this world comes by communion in Ideal-Form.", "All shapelessness whose kind admits of pattern and form, as long as it remains outside of Reason and Idea, is ugly from that very isolation from the Divine-Thought.", "Agents that interact in various environments have to handle multiple observation distributions .", "Domain adaptation BID0 ) is a methodology employed to exploit deep generative models, such as adversarial learning BID2 and variational inference BID8 , that can handle distributions that vary with environments and other agents.", "Further, multi-task learning and domain transfer are examples of how domain adaptation methodology is used.", "We focus on domain transfer involving transfers across a distribution between domains.", "For instance, pix2pix BID5 ) outputs a sample from the target domain that corresponds to the input sample from the source domain.", "This can be achieved by learning the pair relation of samples from the source and target domains.", "CycleGAN BID21 transfers the samples between two domains using samples obtained from both domains.", "Similarly, UNIT BID12 , DiscoGAN , and DTN BID20 have been proposed in previous studies.However, the aforementioned method requires samples that are obtained from the target domains, and because of this requirement, it cannot be applied to domains for which direct sampling is expensive or often impossible.", "For example, the desired, continuous, high-dimensional action in the environment, intrinsic reward (e.g., preference and curiosity) and the policy of interacting agents other than itself cannot be sampled from inside, and they can only discriminate the proposed input.", "Even for ourselves, the concept of beauty or interest in our conscious is subjective, complex, and difficult to be sampled from the inside, although it is easy to discriminate on the outside.", "The key concept of variational domain adaptation.", "a) Given the proposal drawn from the prior, the discriminator discriminates the target domain from the others.", "Each domain is posterior for the prior N (z|0, 1); further, the distribution in the latent space is observed to be a normal distribution using the conjugate likelihood.", "b) Domain transfer is represented by the mean shift in the latent space.", "c) Domain embedding: After training, all the domains can only be represented by vectors µ i .In", "this study, we propose variational domain adaptation, which is a framework for targets that pose challenges with respect to direct sampling. One", "solution is multi-domain semi-supervision, which converts the problem to semi-supervised learning, thereby making is possible to perform variational inference. In", "this supervision, a source domain is regarded as a prior p(x) and a target domain is considered to be a posterior p(x|D i ) by referring to the label given by a supervised discriminator p(D i |x) that distinguishes the target domain from others. Our", "model imitates the behavior of the discriminator and models the target domain using a simple conclusion of the Bayesian theorem, p θ (x|D i ) ∝ p θ (D i |x)p θ (x). The", "end-to-end learning framework also makes it possible to learn good prior p θ (x) with respect to all the domains. After", "the training was completed, the posterior p θ (x|D i ) succeeded in deceiving the discriminator p(D i |x). This", "concept is similar to rejection sampling in the Monte Carlo methods. Further", ", variational domain adaptation is the first important contribution from this study.The second contribution from this study is a model of dual variational autoencoder (DualVAE), which is a simple extension of the conditional VAE BID9 ), employed to demonstrate our concept of multi-domain semi-supervision. DualVAE", "learns multiple domains in one network by maximizing the variational lower bound of the total negative KL-divergence between the target domain and the model. DualVAE", "uses VAE to model the prior p(x) and an abstract representation for the discriminator p(D i |x). The major", "feature of DualVAE is domain embedding that states that all the posteriors are modeled as a normal distribution N (z|µ i , σ 2 ) in the same latent space Z using the conjecture distribution of the prior. Here, µ i", "is the domain embedding that represents the domain D i . This enables", "us to sample from p θ (x|D i ). Our major finding", "was that the discriminator of DualVAE was a simple inner product between the two means of domain embedding and the VAE output: DISPLAYFORM0 that acts as a natural paring between the sample and the domain. The probabilistic", "end-to-end model learns multiple domains in a single network, making it possible to determine the effect of transfer learning and to learn data that multi-domains cannot observe from sparse feedback. Domain embedding", "is a powerful tool and allows us to use VAEs instead of GANs.The third contribution of this study is that DualVAE was validated for use in a recommendation task using celebA BID13 . In the experiment", ", using celebA and face imaging data obtained based on evaluations by 60 users, an image was generated based on the prediction of user evaluation and an ideal image that was determined to be good by multiple users. We demonstrated", "that the image could be modified to improve the evaluation by interpolating the image, and the image was evaluated using the domain inception score (DIS), which is the score of the model that has learned the preference of each user. We present the", "beauty inside each evaluator by simply sampling p θ (x|D i ). The DIS of DualVAE", "is higher than that of a single domain, and the dataset and code are available online.", "Variational domain adaptation, which is a unified framework for learning multiple distributions in a single network, is proposed in this study.", "Our framework uses one known source as a prior p(x) and binary discriminator p(D i |x), thereby discriminating the target domain D i from the others; this is in contrast with the existing frameworks in which samples undergo domain transfer through deep generative models.", "Consequently, our framework regards the target as a posterior that is characterized through Bayesian inference, p(x|D i ) ∝ p(D i |x)p(x).", "This was exhibited by the proposed DualVAE.", "The major feature of the DualVAE is domain embedding, which is a powerful tool that encodes all the domains and the samples obtained from the prior into normal distributions in the same latent space as that learned by a unified network through variational inference.", "In the experiment, we applied our framework and model to a multi-domain image generation task.", "celebA and face image data that were obtained based on evaluation by 60 users were used, and the result revealed that the DualVAE method outperformed StarGAN and UFDN.Several directions should be considered for future research.", "First, we intend to expand DualVAEs for learning in complex domains, such as high-resolution images with several models, for example, glow BID7 .", "Second, we will perform an experiment to consider wider domains with respect to beauty.", "We expect that our proposed method will contribute to society in a number of ways and will help to deal with the paradigm of multiple contexts-multimodal, multi-task, and multi-agent contexts." ]

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[ "This paper proposes variational domain adaptation, a unified, scalable, simple framework for learning multiple distributions through variational inference" ]

[ "We propose a new method to train neural networks based on a novel combination of adversarial training and provable defenses.", "The key idea is to model training as a procedure which includes both, the verifier and the adversary.", "In every iteration, the verifier aims to certify the network using convex relaxation while the adversary tries to find inputs inside that convex relaxation which cause verification to fail.", "We experimentally show that this training method is promising and achieves the best of both worlds – it produces a model with state-of-the-art accuracy (74.8%) and certified robustness (55.9%) on the challenging CIFAR-10 dataset with a 2/255 L-infinity perturbation.", "This is a significant improvement over the currently known best results of 68.3% accuracy and 53.9% certified robustness, achieved using a 5 times larger network than our work.", "The discovery of adversarial examples in deep learning (Szegedy et al., 2013) has increased the importance of creating new training methods which produce accurate and robust neural networks with provable guarantees.", "Existing work: adversarial and provable defenses Adversarial training (Goodfellow et al., 2015; Kurakin et al., 2017) provides a basis framework which augments the training procedure with adversarial inputs produced by an adversarial attack.", "Madry et al. (2018) instantiated adversarial training using a strong iterative adversary and showed that their approach can train models which are highly robust against the strongest known adversarial attacks (Carlini & Wagner, 2017) .", "This method has also been used to train robust ImageNet models (Xie et al., 2019) .", "While promising, the main drawback of the method is that when instantiated in practice, via an approximation of an otherwise intractable optimization problem, it provides no guarantees -it does not produce a certificate that there are no possible adversarial attacks which could potentially break the model.", "To address this lack of guarantees, recent line of work on provable defenses Raghunathan et al., 2018; has proposed to train neural networks which are certifiably robust under a specific attacker threat model.", "However, these guarantees come at the cost of a significantly lower standard accuracy than models trained using adversarial training.", "This setting raises a natural question -can we leverage ideas from both, adversarial training techniques and provable defense methods, so to obtain models with high accuracy and certified robustness?", "This work: combining adversarial and provable defenses In this work, we take a step towards addressing this challenge.", "We show that it is possible to train more accurate and provably robust neural networks using the same convex relaxations as those used in existing, state-of-the-art provable defense methods, but with a new, different optimization procedure inspired by adversarial training.", "Our optimization works as follows:", "(i) to certify a property (e.g., robustness) of the network, the verifier produces a convex relaxation of all possible intermediate vector outputs in the neural network, then", "(ii) an adversary now searches over this (intermediate) convex regions in order to find, what we refer to as a latent adversarial example -a concrete intermediate input contained in the relaxation that when propagated through the network causes a misclassification that prevents verification, and finally", "(iii) the resulting latent adversarial examples are now incorporated into our training scheme using adversarial training.", "Overall, we can see this method as bridging the gap between adversarial training and provable defenses (it can conceptually be instantiated with any convex relaxation).", "We experimentally show that the method is promising and results in a neural network with state-of-theart 78.8% accuracy and 58.1% certified robustness on the challenging CIFAR-10 dataset with 2/255 L ∞ perturbation (the best known existing results are 68.3% accuracy and 53.9% certified robustness using 5 times larger network ).", "We presented a new method to train certified neural networks.", "The key concept was to combine techniques from provable defenses using convex relaxations with those of adversarial training.", "Our method achieves state-of-the-art 78.8% accuracy and 58.1% certified robustness on CIFAR-10 with a 2/255 L ∞ perturbation, significantly outperforming prior work when considering a single network (it also achieves competitive results on 8/255 L ∞ ).", "The method is general and can be instantiated with any convex relaxation.", "A promising future work item is scaling to larger networks: this will require tight convex relaxations with a low memory footprint that allow for efficient projection.", "Here we provide additional details that were omitted in the main body of the paper." ]

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[ "We propose a novel combination of adversarial training and provable defenses which produces a model with state-of-the-art accuracy and certified robustness on CIFAR-10. " ]

[ "Learning tasks on source code (i.e., formal languages) have been considered recently, but most work has tried to transfer natural language methods and does not capitalize on the unique opportunities offered by code's known syntax.", "For example, long-range dependencies induced by using the same variable or function in distant locations are often not considered.", "We propose to use graphs to represent both the syntactic and semantic structure of code and use graph-based deep learning methods to learn to reason over program structures.\n\n", "In this work, we present how to construct graphs from source code and how to scale Gated Graph Neural Networks training to such large graphs.", "We evaluate our method on two tasks: VarNaming, in which a network attempts to predict the name of a variable given its usage, and VarMisuse, in which the network learns to reason about selecting the correct variable that should be used at a given program location.", "Our comparison to methods that use less structured program representations shows the advantages of modeling known structure, and suggests that our models learn to infer meaningful names and to solve the VarMisuse task in many cases.", "Additionally, our testing showed that VarMisuse identifies a number of bugs in mature open-source projects.", "The advent of large repositories of source code as well as scalable machine learning methods naturally leads to the idea of \"big code\", i.e., largely unsupervised methods that support software engineers by generalizing from existing source code BID4 .", "Currently, existing deep learning models of source code capture its shallow, textual structure, e.g. as a sequence of tokens BID15 BID22 BID3 , as parse trees BID18 , or as a flat dependency networks of variables BID23 .", "Such models miss out on the opportunity to capitalize on the rich and well-defined semantics of source code.", "In this work, we take a step to alleviate this by including two additional signal sources in source code: data flow and type hierarchies.", "We do this by encoding programs as graphs, in which edges represent syntactic relationships (e.g. \"token before/after\") as well as semantic relationships (\"variable last used/written here\", \"formal parameter for argument is called stream\", etc.).", "Our key insight is that exposing these semantics explicitly as structured input to a machine learning model lessens the requirements on amounts of training data, model capacity and training regime and allows us to solve tasks that are beyond the current state of the art.We explore two tasks to illustrate the advantages of exposing more semantic structure of programs.", "First, we consider the VARNAMING task BID1 BID23 , in which given some source code, the \"correct\" variable name is inferred as a sequence of subtokens.", "This requires some understanding of how a variable is used, i.e., requires reasoning about lines of code far var clazz=classTypes [\"Root\"] .Single", "() as JsonCodeGenerator.ClassType; Assert.NotNull(clazz); var first=classTypes [\"RecClass\"] .Single", "() as JsonCodeGenerator.ClassType; Assert.NotNull( clazz ); Assert.Equal(\"string\", first.Properties [\"Name\"] .Name); Assert.False(clazz.Properties [\"Name\"] .IsArray); Figure 1 : A snippet of a detected bug in RavenDB an open-source C# project. The code", "has been slightly simplified. Our model", "detects correctly that the variable used in the highlighted (yellow) slot is incorrect. Instead,", "first should have been placed at the slot. We reported", "this problem which was fixed in PR 4138. apart in the", "source file. Secondly, we", "introduce the variable misuse prediction task (VARMISUSE), in which the network aims to infer which variable should be used in a program location. To illustrate", "the task, Figure 1 shows a slightly simplified snippet of a bug our model detected in a popular open-source project. Specifically,", "instead of the variable clazz, variable first should have been used in the yellow highlighted slot. Existing static", "analysis methods cannot detect such issues, even though a software engineer would easily identify this as an error from experience.To achieve high accuracy on these tasks, we need to learn representations of program semantics. For both tasks,", "we need to learn the semantic role of a variable (e.g., \"is it a counter?\", \"is it a filename?\"). Additionally, for", "VARMISUSE, learning variable usage semantics (e.g., \"a filename is needed here\") is required. This \"fill the blank", "element\" task is related to methods for learning distributed representations of natural language words, such as Word2Vec BID20 and GLoVe BID21 . However, we can learn", "from a much richer structure such as data flow information. This work is a step towards", "learning program representations, and we expect them to be valuable in a wide range of other tasks, such as code completion (\"this is the variable you are looking for\") and more advanced bug finding (\"you should lock before using this object\").To summarize, our contributions", "are: (i) We define the VARMISUSE task", "as a challenge for machine learning modeling of source code, that requires to learn (some) semantics of programs (cf. section 3).(ii) We present deep learning models", "for solving the VARNAMING and VARMISUSE tasks by modeling the code's graph structure and learning program representations over those graphs (cf. section 4). (iii) We evaluate our models on a large", "dataset of 2.9 million lines of real-world source code, showing that our best model achieves 32.9% accuracy on the VARNAMING task and 85.5% accuracy on the VARMISUSE task, beating simpler baselines (cf. section 5). (iv) We document practical relevance of", "VARMISUSE by summarizing some bugs that we found in mature open-source software projects (cf. subsection 5.3). Our implementation of graph neural networks", "(on a simpler task) can be found at https://github.com/Microsoft/gated-graph-neural-network-samples and the dataset can be found at https://aka.ms/iclr18-prog-graphs-dataset.", "Although source code is well understood and studied within other disciplines such as programming language research, it is a relatively new domain for deep learning.", "It presents novel opportunities compared to textual or perceptual data, as its (local) semantics are well-defined and rich additional information can be extracted using well-known, efficient program analyses.", "On the other hand, integrating this wealth of structured information poses an interesting challenge.", "Our VARMISUSE task exposes these opportunities, going beyond simpler tasks such as code completion.", "We consider it as a first proxy for the core challenge of learning the meaning of source code, as it requires to probabilistically refine standard information included in type systems.", "A PERFORMANCE CURVES FIG4 shows the ROC and precision-recall curves for the GGNN model.", "As the reader may observe, setting a false positive rate to 10% we get a true positive rate 5 of 73% for the SEENPROJTEST and 69% for the unseen test.", "This suggests that this model can be practically used at a high precision setting with acceptable performance." ]

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[ "Programs have structure that can be represented as graphs, and graph neural networks can learn to find bugs on such graphs" ]

[ "Overfitting is an ubiquitous problem in neural network training and usually mitigated using a holdout data set.\n", "Here we challenge this rationale and investigate criteria for overfitting without using a holdout data set.\n", "Specifically, we train a model for a fixed number of epochs multiple times with varying fractions of randomized labels and for a range of regularization strengths. \n", "A properly trained model should not be able to attain an accuracy greater than the fraction of properly labeled data points.", "Otherwise the model overfits. \n", "We introduce two criteria for detecting overfitting and one to detect underfitting.", "We analyze early stopping, the regularization factor, and network depth.\n", "In safety critical applications we are interested in models and parameter settings which perform well and are not likely to overfit.", "The methods of this paper allow characterizing and identifying such models.", "Deep neural networks have shown superior performance for a wide range of machine learning task such as speech recognition BID4 ), image classification BID8 ), playing board games BID13 ); machine translation ); beating previous methods by orders of magnitudes.", "To apply neural networks to safety critical problems such as autonomous driving it is necessary to evaluate their performance on new previously unseen data.One of the major problems of neural networks is their vulnerability to adversarial attacks.", "It has been shown that tiny unrecognizable changes of the input can fool the network to predict any class the attacker has chosen.", "One way to interpret this vulnerability is that the neural network overfits to the training data, with the output varying rapidly around each training point and thus slight changes of the input can lead to big changes in the output.", "It is thus highly desirable to prevent the network from overfitting during training.Previously reported methods reduce the chance of overfitting by evaluating the neural network on some holdout set, or by penalizing the complexity of the model class.", "This has the disadvantage that a holdout set can only be used once.", "By using design choices proven to be successful in the past the model becomes dependent on the holdout set.", "Penalizing the model class is only a heuristic remedy to overfitting.", "In the present paper we devise a method which prevents overfitting by relying on the training data only.", "We motivate l 1 -regularization of the kernel weights as a preferable choice to control the network complexity.", "Using no holdout set requires an alternative notion of overfitting.", "In the paper, we say that a model overfits if it is able to learn noise.", "In the paper we measure the capacity of a neural network by injecting different noise levels in the training data.", "The criteria we introduced in the paper are based on the assumption that the network should only be able to achieve a training accuracy corresponding to the injected noise level.", "This advances previous method in the neural network setting as they rely on either a hold out set, heuristics, or generalization theory.", "All of which are not mature enough to detect overfitting at present.", "In our experiments we saw that the hyper parameters fall in two classes, one which has no effect on overfitting (kernel size) and another which controls overfitting (regularization factor, number of iterations).", "In other experiments on mnist and cifar10 we observed the dominance of l 1 regularization for overfitting, while structural parameters such as network width, depth did not had an effect.The convexity criterion is the most reliable, as outliers and high variance are easily detected.", "On the downside it requires the most training runs.", "The steep decrease criterion only requires to train the model on the real data and and the fully random data.", "It can be used to narrow the parameter range.", "On the down side correlation between the classes are not easily detected by the steep decrease criterion.", "The mode criterion, is the most easiest to use as only the totally randomized training data is used.", "On the downside the margin plots are not always easy to interpret.", "Either the entire margin is positive, then the model clearly overfits, or two modes are observed in the plots, then the model clearly underfits.", "Yet most of the time, the margin is somewhere in between, which makes it hard to make a judgment based on the margin histograms alone.Let us put criteria (C2) and (C3) in perspective.", "Criterion (C2) comes close to what has been done before.", "We basically train a network on true and randomly shuffled labels, and analyze the attained accuracies.", "An analysis of the margin histograms for networks trained on true labels and random labels has been explored before.", "For example in BID2 margin histograms are used to conclude that regularization only seems to bring minor benefits to test error, BID10 use the margin histograms of networks trained on fully randomized labels and true labels to discuss normalization effects.", "Our contribution is to show that the regularization parameter can be set such that network does train on true labels, but is unable to do so for random labels.", "Both criteria are able to note this effect.All criteria can be numerically evaluated and put into an automated parameter search.", "At present it seems that the number of parameters do not contribute to overfitting.", "Thus to use the criteria of this paper one would proceed in two steps: search for an architecture which achieves zero training error, and then reducing the complexity of the model by regularizing it such that it does not overfit.", "So the additional burden is not that much .Analyzing", "neural networks with randomized training data has been done before BID15 ). In the paper", "the authors show that a neural network is able to train random labels, and they note that regularization ... is neither necessary nor by itself sufficient for controlling generalization error. In the paper", "we argued that l 1 -normalization of the kernel weights is a good measure to control the capacity of a network. In the experiment", "we saw that adjusting l 1 -normalization leads to models which do not overfit and hence we expect them to generalize better. Using an l 1 regularization", "(the LASSO) is one of the popular choices for regularization. The rational is typically to", "enforce sparsity of the network weights. Our Lemma 3.1.1 adds another", "reason to the list why it might be a good choice for convolutional networks.We want to highlight another unexpected illustrative result. By tuning the hyper parameter", "to pass our overfitting tests, we see that the test accuracy of the model is much higher than the training accuracy. This shows that our criteria", "can also be used to learn from noisy data and that a generalization gap does not need to be a bad thing.Although the paper focused on neural networks the methods can be applied for other machine learning algorithms as well. For example it would be interesting", "to apply our criteria for a systematic architecture search. Another line of research could investigate", "whether the criteria make adversarial attacks more difficult. Figure 5: The plots shows the accuracy of", "the network trained on cifar10 over different degrees of randomness with increasing degree of l 1 -regularization. The network trained for 199999 iterations", ". For the error curves five different samples", "were sampled for each data point. The network was evaluated on the training set", "(depicted in blue) and on the test set (depicted in red). We observe that the model does not overfit for", "λ = 0.00011. Furthermore, we note that with this choice of", "λ the model is able to learn from noise data, as the red curve is clearly above the green noise level curve." ]

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[ "We introduce and analyze several criteria for detecting overfitting." ]

[ "Partially observable Markov decision processes (POMDPs) are a widely-used framework to model decision-making with uncertainty about the environment and under stochastic outcome.", "In conventional POMDP models, the observations that the agent receives originate from fixed known distribution.", "However, in a variety of real-world scenarios the agent has an active role in its perception by selecting which observations to receive.", "Due to combinatorial nature of such selection process, it is computationally intractable to integrate the perception decision with the planning decision.", "To prevent such expansion of the action space, we propose a greedy strategy for observation selection that aims to minimize the uncertainty in state. \n", "We develop a novel point-based value iteration algorithm that incorporates the greedy strategy to achieve near-optimal uncertainty reduction for sampled belief points.", "This in turn enables the solver to efficiently approximate the reachable subspace of belief simplex by essentially separating computations related to perception from planning.\n", "Lastly, we implement the proposed solver and demonstrate its performance and computational advantage in a range of robotic scenarios where the robot simultaneously performs active perception and planning.", "In the era of information explosion it is crucial to develop decision-making platforms that are able to judiciously extract useful information to accomplish a defined task.", "The importance of mining useful data appears in many applications including artificial intelligence, robotics, networked systems and Internet of things.", "Generally in these applications, a decision-maker, called an agent, must exploit the available information to compute an optimal strategy toward a given objective.Partially observable Markov decision processes (POMDPs) provide a framework to model sequential decision-making with partial perception of the environment and under stochastic outcomes.", "The flexibility of POMDPs and their variants in modeling real-world problems has led to extensive research on developing efficient algorithms for finding near-optimal policies.", "Nevertheless, the majority of previous work on POMDPs either deal with sole perception or sole planning.While independent treatment of perception and planning deteriorates performance, an integrated approach usually becomes computationally intractable.", "Thereupon, one must establish a trade-off between optimality and tractability when determining how much perception and planning rely on each other.", "We show that by restricting the perception to the class of subset selection problems and exploiting submodular optimization techniques, it is possible to partially decouple computing perception and planning policies while considering their mutual effect on the overall policy value.In this work, we consider joint perception and planning in POMDPs.", "More specifically, we consider an agent that decides about two sets of actions; perception actions and planning actions.", "The perception actions, such as employing a sensor, only affect the belief of the agent regarding the state of the environment.", "The planning actions, such as choosing navigation direction, are the ones that affect the transition of the environment from one state to another.", "In subset selection problems, at each time step, due to power, processing capability, and cost constraints, the agent can pick a subset of available information sources along a planning action.", "The subset selection problem arise in various applications in control systems and signal processing, in wireless sensor networks, as well as machine learning BID7 and have been widely-studied (Shamaiah et al., 2010; BID11 .", "However, the previous work on sensor selection problems assume that the planning strategy is known, while in this work, we simultaneously learn a selection strategy and a planning strategy.", "In this paper, we studied joint active perception and planning in POMDP models.", "To capture the structure of the problem, we introduced AP 2 -POMDPs that have to pick a cardinality-constrained subset of observations, in addition to original planning action.", "To tackle the computational challenge of adding combinatorial actions, we proposed a greedy scheme for observation selection.", "The greedy scheme aims to minimize the conditional entropy of belief which is a metric of uncertainty about the state.", "We provided a theoretical analysis for the greedy algorithm that led to boundedness of value function difference between optimal entropy reduction and its greedy counterpart.", "Furthermore, founded upon the theoretical guarantee of greedy active perception, we developed a point-based value iteration solver for AP 2 -POMDPs.", "The idea introduced in the solver to address active perception is general and can be applied on state-of-the-art point-based solvers.", "Lastly, we implemented and evaluated the proposed solver on a variety of robotic navigation scenarios." ]

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[ "We develop a point-based value iteration solver for POMDPs with active perception and planning tasks." ]

[ "Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements.", "This success can be attributed in part to their ability to represent and generate natural images well.", "Contrary to classical tools such as wavelets, image-generating deep neural networks have a large number of parameters---typically a multiple of their output dimension---and need to be trained on large datasets. \n", "In this paper, we propose an untrained simple image model, called the deep decoder, which is a deep neural network that can generate natural images from very few weight parameters.\n", "The deep decoder has a simple architecture with no convolutions and fewer weight parameters than the output dimensionality.", "This underparameterization enables the deep decoder to compress images into a concise set of network weights, which we show is on par with wavelet-based thresholding.", "Further, underparameterization provides a barrier to overfitting, allowing the deep decoder to have state-of-the-art performance for denoising.", "The deep decoder is simple in the sense that each layer has an identical structure that consists of only one upsampling unit, pixel-wise linear combination of channels, ReLU activation, and channelwise normalization.", "This simplicity makes the network amenable to theoretical analysis, and it sheds light on the aspects of neural networks that enable them to form effective signal representations.", "Data models are central for signal and image processing and play a key role in compression and inverse problems such as denoising, super-resolution, and compressive sensing.", "These data models impose structural assumptions on the signal or image, which are traditionally based on expert knowledge.", "For example, imposing the assumption that an image can be represented with few non-zero wavelet coefficients enables modern (lossy) image compression BID1 and efficient denoising BID6 .In", "recent years, it has been demonstrated that for a wide range of imaging problems, from compression to denoising, deep neural networks trained on large datasets can often outperform methods based on traditional image models BID19 BID0 BID18 BID4 BID22 . This", "success can largely be attributed to the ability of deep networks to represent realistic images when trained on large datasets. Examples", "include learned representations via autoencoders BID12 and generative adversarial models BID8 . Almost exclusively", ", three common features of the recent success stories of using deep neural network for imaging related tasks are i) that the corresponding", "networks are over-parameterized (i.e., they have much more parameters than the dimension of the image that they represent or generate), ii) that the networks have", "a convolutional structure, and perhaps most importantly, iii) that the networks are", "trained on large datasets.An important exception that breaks with the latter feature is a recent work by Ulyanov et al. BID20 , which provides an algorithm, called the deep image prior (DIP), based on deep neural networks, that can solve inverse problems well without any training. Specifically, Ulyanov et al.", "demonstrated that fitting the weights of an over-parameterized deep convolutional network to a single image, together with strong regularization by early stopping of the optimization, performs competitively on a variety of image restoration problems. This result is surprising because", "it does not involve a training dataset, which means that the notion of what makes an image 'natural' is contained in a combination of the network structure and the regularization. However, without regularization the", "proposed network has sufficient capacity to overfit to noise, preventing meaningful image denoising.These prior works demonstrating the effectiveness of deep neural networks for image generation beg the question whether there may be a deep neural network model of natural images that is underparameterized and whose architecture alone, without algorithmic assistance, forms an efficient model for natural images.In this paper, we propose a simple image model in the form of a deep neural network that can represent natural images well while using very few parameters. This model thus enables image compression", ", denoising, and solving a variety of inverse problems with close to or state of the art performance. We call the network the deep decoder, due", "to its resemblance to the decoder part of an autoencoder. The network does not require training, and", "contrary to previous approaches, the network itself incorporates all assumptions on the data, is under-parameterized, does not involve convolutions, and has a simplicity that makes it amenable to theoretical analysis. The key contributions of this paper are as", "follows:• The network is under-parameterized. Thus, the network maps a lower-dimensional", "space to a higher-dimensional space, similar to classical image representations such as sparse wavelet representations. This feature enables image compression by", "storing the coefficients of the network after its weights are optimized to fit a single image. In Section 2, we demonstrate that the compression", "is on-par with wavelet thresholding BID1 , a strong baseline that underlies JPEG-2000. An additional benefit of underparameterization is", "that it provides a barrier to overfitting, which enables regularization of inverse problems.• The network itself acts as a natural data model.", "Not only does the network require no training (just", "as the DIP BID20 ); it also does not critically rely on regularization, for example by early stopping (in contrast to the DIP). The property of not involving learning has at least", "two benefits: The same network and code is usable for a number of applications, and the method is not sensitive to a potential misfit of training and test data.• The network does not use convolutions. Instead, the", "network does have pixelwise linear combinations", "of channels, and, just like in a convolutional neural network, the weights are shared among spatial positions. Nonetheless, these are not convolutions because they provide", "no spatial coupling between pixels, despite how pixelwise linear combinations are sometimes called '1x1 convolutions.' In contrast, the majority of the networks for image compression", ", restoration, and recovery have convolutional layers with filters of nontrivial spatial extent BID19 ; BID0 ; BID18 ; BID4 BID22 . This work shows that relationships characteristic of nearby pixels", "of natural images can be imposed directly by upsampling layers.• The network only consists of a simple combination of few building", "blocks, which makes it amenable to analysis and theory. For example, we prove that the deep decoder can only fit a small proportion", "of noise, which, combined with the empirical observation that it can represent natural images well, explains its denoising performance.The remainder of the paper is organized as follows. In Section 2, we first demonstrate that the deep decoder enables concise image", "representations. We formally introduce the deep decoder in Section 3. In Section 4, we show the", "performance of the deep decoder on a number of inverse", "problems such as denoising. In Section 5 we discuss related work, and finally, in Section 6 we provide theory", "and explanations on what makes the deep decoder work.", "In the previous sections we empirically showed that the deep decoder can represent images well and at the same time cannot fit noise well.", "In this section, we formally show that the deep decoder can only fit a small proportion of the noise, relative to the degree of underparameterization.", "In addition, we provide insights into how the components of the deep decoder contribute to representing natural images well, and we provide empirical observations on the sensitivity of the parameters and their distribution." ]

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[ "We introduce an underparameterized, nonconvolutional, and simple deep neural network that can, without training, effectively represent natural images and solve image processing tasks like compression and denoising competitively." ]

[ "In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU).", "We give an algorithm to train a ReLU DNN with one hidden layer to {\\em global optimality} with runtime polynomial in the data size albeit exponential in the input dimension.", "Further, we improve on the known lower bounds on size (from exponential to super exponential) for approximating a ReLU deep net function by a shallower ReLU net.", "Our gap theorems hold for smoothly parametrized families of ``hard'' functions, contrary to countable, discrete families known in the literature. ", "An example consequence of our gap theorems is the following: for every natural number $k$ there exists a function representable by a ReLU DNN with $k^2$ hidden layers and total size $k^3$, such that any ReLU DNN with at most $k$ hidden layers will require at least $\\frac12k^{k+1}-1$ total nodes.", "Finally, for the family of $\\R^n\\to \\R$ DNNs with ReLU activations, we show a new lowerbound on the number of affine pieces, which is larger than previous constructions in certain regimes of the network architecture and most distinctively our lowerbound is demonstrated by an explicit construction of a \\emph{smoothly parameterized} family of functions attaining this scaling.", "Our construction utilizes the theory of zonotopes from polyhedral theory.", "Deep neural networks (DNNs) provide an excellent family of hypotheses for machine learning tasks such as classification.", "Neural networks with a single hidden layer of finite size can represent any continuous function on a compact subset of R n arbitrary well.", "The universal approximation result was first given by Cybenko in 1989 for sigmoidal activation function BID4 , and later generalized by Hornik to an arbitrary bounded and nonconstant activation function BID15 .", "Furthermore, neural networks have finite VC dimension (depending polynomially on the number of edges in the network), and therefore, are PAC (probably approximately correct) learnable using a sample of size that is polynomial in the size of the networks BID1 .", "However, neural networks based methods were shown to be computationally hard to learn BID1 and had mixed empirical success.", "Consequently, DNNs fell out of favor by late 90s.to address the issue of efficiently training DNNs.", "These include heuristics such as dropouts BID39 , but also considering alternate deep architectures such as convolutional neural networks BID33 , deep belief networks BID14 , and deep Boltzmann machines BID31 .", "In addition, deep architectures based on new non-saturating activation functions have been suggested to be more effectively trainable -the most successful and widely popular of these is the rectified linear unit (ReLU) activation, i.e., σ(x) = max{0, x}, which is the focus of study in this paper.In this paper, we formally study deep neural networks with rectified linear units; we refer to these deep architectures as ReLU DNNs.", "Our work is inspired by these recent attempts to understand the reason behind the successes of deep learning, both in terms of the structure of the functions represented by DNNs, Telgarsky (2015; ; BID17 ; BID36 , as well as efforts which have tried to understand the non-convex nature of the training problem of DNNs better BID18 ; BID10 .", "Our investigation of the function space represented by ReLU DNNs also takes inspiration from the classical theory of circuit complexity; we refer the reader to BID2 ; BID37 ; BID16 ; BID32 ; BID0 for various surveys of this deep and fascinating field.", "In particular, our gap results are inspired by results like the ones by BID12 , BID27 and BID38 which show a strict separation of complexity classes.", "We make progress towards similar statements with deep neural nets with ReLU activation.", "The running time of the algorithm that we give in this work to find the exact global minima of a two layer ReLU-DNN is exponential in the input dimension n and the number of hidden nodes w.", "The exponential dependence on n can not be removed unless P = N P ; see BID35 ; BID3 ; BID6 .", "However, we are not aware of any complexity results which would rule out the possibility of an algorithm which trains to global optimality in time that is polynomial in the data size and/or the number of hidden nodes, assuming that the input dimension is a fixed constant.", "Resolving this dependence on network size would be another step towards clarifying the theoretical complexity of training ReLU DNNs and is a good open question for future research, in our opinion.", "Perhaps an even better breakthrough would be to get optimal training algorithms for DNNs with two or more hidden layers and this seems like a substantially harder nut to crack.", "It would also be a significant breakthrough to get gap results between consecutive constant depths or between logarithmic and constant depths." ]

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[ "This paper 1) characterizes functions representable by ReLU DNNs, 2) formally studies the benefit of depth in such architectures, 3) gives an algorithm to implement empirical risk minimization to global optimality for two layer ReLU nets." ]

[ "The backpropagation of error algorithm (BP) is often said to be impossible to implement in a real brain.", "The recent success of deep networks in machine learning and AI, however, has inspired a number of proposals for understanding how the brain might learn across multiple layers, and hence how it might implement or approximate BP.", "As of yet, none of these proposals have been rigorously evaluated on tasks where BP-guided deep learning has proved critical, or in architectures more structured than simple fully-connected networks.", "Here we present the first results on scaling up a biologically motivated model of deep learning to datasets which need deep networks with appropriate architectures to achieve good performance.", "We present results on CIFAR-10 and ImageNet. ", "For CIFAR-10 we show that our algorithm, a straightforward, weight-transport-free variant of difference target-propagation (DTP) modified to remove backpropagation from the penultimate layer, is competitive with BP in training deep networks with locally defined receptive fields that have untied weights. ", "For ImageNet we find that both DTP and our algorithm perform significantly worse than BP, opening questions about whether different architectures or algorithms are required to scale these approaches.", "Our results and implementation details help establish baselines for biologically motivated deep learning schemes going forward.", "The suitability of the backpropagation of error (BP) algorithm BID27 for explaining learning in the brain was questioned soon after its popularization BID8 BID5 .", "Weaker objections included undesirable characteristics of artificial networks in general, such as their violation of Dale's Law, their lack of cell-type variability, and the need for the gradient signals to be both positive and negative.", "Much more serious objections were: (1) The need for the feedback connections carrying the gradient to have the same weights as the corresponding feedforward connections and (2) The need for a distinct form of information propagation (error propagation) that does not influence neural activity, and hence does not conform to known biological feedback mechanisms underlying neural communication.Researchers have long sought biologically plausible and empirically powerful learning algorithms that avoid some of these flaws BID1 BID25 BID0 BID23 Xie & Seung, 2003; BID12 BID14 BID10 BID21 .", "A common theme of some of the most promising approaches -such as Contrastive Hebbian Learning BID22 , and Generalized Recirculation BID23 -is to use feedback connections to influence neural activity, and to use differences in feedfoward-driven and feedback-driven activities or products of activities to locally approximate gradients BID0 BID26 BID23 Xie & Seung, 2003; BID30 Whittington & Bogacz, 2017) .", "Since these activity propagation methods don't require explicit propagation of gradients through the network, they go a long way towards answering the second serious objection noted above.", "However, many of these methods require long \"positive\" and \"negative\" settling phases for computing the activities or activity products whose differences provide the learning signal.", "Proposals for shortening the phases BID11 BID4 are not entirely satisfactory as they still fundamentally depend on a settling process, and, in general, any settling process will likely be too slow for a brain that needs to quickly compute hidden activities.", "Indeed, for the same reason, only a handful of the algorithms that require settling have ever been used on large scale problems in machine learning.Perhaps the most practical among this family of \"activity propagation\" algorithms is target propagation (TP) and its variants BID17 BID11 BID2 .", "The intuition for TP is as follows: Suppose you have a feedforward neural network and have the capacity to compute perfect inverses backwards through the network (i.e., given the activities in layer h l+1 , we can compute h l = f −1 (h l+1 ; θ l+1 )).", "If we impose an output target (for a given input) on the output layer, then we can propagate activity backwards through the network to infer what the activities should be to produce the output target.", "These backwards propagated activities are denoted the layer targets, or simply targets.", "Then, when computing a feedfoward propagation through the network given some input, we can layer-wise compare the feedforward activations to what they should have been (i.e., the targets), and use the differences to compute weight changes.", "TP algorithms do not require settling dynamics, and thus can compute forward passes and updates quickly.", "As well, for one TP variant , it has been shown that weight changes that cause future feedforward activity to be nudged towards their targets approximate the weight changes computed by BP.While TP and its variants are promising as biologically-plausible algorithms, there are some lingering questions about their applicability to the brain.", "First, the only variant explored empirically -difference target propagation (DTP) -still depends on explicit gradient computation via backpropagation for learning the penultimate layer's outgoing synaptic weights (see Algorithm Box 1 in ).", "Second, they have not been tested on datasets more difficult than MNIST.", "And third, they have not been incorporated into architectures more complicated than simple multi-layer perceptrons (MLPs).In", "this work we address each of these issues. Our", "contribution is threefold: (1) We examine the learning and performance of a biologically-motivated algorithm, Difference Target-propagation (DTP), on MNIST, CIFAR, and ImageNet, (2) We develop a variant of DTP called Simplified Difference Target Propagation (SDTP), which eliminates significant lingering biologically implausible features from DTP, and (3) We investigate the role of weight-sharing convolutions, which are key to performance on difficult datasets in artificial neural networks, by testing the effectiveness of locally connected architectures trained with BP, DTP, and SDTP.Sharing the weights of locally connected units greatly reduces the number of free parameters and this has several very beneficial effects on computer simulations of large neural nets. It", "improves generalization and it drastically reduces both the amount of memory needed to store the parameters and the amount of communication required between replicas of the same model running on different subsets of the data on different processors. From", "a biological perspective we are interested in how STDP compares with BP without using weight sharing, so both our BP results and our SDTP results are considerably worse than convolutional neural nets and take far longer to produce.", "Historically, there has been significant disagreement about whether BP can tell us anything interesting about learning in the brain BID5 BID8 .", "Indeed, from the mid 1990s to 2010, work on applying BP to the brain all but disappeared.", "Recent progress in machine learning has prompted a revival of this debate; where other approaches have failed, deep networks trained via BP have been key to achieving impressive performance on difficult datasets such as ImageNet.", "It is once again natural to wonder whether some approximation of BP might underlie learning in the brain.However, none of the algorithms proposed as approximations of BP have been tested on the datasets that were instrumental in convincing the machine learning and neuroscience communities to revisit these questions.Here we introduced a straightforward variant of difference target-propogation that completely removed gradient propagation and weight transport and tested it on the challenging task of classifying CIFAR and ImageNet images.", "We also investigated and reported results on the use of local connectivity.", "We demonstrated that networks trained with SDTP without any weight sharing (i.e. weight transport in the backward pass or weight tying in convolutions) are generally able to compete with those trained with BP on difficult tasks such as CIFAR.", "However, BP significantly outperforms both DTP and SDTP on ImageNet, and more work is required to understand why this issue arises at scale.We note that although activity-propagation-based algorithms go a long way towards biological plausibility, there are still many biological constraints that we did not address here.", "For example, we've set aside the question of spiking neurons entirely to focus on asking whether variants of TP can scale up to solve difficult problems at all.", "The question of spiking networks is an important one BID29 BID9 ), but it is nevertheless possible to gain algorithmic insight to the brain without tackling all of the elements of biological complexity simultaneously.", "Similarly, we also ignore Dale's law in all of our experiments BID24 .", "In general, we've aimed at the simplest models that allow us to address questions around (1) weight sharing, and (2) the form and function of feedback communication.Algorithms that contend for a role in helping us understand learning in cortex should be able to perform well on difficult domains without relying on weight transport or tying.", "Thus, our results offer a new benchmark for future work looking to evaluate the effectiveness of potential biologically plausible algorithms in more powerful architectures and on more difficult datasets." ]

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[ "Benchmarks for biologically plausible learning algorithms on complex datasets and architectures" ]

[ "Deep neural networks (DNNs) usually contain millions, maybe billions, of parameters/weights, making both storage and computation very expensive.", "This has motivated a large body of work to reduce the complexity of the neural network by using sparsity-inducing regularizers. ", "Another well-known approach for controlling the complexity of DNNs is parameter sharing/tying, where certain sets of weights are forced to share a common value.", "Some forms of weight sharing are hard-wired to express certain in- variances, with a notable example being the shift-invariance of convolutional layers.", "However, there may be other groups of weights that may be tied together during the learning process, thus further re- ducing the complexity of the network.", "In this paper, we adopt a recently proposed sparsity-inducing regularizer, named GrOWL (group ordered weighted l1), which encourages sparsity and, simulta- neously, learns which groups of parameters should share a common value.", "GrOWL has been proven effective in linear regression, being able to identify and cope with strongly correlated covariates.", "Unlike standard sparsity-inducing regularizers (e.g., l1 a.k.a.", "Lasso), GrOWL not only eliminates unimportant neurons by setting all the corresponding weights to zero, but also explicitly identifies strongly correlated neurons by tying the corresponding weights to a common value.", "This ability of GrOWL motivates the following two-stage procedure: (i) use GrOWL regularization in the training process to simultaneously identify significant neurons and groups of parameter that should be tied together; (ii) retrain the network, enforcing the structure that was unveiled in the previous phase, i.e., keeping only the significant neurons and enforcing the learned tying structure.", "We evaluate the proposed approach on several benchmark datasets, showing that it can dramatically compress the network with slight or even no loss on generalization performance.\n", "Deep neural networks (DNNs) have recently revolutionized machine learning by dramatically advancing the state-of-the-art in several applications, ranging from speech and image recognition to playing video games BID20 .", "A typical DNN consists of a sequence of concatenated layers, potentially involving millions or billions of parameters; by using very large training sets, DNNs are able to learn extremely complex non-linear mappings, features, and dependencies.A large amount of research has focused on the use of regularization in DNN learning BID20 , as a means of reducing the generalization error.", "It has been shown that the parametrization of many DNNs is very redundant, with a large fraction of the parameters being predictable from the remaining ones, with no accuracy loss BID14 .", "Several regularization methods have been proposed to tackle the potential over-fitting due to this redundancy.", "Arguably, the earliest and simplest choice is the classical 2 norm, known as weight decay in the early neural networks literature , and as ridge regression in statistics.", "In the past two decades, sparsity-inducing regularization based on the 1 norm (often known as Lasso) BID35 , and variants thereof, became standard tools in statistics and machine learning, including in deep learning BID20 .", "Recently, BID32 used group-Lasso (a variant of Lasso that assumes that parameters are organized in groups and encourages sparsity at the group level BID37 ) in deep learning.", "One of the effects of Lasso or group-Lasso regularization in learning a DNN is that many of the parameters may become exactly zero, thus reducing the amount of memory needed to store the model, and lowering the computational cost of applying it.Figure 1: A DNN is first trained with GrOWL regularization to simultaneously identify the sparse but significant connectivities and the correlated cluster information of the selected features.", "We then retrain the neural network only in terms of the selected connectivities while enforcing parameter sharing within each cluster.It has been pointed out by several authors that a major drawback of Lasso (or group-Lasso) regularization is that in the presence of groups of highly correlated covariates/features, it tends to select only one or an arbitrary convex combination of features from each group BID6 BID7 BID17 BID28 BID42 .", "Moreover, the learning process tends to be unstable, in the sense that subsets of parameters that end up being selected may change dramatically with minor changes in the data or algorithmic procedure.", "In DNNs, it is almost unavoidable to encounter correlated features, not only due to the high dimensionality of the input to each layer, but also because neurons tend to co-adapt, yielding strongly correlated features that are passed as input to the subsequent layer BID34 .In", "this work, we propose using, as a regularizer for learning DNNs, the group version of the ordered weighted 1 (OWL) norm BID17 , termed group-OWL (GrOWL), which was recently proposed by BID28 . In", "a linear regression context, GrOWL regularization has been shown to avoid the above mentioned deficiency of group-Lasso regularization. In", "addition to being a sparsity-inducing regularizer, GrOWL is able to explicitly identify groups of correlated features and set the corresponding parameters/weights to be very close or exactly equal to each other, thus taking advantage of correlated features, rather than being negatively affected by them. In", "deep learning parlance, this corresponds to adaptive parameter sharing/tying, where instead of having to define a priori which sets of parameters are forced to share a common value, these sets are learned during the training process. We", "exploit this ability of GrOWL regularization to encourage parameter sparsity and group-clustering in a two-stage procedure depicted in Fig. 1 : we first use GrOWL to identify the significant parameters/weights of the network and, simultaneously, the correlated cluster information of the selected features; then, we retrain the network only in terms of the selected features, while enforcing the weights within the same cluster to share a common value.The experiments reported below confirm that using GrOWL regularization in learning DNNs encourages sparsity and also yields parameter sharing, by forcing groups of weights to share a common absolute value. We", "test the proposed approach on two benchmark datasets, MNIST and CIFAR-10, comparing it with weight decay and group-Lasso regularization, and exploring the accuracy-memory trade-off. Our", "results indicate that GrOWL is able to reduce the number of free parameters in the network without degrading the accuracy, as compared to other approaches.", "We have proposed using the recent GrOWL regularizer for simultaneous parameter sparsity and tying in DNN learning.", "By leveraging on GrOWL's capability of simultaneously pruning redundant parameters and tying parameters associated with highly correlated features, we achieve significant reduction of model complexity, with a slight or even no loss in generalization accuracy.", "We evaluate the proposed method on both a fully connected neural network and a deep convolutional neural network.", "The results show that GrOWL can compress large DNNs by factors ranging from 11.4 to 14.5, with negligible loss on accuracy.The correlation patterns identified by GrOWL are close to those of the input features to each layer.", "This may be important to reveal the structure of the features, contributing to the interpretability of deep learning models.", "On the other hand, by automatically tying together the parameters corresponding to highly correlated features, GrOWL alleviates the negative effect of strong correlations that might be induced by the noisy input or the co-adaption tendency of DNNs.The gap in the accuracy vs memory trade-off obtained by applying GrOWL and group-Lasso decreases as we move to large DNNs.", "Although we suspect this can be caused by running a much larger network on a simple dataset, it motivates us to explore different ways to apply GrOWL to compress neural networks.", "One possible approach is to apply GrOWL within each neuron by predefining each 2D convolutional filter as a group (instead all 2D convolutional filters corresponding to the same input features).", "By doing so, we encourage parameter sharing among much smaller units, which in turn would further improve the diversity vs parameter sharing trade-off.", "We leave this for future work." ]

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[ "We have proposed using the recent GrOWL regularizer for simultaneous parameter sparsity and tying in DNN learning. " ]

[ "Weight-sharing—the simultaneous optimization of multiple neural networks using the same parameters—has emerged as a key component of state-of-the-art neural architecture search.", "However, its success is poorly understood and often found to be surprising.", "We argue that, rather than just being an optimization trick, the weight-sharing approach is induced by the relaxation of a structured hypothesis space, and introduces new algorithmic and theoretical challenges as well as applications beyond neural architecture search.", "Algorithmically, we show how the geometry of ERM for weight-sharing requires greater care when designing gradient- based minimization methods and apply tools from non-convex non-Euclidean optimization to give general-purpose algorithms that adapt to the underlying structure.", "We further analyze the learning-theoretic behavior of the bilevel optimization solved by practical weight-sharing methods.", "Next, using kernel configuration and NLP feature selection as case studies, we demonstrate how weight-sharing applies to the architecture search generalization of NAS and effectively optimizes the resulting bilevel objective.", "Finally, we use our optimization analysis to develop a simple exponentiated gradient method for NAS that aligns with the underlying optimization geometry and matches state-of-the-art approaches on CIFAR-10.", "Weight-sharing neural architecture search (NAS) methods have achieved state-of-the-art performance while requiring computation training of just a single shared-weights network (Pham et al., 2018; Li and Talwalkar, 2019; .", "However, weight-sharing remains poorly understood.", "In this work, we present a novel perspective on weight-sharing NAS motivated by the key observation that these methods subsume the architecture hyperparameters as another set of learned parameters of the shared-weights network, in effect extending the hypothesis class.", "An important ramification of this insight is that weight-sharing is not NAS-specific and can be used to tune hyperparameters corresponding to parameterized feature maps of the input data.", "We refer this larger subset of hyperparameter optimization problems as architecture search, and we study the following two questions associated with weight-sharing applied to the architecture search problem:", "1. How can we efficiently optimize the objective induced by applying weight sharing to architecture search, namely minimizing empirical risk in the joint space of model and architecture parameters?", "For large structured search spaces that preclude brute force search, a natural approach to architecture search with weight-sharing is to use gradient-based methods to minimize the empirical risk over a continuous relaxation of the discrete space .", "Although this has allowed NAS researchers to apply their preferred optimizers to determine architecture weights, it is far from clear that the success of established methods for unconstrained optimization in training neural networks will naturally extend to these constrained and often non-Euclidean environments.", "As we foresee that architecture search spaces will continue to become more complex and multi-faceted, we argue for and develop a more principled, geometry-aware formulation of the optimization problem.", "Drawing upon the mirror descent meta-algorithm (Beck and Teboulle, 2003) and successive convex approximation, we give non-asymptotic stationary-point convergence guarantees for the empirical risk minimization (ERM) objective associated with weight-sharing via algorithms that simultaneously connect to the underlying problem structure and handle the alternating-block nature of the architecture search.", "Our guarantees inform the design of gradient-based weight-sharing methods by explicitly quantifying the impact of optimizing in the right geometry on convergence rates.", "2. What are the generalization benefits of solving a bilevel optimization for the architecture search problem commonly considered in practice?", "At its core, the goal of architecture search is to find a configuration that achieves good generalization performance.", "Consequently, a bilevel objective that optimizes the architecture weights using a separate validation loss is commonly used in practice in lieu of the ERM objective naturally induced by weight sharing (Pham et al., 2018; Cai et al., 2019) .", "The learning aspects of this approach have generally been studied in settings with much stronger control over the model complexity (Kearns et al., 1997) .", "We provide generalization guarantees for this objective over structured hypothesis spaces associated with a finite set of architectures; this leads to meaningful bounds for simple feature map selection problems as well as insightful results for the NAS problem that depend on the size of the space of global optima.", "To validate our theoretical results, we conduct empirical studies of weight-sharing in two settings: (1) shallow feature map selection, i.e., tuning the hyperparameters of kernel classification and NLP featurization pipelines, and (2) CNN neural architecture search.", "In (1) we demonstrate that weightsharing efficiently optimizes the bilevel objective and achieves low generalization error with respect to the best architecture setting.", "For (2), motivated by insights from our convergence analysis, we develop a simple exponentiated gradient version of DARTS called EDARTS that better exploits the geometry of the optimization problem.", "We evaluate EDARTS on the design of CNN architectures for CIFAR-10 and demonstrate that EDARTS finds better architectures than DARTS in less than half the time.", "We also achieve very competitive results relative to state-of-the-art architectures when using an extended evaluation routine.", "Related Work: Our work on optimization for weight-sharing benefits from the literature on firstorder stochastic optimization (Hazan and Kale, 2014; Beck, 2017) and in particular the mirror descent framework (Beck and Teboulle, 2003) .", "Specifically, we use successive convex approximation (Razaviyayn et al., 2013; Mairal, 2015) to show convergence of alternating minimization and derive geometry-dependent rates comparable to existing work on non-convex stochastic mirror descent (Dang and Lan, 2015; Zhang and He, 2018) .", "Our result generalizes to the constrained, nonEuclidean, and multi-block setting an approach of Agarwal et al. (2019) for obtaining non-convex convergence from strongly convex minimization, which may be of independent interest.", "Previous optimization results for NAS have generally only shown bounds on auxiliary quantities such as regret that are not well-connected to the learning objective Carlucci et al., 2019) or have only given monotonic improvement or asymptotic guarantees (Akimoto et al., 2019; Yao et al., 2019) .", "However, due to the generality of mirror descent, the approaches in the middle three papers can be seen as special cases of our analysis.", "Finally, our analysis of the properties of the bilevel optimization is related to work on model selection (Vuong, 1989; Kearns et al., 1997) , but does not consider the configuration parameters as explicit controls on the model complexity.", "Our learning results are broadly related to hyperparameter optimization, although most work focuses on algorithmic and not statistical questions (Li et al., 2018; Kandasamy et al., 2017) ." ]

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[ "An analysis of the learning and optimization structures of architecture search in neural networks and beyond." ]

[ "Deep latent variable models have seen recent success in many data domains.", "Lossless compression is an application of these models which, despite having the potential to be highly useful, has yet to be implemented in a practical manner.", "We present '`Bits Back with ANS' (BB-ANS), a scheme to perform lossless compression with latent variable models at a near optimal rate.", "We demonstrate this scheme by using it to compress the MNIST dataset with a variational auto-encoder model (VAE), achieving compression rates superior to standard methods with only a simple VAE.", "Given that the scheme is highly amenable to parallelization, we conclude that with a sufficiently high quality generative model this scheme could be used to achieve substantial improvements in compression rate with acceptable running time.", "We make our implementation available open source at https://github.com/bits-back/bits-back .", "The connections between information theory and machine learning have long been known to be deep, and indeed the two fields are so closely related that they have been described as 'two sides of the same coin' BID18 .", "One particularly elegant connection is the essential equivalence between probabilistic models of data and lossless compression methods.", "The source coding theorem BID22 can be thought of as the fundamental theorem describing this idea, and Huffman coding BID13 , arithmetic coding BID28 and the more recently developed asymmetric numeral systems BID3 ) are actual algorithms for implementing lossless compression, given some kind of probabilistic model.The field of machine learning has experienced an explosion of activity in recent years, and we have seen a number of papers looking at applications of modern deep learning methods to lossy compression.", "BID7 discusses applications of a deep latent Gaussian model to compression, with an emphasis on lossy compression.", "BID0 , BID23 , BID1 , and BID19 all implement lossy compression using (variational) auto-encoder style models, and BID24 train a model for lossy compression using a GAN-like objective.", "Applications to lossless compression have been less well covered in recent works.", "We seek to advance in this direction, and we focus on lossless compression using latent variable models.The lossless compression algorithms mentioned above do not naturally cater for latent variables.", "However there is a method, known as 'bits back coding' BID27 BID10 , first introduced as a thought experiment, but later implemented in BID5 and BID4 , which can be used to extend those algorithms to cope with latent variables.Although bits back coding has been implemented in restricted cases by BID4 , there is no known efficient implementation for modern neural net-based models or larger datasets.", "There is, in fact, a fundamental incompatibility between bits back and the arithmetic coding scheme with which it has previously been implemented.", "We resolve this issue, describing a scheme that instead implements bits back using asymmetric numeral systems.", "We term this new coding scheme 'Bits Back with ANS' (BB-ANS).", "Our scheme improves on existing implementations of bits back coding in terms of compression rate and code complexity, allowing for efficient lossless compression of arbitrarily large datasets with deep latent variable models.", "We demonstrate the efficiency of BB-ANS by losslessly compressing the MNIST dataset with a variational auto-encoder (VAE), a deep latent variable model with continuous latent variables BID15 BID20 .", "As far as we are aware, this is the first time bits back coding has been implemented with continuous latent variables.We find that BB-ANS with a VAE outperforms generic compression algorithms for both binarized and raw MNIST, even with a very simple model architecture.", "We extrapolate these results to predict that the performance of BB-ANS with larger, state of the art models would be significantly better than generic compression algorithms.", "Probabilistic modelling of data is a highly active research area within machine learning.", "Given the progress within this area, it is of interest to study the application of probabilistic models to lossless compression.", "Indeed, if practical lossless compression schemes using these models can be developed then there is the possibility of significant improvement in compression rate over existing methods.We have shown the existence of a scheme, BB-ANS, which can be used for lossless compression using latent variable models.", "We demonstrated BB-ANS by compressing the MNIST dataset, achieving compression rates superior to generic algorithms.", "We have shown how to handle the issue of latent discretization.", "Crucially, we were able to compress to sizes very close to the negative ELBO for a large dataset.", "This is the first time this has been achieved with a latent variable model, and implies that state-of-the-art latent variable models could be used in conjunction with BB-ANS to achieve significantly better lossless compression rates than current methods.", "Given that all components of BB-ANS are readily parallelizable, we believe that BB-ANS can be implemented to run on GPU hardware, yielding a fast and powerful lossless compression system." ]

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[ "We do lossless compression of large image datasets using a VAE, beat existing compression algorithms." ]

[ "Hyperparameter tuning is arguably the most important ingredient for obtaining state of art performance in deep networks. ", "We focus on hyperparameters that are related to the optimization algorithm, e.g. learning rates, which have a large impact on the training speed and the resulting accuracy.", "Typically, fixed learning rate schedules are employed during training.", "We propose Hyperdyn a dynamic hyperparameter optimization method that selects new learning rates on the fly at the end of each epoch.", "Our explore-exploit framework combines Bayesian optimization (BO) with a rejection strategy, based on a simple probabilistic wait and watch test. ", "We obtain state of art accuracy results on CIFAR and Imagenet datasets, but with significantly faster training, when compared with the best manually tuned networks.", "Hyperparameter tuning is arguably the most important ingredient for obtaining state of art performance in deep neural networks.", "Currently, most networks are manually tuned after extensive trial and error, and this is derisively referred to as graduate student descent.", "Hyperparameter optimization (HPO), on the other hand, attempts to automate the entire process and remove the need for human intervention.", "Previous works on HPO propose various strategies to either adaptively select good configurations BID12 or to speed up configuration evaluations BID7 .One", "drawback behind existing HPO frameworks is that they do not distinguish between different kinds of hyperparameters and treat them all uniformly. Broadly", "there are two categories of hyperparameters: those that are fixed throughout the training process and those that need to be varied during training. The former", "class is mostly structural (e.g. network depth and width), while the latter is mostly related to the optimization algorithm (e.g. learning rates, regularization). The two classes", "of hyperparameters have very different behaviors. For structural", "hyperparameters, online evaluation is not possible, and we need to wait for the entire training process to be completed, which is very expensive. On the other hand", ", for time-varying hyperparameters, it is possible to select parameters on the fly without waiting for training to finish. In this work we", "keep the structural hyperparameters fixed and focus on optimizing the time-varying hyperparameters to improve efficiency, stability, and accuracy of the training process.", "In this work we introduced a general framework for a certain class of hyperparameter optimization.", "The algorithm here has the advantage that it is fast, flexible -can be used on any objective function and training method, and stable on larger batch sizes.", "We demonstrated that our proposed optimizer is faster and at least as accurate as SGD (with momentum) or Adam.", "We also show that Hyperdyn is stable for larger batch sizes on Imagenet (achieves acceptable accuracy with 4x speed).", "We demonstrate how too much exploration can be detrimental to generalization accuracy of a training process, and propose a probabilistic \"wait-and-watch\" strategy.Currently we do not parallelize Hyperdyn ; however, computing Validation Accuracy on the suggestion from One Step BO can be easily parallelized.", "At each epoch we make only suggestion and the validation accuracy on this suggestion can be computed independently of the current hyperparameter setting.", "In the general case, when we make multiple suggestions we can parallelize in a similar fashion to BID12 .", "We also observe that epoch-based BO in FIG1 outperforms Hyperdyn in the initial epochs.", "One future direction maybe to have time varying temperature in Check Accuracy Trend based on epoch.", "We can also exploit the temporal gains obtained by using a backtrack algorithm at the later stages of the algorithm -at a stage when accuracy is sufficiently high but more sophisticated tuning is required to get the best error rates." ]

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[ "Bayesian optimization based online hyperparameter optimization." ]

[ "Multi-hop text-based question-answering is a current challenge in machine comprehension. \n", "This task requires to sequentially integrate facts from multiple passages to answer complex natural language questions.\n", "In this paper, we propose a novel architecture, called the Latent Question Reformulation Network (LQR-net), a multi-hop and parallel attentive network designed for question-answering tasks that require reasoning capabilities.\n", "LQR-net is composed of an association of \\textbf{reading modules} and \\textbf{reformulation modules}.\n", "The purpose of the reading module is to produce a question-aware representation of the document.\n", "From this document representation, the reformulation module extracts essential elements to calculate an updated representation of the question.\n", "This updated question is then passed to the following hop.\n", "We evaluate our architecture on the \\hotpotqa question-answering dataset designed to assess multi-hop reasoning capabilities.\n", "Our model achieves competitive results on the public leaderboard and outperforms the best current \\textit{published} models in terms of Exact Match (EM) and $F_1$ score.\n", "Finally, we show that an analysis of the sequential reformulations can provide interpretable reasoning paths.", "The ability to automatically extract relevant information from large text corpora remains a major challenge.", "Recently, the task of question-answering has been largely used as a proxy to evaluate the reading capabilities of neural architectures.", "Most of the current datasets for question-answering focus on the ability to read and extract information from a single piece of text, often composed of few sentences (Rajpurkar et al., 2016; Nguyen et al., 2016) .", "This has strengthened the emergence of easy questions in the sense of Sugawara et al. (2018) and influenced the recent state-of-the-art models to be good at detecting patterns and named entities (Devlin et al., 2018; Yu et al., 2018; Wang et al., 2017) .", "However they still lack actual reasoning capabilities.", "The problem of reasoning requires machine comprehension models to gather and compose over different pieces of evidence spread across multiple paragraphs.", "In this work, we propose an original neural architecture that repeatedly reads from a set of paragraphs to aggregate and reformulate information.", "In addition to the sequential reading, our model is designed to collect pieces of information in parallel and to aggregate them in its last layer.", "Throughout the model, the important pieces of the document are highlighted by what we call a reading module and integrated into a representation of the question via our reformulation module.", "Our contributions can be summarised as follows:", "• We propose a machine reading architecture, composed of multiple token-level attention modules, that collect information sequentially and in parallel across a document to answer a question, • We propose to use an input-length invariant question representation updated via a dynamic max-pooling layer that compacts information form a variable-length text sequence into a fixed size matrix, • We introduce an extractive reading-based attention mechanism that computes the attention vector from the output layer of a generic extractive machine reading model,", "• We illustrate the advantages of our model on the HOTPOTQA dataset.", "The remainder of the paper is organized as follows: Section 2 presents the multi-hop machine reading task, and analyses the required reasoning competencies.", "In Section 3, we detail our novel reading architecture and present its different building blocks.", "Section 4 presents the conducted experiments, several ablation studies, and qualitative analysis of the results.", "Finally, Section 5 discusses related work.", "Our code to reproduce the results is publicly available at (removed for review).", "2 TEXT-BASED QUESTION-ANSWERING AND MACHINE REASONING Figure 1 : Examples of reasoning paths to answer two questions of the HOTPOTQA dataset.", "In this picture, we do not display the full paragraphs, but only the supporting facts.", "The task of extractive machine reading can be summarized as follows: given a document D and a question Q, the goal is to extract the span of the document that answers the question.", "In this work, we consider the explainable multi-hop reasoning task described in Yang et al. (2018) and its associated dataset: HOTPOTQA .", "We focus our experiments on the \"distractor\" configuration of the dataset.", "In this task, the input document D is not a single paragraph but a set of ten paragraphs coming from different English Wikipedia articles.", "Answering each question requires gathering and integrating information from exactly two paragraphs; the eight others are distractors selected among the results of a tf-idf retriever (Chen et al., 2017) .", "These required paragraphs are called the gold paragraphs.", "There are two types of questions proposed in this dataset: extractive ones where the answer is a span of text extracted from the document and binary yes/no questions.", "In addition to the answer, it is required to predict the sentences, also called supporting facts, that are necessary to produce the correct answer.", "This task can be decomposed in three subtasks: (1) categorize the answer among the three following classes: yes, no, text span, (2) if it is a span, predict the start and end positions of this span in the document, and (3) predict the supporting sentences required to answer the question.", "In addition to the \"distractor\" experiments, we show how our proposed approach can be used for opendomain question answering and evaluate the entire reading pipeline on the \"fullwiki\" configuration of the HotpotQA dataset.", "In this configuration, no supporting documents are provided, and it is required to answer the question from the entire Wikipedia corpus.", "Among the competencies that multi-hop machine reading requires, we identify two major reasoning capabilities that human readers naturally exploit to answer these questions: sequential reasoning and parallel reasoning.", "Sequential reasoning requires reading a document, seeking a piece of information, then reformulating the question and finally extracting the correct answer.", "This is called multi-hop question-answering and refers to the bridge questions in HOTPOTQA .", "Another reasoning pattern is parallel reasoning, required to collect pieces of evidence for comparisons or question that required checking multiple properties in the documents.", "Figure 1 presents two examples from HOTPOTQA that illustrate such required competencies.", "We hypothesize that these two major reasoning patterns should condition the design of the proposed neural architectures to avoid restricting the model to one or the other reasoning skill.", "In this paper, we propose a novel multi-hop reading model designed for question-answering tasks that explicitly require reasoning capabilities.", "We have designed our model to gather information sequentially and in parallel from a given set of paragraphs to answer a natural language question.", "Our neural architecture, uses a sequence of token-level attention mechanisms to extract relevant information from the paragraphs and update a latent representation of the question.", "Our proposed model achieves competitive results on the HOTPOTQA reasoning task and performs better than the current best published approach in terms of both Exact Match and F 1 score.", "In addition, we show that an analysis of the sequential attentions can possibly provide human-interpretable reasoning chains." ]

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[ "In this paper, we propose the Latent Question Reformulation Network (LQR-net), a multi-hop and parallel attentive network designed for question-answering tasks that require reasoning capabilities." ]

[ "We propose a method to automatically compute the importance of features at every observation in time series, by simulating counterfactual trajectories given previous observations.", "We define the importance of each observation as the change in the model output caused by replacing the observation with a generated one.", "Our method can be applied to arbitrarily complex time series models.", "We compare the generated feature importance to existing methods like sensitivity analyses, feature occlusion, and other explanation baselines to show that our approach generates more precise explanations and is less sensitive to noise in the input signals.", "Multi-variate time series data are ubiquitous in application domains such as healthcare, finance, and others.", "In such high stakes applications, explaining the model outcome is crucial to build trust among end-users.", "Finding the features that drive the output of time series models is a challenging task due to complex non-linear temporal dependencies and cross-correlations in the data.", "The explainability problem is significantly exacerbated when more complex models are used.", "Most of the current work in time series settings focus on evaluating globally relevant features Hmamouche et al., 2017) .", "However, often global feature importance represents relevant features for the entire population, that may not characterize local explanations for individual samples.", "Therefore we focus our work on individualized feature importance in time series settings.", "In addition, besides identifying relevant features, we also identify the relevant time instances for those specific features, i.e., we identify the most relevant observations.", "To the best of our knowledge this is the first sample-specific feature importance explanation benchmark at observation level for time series models.", "In this work, we propose a counterfactual based method to learn the importance of every observation in a multivariate time series model.", "We assign importance by evaluating the expected change in model prediction had an observation been different.", "We generate plausible counterfactual observations based on signal history, to asses temporal changes in the underlying dynamics.", "The choice of the counterfactual distribution affects the quality of the explanation.", "By generating counterfactuals based on signal history, we ensure samples are realistic under individual dynamics, giving explanations that are more reliable compared to other ad-hoc counterfactual methods.", "In this section we describe our method, Feed Forward Counterfactual (FFC), for generating explanation for time series models.", "A feature is considered important if it affects the model output the most.", "In time series, the dynamics of the features also change over time, which may impact model outcome.", "As such it is critical to also identify the precise time points of such changes.", "We propose a new definition for obtaining sample-based feature importance for high-dimensional time series data.", "We evaluate the importance of each feature at every time point, to locate highly important observations.", "We define important observations as those that cause the biggest change in model output had they been different from the actual observation.", "This counterfactual observation is generated by modeling the conditional distribution of the underlying data dynamics.", "We propose a generative model to sample such counterfactuals.", "We evaluate and compare the proposed definition and algorithm to several existing approaches.", "We show that our method is better at localizing important observations over time.", "This is one of the first methods that provides individual feature importance over time.", "Future extension to this work will include analysis on real datasets annotated with feature importance explanations.", "The method will also be extended to evaluate change in risk based on most relevant subsets of observations." ]

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[ "Explaining Multivariate Time Series Models by finding important observations in time using Counterfactuals" ]

[ "This paper addresses unsupervised domain adaptation, the setting where labeled training data is available on a source domain, but the goal is to have good performance on a target domain with only unlabeled data.", "Like much of previous work, we seek to align the learned representations of the source and target domains while preserving discriminability.", "The way we accomplish alignment is by learning to perform auxiliary self-supervised task(s) on both domains simultaneously. ", "Each self-supervised task brings the two domains closer together along the direction relevant to that task.", "Training this jointly with the main task classifier on the source domain is shown to successfully generalize to the unlabeled target domain. ", "The presented objective is straightforward to implement and easy to optimize.", "We achieve state-of-the-art results on four out of seven standard benchmarks, and competitive results on segmentation adaptation.", "We also demonstrate that our method composes well with another popular pixel-level adaptation method." ]

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[ "We use self-supervision on both domain to align them for unsupervised domain adaptation." ]

[ "We introduce simple, efficient algorithms for computing a MinHash of a probability distribution, suitable for both sparse and dense data, with equivalent running times to the state of the art for both cases.", "The collision probability of these algorithms is a new measure of the similarity of positive vectors which we investigate in detail.", "We describe the sense in which this collision probability is optimal for any Locality Sensitive Hash based on sampling.", "We argue that this similarity measure is more useful for probability distributions than the similarity pursued by other algorithms for weighted MinHash, and is the natural generalization of the Jaccard index.", "MinHashing BID0 is a popular Locality Sensitive Hashing algorithm for clustering and retrieval on large datasets.", "Its extreme simplicity and efficiency, as well as its natural pairing with MapReduce and key-value datastores, have made it a basic building block in many domains, particularly document clustering BID0 BID1 and graph clustering BID2 BID3 .Given", "a finite set U , and a uniformly random permutation π, the map X → arg min i∈X π(i) provides a representation of any subset X of U that is stable under small changes to X. If X, Y are both subsets of U the well-known Jaccard index BID4 Practically, this random permutation is generated by applying some hash function to each i with a fixed random seed, hence \"MinHashing.\"In order to hash objects other than sets, Chum et al. BID5 introduced two algorithms for incorporating weights in the computation of MinHashes. The first", "algorithm associates constant global weights with the set members, suitable for idf weighting. The collision", "probability that results is ∑ i∈X∩Y wi ∑ i∈X∪Y wi . The second algorithm", "computesMinHashes of vectors of positive integers, yielding a collision probability of J W (x, y) = ∑ i min (x i , y i ) ∑ i max (x i , y i ) Subsequent work BID6 [8] BID8 has improved the efficiency of the second algorithm and extended it to arbitrary positive weights, while still achieving J W as the collision probability.J W is one of several generalizations of the Jaccard index to non-negative vectors. It is useful because", "it is monotonic with respect to the L 1 distance between x and y when they are both L 1 normalized, but it is unnatural in many ways for probability distributions.If we convert sets to binary vectors x, y, with x i , y i ∈ {0, 1}, then J W (x, y) = J(X, Y ). But if we convert these", "vectors to probability distributions by normalizing them so that x i ∈ { 0, As a consequence, switching a system from an unweighted MinHash to a MinHash based on J W will generally decrease the collision probabilities. Furthermore, J W is insensitive", "to important differences between probability distributions. It counts all differences on an", "element in the same linear scale regardless of the mass the distributions share on that element. For instance, J W ((a, b, c, 0)", ", (a, b, 0, c)) = J W ((a + c, b), (a, b +", "c)). This makes it", "a poor choice", "when", "the ultimate goal is to measure similarity using an expression based in information-theory or likelihood where having differing support typically results in the worst possible score.For a drop-in replacement for the Jaccard index that treats its input as a probability distribution, we'd like it to have the following properties.", "We've described a new generalization of the Jaccard index, and shown several qualities that motivate it as the natural extension to probability distributions.", "In particular, we proved that it is optimal on all distributions in the same sense that the Jaccard index is optimal on uniform distributions.", "We've demonstrated its utility by showing J P 's similarity in practice to the Jensen-Shannon divergence, a popular clustering criterion.", "We've described two MinHashing algorithms that achieve this as their collision probability with equivalent running time to the state of the art on both sparse and dense data." ]

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[ "The minimum of a set of exponentially distributed hashes has a very useful collision probability that generalizes the Jaccard Index to probability distributions." ]

[ "Recently, progress has been made towards improving relational reasoning in machine learning field.", "Among existing models, graph neural networks (GNNs) is one of the most effective approaches for multi-hop relational reasoning.", "In fact, multi-hop relational reasoning is indispensable in many natural language processing tasks such as relation extraction.", "In this paper, we propose to generate the parameters of graph neural networks (GP-GNNs) according to natural language sentences, which enables GNNs to process relational reasoning on unstructured text inputs.", "We verify GP-GNNs in relation extraction from text.", "Experimental results on a human-annotated dataset and two distantly supervised datasets show that our model achieves significant improvements compared to the baselines.", "We also perform a qualitative analysis to demonstrate that our model could discover more accurate relations by multi-hop relational reasoning.", "Recent years, graph neural networks (GNNs) have been applied to various fields of machine learning, including node classification BID10 , relation classification BID22 , molecular property prediction BID6 , few-shot learning BID5 , and achieve promising results on these tasks.", "These works have demonstrated GNNs' strong power to process relational reasoning on graphs.Relational reasoning aims to abstractly reason about entities/objects and their relations, which is an important part of human intelligence.", "Besides graphs, relational reasoning is also of great importance in many natural language processing tasks such as question answering, relation extraction, summarization, etc.", "Consider the example shown in Fig. 1 , existing relation extraction models could easily extract the facts that Luc Besson directed a film Léon: The Professional and that the film is in English, but fail to infer the relationship between Luc Besson and English without multi-hop relational reasoning.", "By considering the reasoning patterns, one can discover that Luc Besson could speak English following a reasoning logic that Luc Besson directed Léon: The Professional and this film is in English indicates Luc Besson could speak English.", "However, most existing GNNs can only process multi-hop relational reasoning on pre-defined graphs and cannot be directly applied in natural language relational reasoning.", "Enabling multi-hop relational reasoning in natural languages remains an open problem.To address this issue, in this paper, we propose graph neural networks with generated parameters (GP-GNNs), to adapt graph neural networks to solve the natural language relational reasoning task.", "GP-GNNs first constructs a fully-connected graph with the entities in the sequence of text.", "After that, it employs three modules to process relational reasoning: (1) an encoding module which enables edges to encode rich information from natural languages, (2) a propagation module which propagates relational information among various nodes, and (3) a classification module which makes predictions with node representations.", "As compared to traditional GNNs, GP-GNNs could learn edges' parameters from natural languages, extending it from performing inferring on only non-relational graphs or graphs with a limited number of edge types to unstructured inputs such as texts.In the experiments, we apply GP-GNNs to a classic natural language relational reasoning task: relation extraction from text.", "We carry out experiments on Wikipedia corpus aligned with Wikidata knowledge base BID25 Figure 1 : An example of relation extraction from plain text.", "Given a sentence with several entities marked, we model the interaction between these entities by generating the weights of graph neural networks.", "Modeling the relationship between \"Léon\" and \"English\" as well as \"Luc Besson\" helps discover the relationship between \"Luc Besson\" and \"English\".model", "outperforms other state-of-the-art models on relation extraction task by considering multihop relational reasoning. We also", "perform a qualitative analysis which shows that our model could discover more relations by reasoning more robustly as compared to baseline models.Our main contributions are in two-fold:(1) We extend a novel graph neural network model with generated parameters, to enable relational message-passing with rich text information, which could be applied to process relational reasoning on unstructured inputs such as natural languages.(2) We verify", "our GP-GNNs in the task of relation extraction from text, which demonstrates its ability on multi-hop relational reasoning as compared to those models which extract relationships separately. Moreover, we", "also present three datasets, which could help future researchers compare their models in different settings.", "We addressed the problem of utilizing GNNs to perform relational reasoning with natural languages.", "Our proposed models, GP-GNNs, solves the relational message-passing task by encoding natural language as parameters and performing propagation from layer to layer.", "Our model can also be considered as a more generic framework for graph generation problem with unstructured input other than text, e.g. images, videos, audios.", "In this work, we demonstrate its effectiveness in predicting the relationship between entities in natural language and bag-level and show that by considering more hops in reasoning the performance of relation extraction could be significantly improved." ]

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[ "A graph neural network model with parameters generated from natural languages, which can perform multi-hop reasoning. " ]

[ "Off-Policy Actor-Critic (Off-PAC) methods have proven successful in a variety of continuous control tasks.", "Normally, the critic’s action-value function is updated using temporal-difference, and the critic in turn provides a loss for the actor that trains it to take actions with higher expected return.", "In this paper, we introduce a novel and flexible meta-critic that observes the learning process and meta-learns an additional loss for the actor that accelerates and improves actor-critic learning.", "Compared to the vanilla critic, the meta-critic network is explicitly trained to accelerate the learning process; and compared to existing meta-learning algorithms, meta-critic is rapidly learned online for a single task, rather than slowly over a family of tasks.", "Crucially, our meta-critic framework is designed for off-policy based learners, which currently provide state-of-the-art reinforcement learning sample efficiency.", "We demonstrate that online meta-critic learning leads to improvements in a variety of continuous control environments when combined with contemporary Off-PAC methods DDPG, TD3 and the state-of-the-art SAC.", "Off-policy Actor-Critic (Off-PAC) methods are currently central in deep reinforcement learning (RL) research due to their greater sample efficiency compared to on-policy alternatives.", "On-policy requires new trajectories to be collected for each update to the policy, and is expensive as the number of gradient steps and samples per step increases with task-complexity even for contemporary TRPO (Schulman et al., 2015) , PPO (Schulman et al., 2017) and A3C (Mnih et al., 2016) algorithms.", "Off-policy methods, such as DDPG (Lillicrap et al., 2016) , TD3 (Fujimoto et al., 2018) and SAC (Haarnoja et al., 2018b) achieve greater sample efficiency due to their ability to learn from randomly sampled historical transitions without a time sequence requirement, thus making better use of past experience.", "Their critic estimates the action-value (Q-value) function using a differentiable function approximator, and the actor updates its policy parameters in the direction of the approximate action-value gradient.", "Briefly, the critic provides a loss to guide the actor, and is trained in turn to estimate the environmental action-value under the current policy via temporal-difference learning (Sutton et al., 2009) .", "In all these cases the learning algorithm itself is hand-crafted and fixed.", "Recently meta-learning, or \"learning-to-learn\" has become topical as a paradigm to accelerate RL by learning aspects of the learning strategy, for example, through learning fast adaptation strategies (Finn et al., 2017; Rakelly et al., 2019; Riemer et al., 2019) , exploration strategies (Gupta et al., 2018) , optimization strategies (Duan et al., 2016b) , losses (Houthooft et al., 2018) , hyperparameters (Xu et al., 2018; Veeriah et al., 2019) , and intrinsic rewards (Zheng et al., 2018) .", "However, the majority of these works perform meta-learning on a family of tasks or environments and amortize this huge cost by deploying the trained strategy for fast learning on a new task.", "In this paper we introduce a novel meta-critic network to enhance existing Off-PAC learning frameworks.", "The meta-critic is used alongside the vanilla critic to provide a loss to guide the actor's learning.", "However compared to the vanilla critic, the meta-critic is explicitly (meta)-trained to accelerate the learning process rather than merely estimate the action-value function.", "Overall, the actor is trained by gradients provided by both critic and meta-critic losses, the critic is trained by temporal-difference as usual, and the meta-critic is trained to generate maximum learning performance improvements in the actor.", "In our framework, both the critic and meta-critic use randomly sampled off-policy transitions for efficient and effective Off-PAC learning, providing superior sam-ple efficiency compared to existing on-policy meta-learners.", "Furthermore, we demonstrate that our meta-critic can be successfully learned online within a single task.", "This is in contrast to the currently widely used meta-learning research paradigm -where entire task families are required to provide enough data for meta-learning, and to provide new tasks to amortize the huge cost of meta-learning.", "Essentially our framework meta-learns an auxiliary loss function, which can be seen as an intrinsic motivation towards optimum learning progress (Oudeyer & Kaplan, 2009) .", "As analogously observed in several recent meta-learning studies (Franceschi et al., 2018) , our loss-learning can be formalized as a bi-level optimization problem with the upper level being meta-critic learning, and lower level being conventional learning.", "We solve this joint optimization by iteratively updating the metacritic and base learner online while solving a single task.", "Our strategy is thus related to the metaloss learning in EPG (Houthooft et al., 2018) , but learned online rather than offline, and integrated with Off-PAC rather than their on-policy policy-gradient learning.", "The most related prior work is LIRPG (Zheng et al., 2018) , which meta-learns an intrinsic reward online.", "However, their intrinsic reward just provides a helpful scalar offset to the environmental reward for on-policy trajectory optimization via policy-gradient (Sutton et al., 2000) .", "In contrast our meta-critic provides a loss for direct actor optimization just based on sampled transitions, and thus achieves dramatically better sample efficiency than LIRPG reward learning in practice.", "We evaluate our framework on several contemporary continuous control benchmarks and demonstrate that online meta-critic learning can be integrated with and improve a selection of contemporary Off-PAC algorithms including DDPG, TD3 and SAC.", "We present Meta-Critic, an auxiliary critic module for Off-PAC methods that can be meta-learned online during single task learning.", "The meta-critic is trained to generate gradients that improve the actor's learning performance over time, and leads to long run performance gains in continuous control.", "The meta-critic module can be flexibly incorporated into various contemporary Off-PAC methods to boost performance.", "In future work, we plan to apply the meta-critic to conventional offline meta-learning with multi-task and multi-domain RL." ]

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[ "We present Meta-Critic, an auxiliary critic module for off-policy actor-critic methods that can be meta-learned online during single task learning." ]

[ "Modern neural networks are highly overparameterized, with capacity to substantially overfit to training data.", "Nevertheless, these networks often generalize well in practice.", "It has also been observed that trained networks can often be ``compressed to much smaller representations.", "The purpose of this paper is to connect these two empirical observations.", "Our main technical result is a generalization bound for compressed networks based on the compressed size that, combined with off-the-shelf compression algorithms, leads to state-of-the-art generalization guarantees.", "In particular, we provide the first non-vacuous generalization guarantees for realistic architectures applied to the ImageNet classification problem.", "Additionally, we show that compressibility of models that tend to overfit is limited.", "Empirical results show that an increase in overfitting increases the number of bits required to describe a trained network.", "A pivotal question in machine learning is why deep networks perform well despite overparameterization.", "These models often have many more parameters than the number of examples they are trained on, which enables them to drastically overfit to training data BID39 .", "In common practice, however, such networks perform well on previously unseen data.Explaining the generalization performance of neural networks is an active area of current research.", "Attempts have been made at adapting classical measures such as VC-dimension BID14 or margin/norm bounds BID4 , but such approaches have yielded bounds that are vacuous by orders of magnitudes.", "Other authors have explored modifications of the training procedure to obtain networks with provable generalization guarantees BID10 .", "Such procedures often differ substantially from standard procedures used by practitioners, and empirical evidence suggests that they fail to improve performance in practice BID38 .We", "begin with an empirical observation: it is often possible to \"compress\" trained neural networks by finding essentially equivalent models that can be described in a much smaller number of bits; see BID9 for a survey. Inspired", "by classical results relating small model size and generalization performance (often known as Occam's razor), we establish a new generalization bound based on the effective compressed size of a trained neural network. Combining", "this bound with off-the-shelf compression schemes yields the first non-vacuous generalization bounds in practical problems. The main", "contribution of the present paper is the demonstration that, unlike many other measures, this measure is effective in the deep-learning regime.Generalization bound arguments typically identify some notion of complexity of a learning problem, and bound generalization error in terms of that complexity. Conceptually", ", the notion of complexity we identify is: complexity = compressed size − remaining structure.(1) The first", "term on the right-hand side represents the link between generalization and explicit compression. The second term", "corrects for superfluous structure that remains in the compressed representation. For instance, the", "predictions of trained neural networks are often robust to perturbations of the network weights. Thus, a representation", "of a neural network by its weights carries some irrelevant information. We show that accounting", "for this robustness can substantially reduce effective complexity.Our results allow us to derive explicit generalization guarantees using off-the-shelf neural network compression schemes. In particular:• The generalization", "bound can be evaluated by compressing a trained network, measuring the effective compressed size, and substituting this value into the bound.• Using off-the-shelf neural network", "compression schemes with this recipe yields bounds that are state-of-the-art, including the first non-vacuous bounds for modern convolutional neural nets.The above result takes a compression algorithm and outputs a generalization bound on nets compressed by that algorithm. We provide a complementary result by", "showing that if a model tends to overfit then there is an absolute limit on how much it can be compressed. We consider a classifier as a (measurable", ") function of a random training set, so the classifier is viewed as a random variable. We show that the entropy of this random", "variable is lower bounded by a function of the expected degree of overfitting. Additionally, we use the randomization", "tests of BID39 to show empirically that increased overfitting implies worse compressibility, for a fixed compression scheme.The relationship between small model size and generalization is hardly new: the idea is a variant of Occam's razor, and has been used explicitly in classical generalization theory BID34 BID5 BID27 BID16 BID33 ). However, the use of highly overparameterized", "models in deep learning seems to directly contradict the Occam principle. Indeed, the study of generalization and the", "study of compression in deep learning has been largely disjoint; the later has been primarily motivated by computational and storage limitations, such as those arising from applications on mobile devices BID9 . Our results show that Occam type arguments", "remain powerful in the deep learning regime. The link between compression and generalization", "is also used in work by BID0 , who study compressibility arising from a form of noise stability. Our results are substantially different, and closer", "in spirit to the work of BID10 ; see Section 3 for a detailed discussion. BID39 study the problem of generalization in deep learning", "empirically. They observe that standard deep net architectures-which generalize", "well on real-world data-are able to achieve perfect training accuracy on randomly labelled data. Of course, in this case the test error is no better than random guessing", ". Accordingly, any approach to controlling generalization error of deep nets", "must selectively and preferentially bound the generalization error of models that are actually plausible outputs of the training procedure applied to real-world data. Following Langford & Caruana (2002) ; BID10 , we make use of the PAC-Bayesian", "framework BID29 BID7 BID30 . This framework allows us to encode prior beliefs about which learned models are", "plausible as a (prior) distribution π over possible parameter settings. The main challenge in developing a bound in the PAC-Bayes framework bound is to", "articulate a distribution π that encodes the relative plausibilities of possible outputs of the training procedure. The key insight is that, implicitly, any compression scheme is a statement about", "model plausibilities: good compression is achieved by assigning short codes to the most probable models, and so the probable models are those with short codes.", "It has been a long standing observation by practitioners that despite the large capacity of models used in deep learning practice, empirical results demonstrate good generalization performance.", "We show that with no modifications, a standard engineering pipeline of training and compressing a network leads to demonstrable and non-vacuous generalization guarantees.", "These are the first such results on networks and problems at a practical scale, and mirror the experience of practitioners that best results are often achieved without heavy regularization or modifications to the optimizer BID38 .The", "connection between compression and generalization raises a number of important questions. Foremost", ", what are its limitations? The fact", "that our bounds are non-vacuous implies the link between compression and generalization is non-trivial. However,", "the bounds are far from tight. If significantly", "better compression rates were achievable, the resulting bounds would even be of practical value. For example, if", "a network trained on ImageNet to 90% training and 70% testing accuracy could be compressed to an effective size of 30 KiB-about one order of magnitude smaller than our current compression-that would yield a sharp bound on the generalization error.A PROOF OF THEOREM 4.3 In this section we describe the construction of the prior π and prove the bound on the KL-divergence claimed in Theorem 4.3. Intuitively, we", "would like to express our prior as a mixture over all possible decoded points of the compression algorithm. More precisely,", "define the mixture component π S,Q,C associated with a triplet (S, Q, C) as: DISPLAYFORM0 We then define our prior π as a weighted mixture over all triplets, weighted by the code length of the triplet: DISPLAYFORM1 where the sum is taken over all S and C which are representable by our code, and all Q = (q 1 , . . . , q k ) ∈ {1, . . . , r} k . In practice, S", "takes values in all possible subsets of {1, . . . , p}, and C takes values in F r , where F ⊆ R is a chosen finite subset of representable real numbers (such as those that may be represented by IEEE-754 single precision numbers), and r is a chosen quantization level. We now give the", "proof of Theorem 4.3.Proof. We have that: DISPLAYFORM2", "where we must have Z ≤ 1 by the same argument as in the proof of Theorem 4.1Suppose that the output of our compression algorithm is a triplet (Ŝ,Q,Ĉ). We recall that our posterior", "ρ is given by a normal centered at w(Ŝ,Q,Ĉ) with variance σ 2 , and we may thus compute the KL-divergence: DISPLAYFORM3 We are now left with the mixture term, which is a mixture of r k many terms in dimension k, and thus computationally untractable. However, we note that we are", "in a special case where the mixture itself is independent across coordinates. Indeed, let φ τ denote the density", "of the univariate normal distribution with mean 0 and variance τ 2 , we note that we may write the mixture as: DISPLAYFORM4 Additionally, as our chosen stochastic estimator ρ is independent over the coordinates, the KLdivergence decomposes over the coordinates, to obtain: DISPLAYFORM5 Plugging the above computation into (13) gives the desired result." ]

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[ "We obtain non-vacuous generalization bounds on ImageNet-scale deep neural networks by combining an original PAC-Bayes bound and an off-the-shelf neural network compression method." ]

[ "Adversarial examples can be defined as inputs to a model which induce a mistake -- where the model output is different than that of an oracle, perhaps in surprising or malicious ways.", "Original models of adversarial attacks are primarily studied in the context of classification and computer vision tasks.", "While several attacks have been proposed in natural language processing (NLP) settings, they often vary in defining the parameters of an attack and what a successful attack would look like.", "The goal of this work is to propose a unifying model of adversarial examples suitable for NLP tasks in both generative and classification settings.", "We define the notion of adversarial gain: based in control theory, it is a measure of the change in the output of a system relative to the perturbation of the input (caused by the so-called adversary) presented to the learner.", "This definition, as we show, can be used under different feature spaces and distance conditions to determine attack or defense effectiveness across different intuitive manifolds.", "This notion of adversarial gain not only provides a useful way for evaluating adversaries and defenses, but can act as a building block for future work in robustness under adversaries due to its rooted nature in stability and manifold theory." ]

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[ "We propose an alternative measure for determining effectiveness of adversarial attacks in NLP models according to a distance measure-based method like incremental L2-gain in control theory." ]

[ "We propose a Warped Residual Network (WarpNet) using a parallelizable warp operator for forward and backward propagation to distant layers that trains faster than the original residual neural network.", "We apply a perturbation theory on residual networks and decouple the interactions between residual units.", "The resulting warp operator is a first order approximation of the output over multiple layers.", "The first order perturbation theory exhibits properties such as binomial path lengths and exponential gradient scaling found experimentally by Veit et al (2016). \n", "We demonstrate through an extensive performance study that the proposed network achieves comparable predictive performance to the original residual network with the same number of parameters, while achieving a significant speed-up on the total training time.", "As WarpNet performs model parallelism in residual network training in which weights are distributed over different GPUs, it offers speed-up and capability to train larger networks compared to original residual networks.", "Deep Convolution Neural Networks (CNN) have been used in image recognition tasks with great success.", "Since AlexNet BID6 , many other neural architectures have been proposed to achieve start-of-the-art results at the time.", "Some of the notable architectures include, VGG BID7 , Inception and Residual networks (ResNet) BID3 .Training", "a deep neural network is not an easy task. As the gradient", "at each layer is dependent upon those in higher layers multiplicatively, the gradients in earlier layers can vanish or explode, ceasing the training process. The gradient vanishing", "problem is significant for neuron activation functions such as the sigmoid, where the gradient approaches zero exponentially away from the origin on both sides. The standard approach", "to combat vanishing gradient is to apply Batch Normalization (BN) BID5 followed by the Rectified Linear Unit (ReLU) BID1 activation. More recently, skip connections", "BID9 have been proposed to allow previous layers propagate relatively unchanged. Using this methodology the authors", "in BID9 were able to train extremely deep networks (hundreds of layers) and about one thousand layers were trained in residual networks BID3 .As the number of layers grows large", ", so does the training time. To evaluate the neural network's output", ", one needs to propagate the input of the network layer by layer in a procedure known as forward propagation. Likewise, during training, one needs to", "propagate the gradient of the loss function from the end of the network to update the model parameters, or weights, in each layer of the network using gradient descent. The complexity of forward and propagation", "is O(K), where K is the number of layers in the network. To speed up the process, one may ask if there", "exist a shallower network that accurately approximates a deep network so that training time is reduced. In this work we show that there indeed exists", "a neural network architecture that permits such an approximation, the ResNet.Residual networks typically consist of a long chain of residual units. Recent investigations suggest that ResNets behave", "as an ensemble of shallow networks BID11 . Empirical evidence supporting this claim includes", "one that shows randomly deactivating residual units during training (similar to drop-out BID8 ) appears to improve performance BID4 . The results imply that the output of a residual unit", "is just a small perturbation of the input. In this work, we make an approximation of the ResNet", "by using a series expansion in the small perturbation. We find that merely the first term in the series expansion", "is sufficient to explain the binomial distribution of path lengths and exponential gradient scaling experimentally observed by BID11 . The approximation allows us to effectively estimate the output", "of subsequent layers using just the input of the first layer and obtain a modified forward propagation rule. We call the corresponding operator the warp operator. The backpropagation", "rule is obtained by differentiating the warp operator", ". We implemented a network using the warp operator and found that our network", "trains faster on image classification tasks with predictive accuracies comparable to those of the original ResNet." ]

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[ "We propose the Warped Residual Network using a parallelizable warp operator for forward and backward propagation to distant layers that trains faster than the original residual neural network. " ]

[ "A plethora of methods attempting to explain predictions of black-box models have been proposed by the Explainable Artificial Intelligence (XAI) community.", "Yet, measuring the quality of the generated explanations is largely unexplored, making quantitative comparisons non-trivial.", "In this work, we propose a suite of multifaceted metrics that enables us to objectively compare explainers based on the correctness, consistency, as well as the confidence of the generated explanations.", "These metrics are computationally inexpensive, do not require model-retraining and can be used across different data modalities.", "We evaluate them on common explainers such as Grad-CAM, SmoothGrad, LIME and Integrated Gradients.", "Our experiments show that the proposed metrics reflect qualitative observations reported in earlier works.", "Over the past few years, deep learning has made significant progress, outperforming the state-ofthe-art in many tasks like image classification (Mahajan et al., 2018) , semantic segmentation (Zhu et al., 2018) , machine translation (Kalchbrenner et al., 2016) and even surpassing humans in the games of Chess and Go (Silver et al., 2016) .", "As these models are deployed in more mission-critical systems, we notice that despite their incredible performance on standard metrics, they are fragile (Szegedy et al., 2013; Goodfellow et al., 2014) and can be easily fooled by small perturbations to the inputs (Engstrom et al., 2017) .", "Further research has also exposed that these models are biased in undesirable ways exacerbating gender and racial biases (Howard et al., 2017; Escudé Font & Costa-Jussà, 2019) .", "These issues have amplified the need for making these black-box models interpretable.", "Consequently, the XAI community has proposed a variety of algorithms that aim to explain predictions of these models (Ribeiro et al., 2016; Lundberg & Lee, 2017; Shrikumar et al., 2017; Smilkov et al., 2017; Selvaraju et al., 2016; Sundararajan et al., 2017) .", "With such an explosion of interpretability methods (hereon referred to as explainers), evaluating them has become non-trivial.", "This is due to the lack of a widely accepted metric to quantitatively compare them.", "There have been several attempts to propose such metrics.", "Unfortunately, they tend to suffer from major drawbacks like computational cost (Hooker et al., 2018) , inability to be extended to non-image domains (Kindermans et al., 2017a) , or simply focusing only one desirable attribute of a good explainer.", "(Yeh et al., 2019) .", "In this paper, we propose a suite of metrics that attempt to alleviate these drawbacks and can be applied across multiple data modalities.", "Unlike the vast majority of prior work, we not only consider the correctness of an explainer, but also the consistency and confidence of the generated explanations.", "We use these metrics to evaluate and compare widely used explainers such as LIME (Ribeiro et al., 2016) , Grad-CAM (Selvaraju et al., 2016) , SmoothGrad (Smilkov et al., 2017) and Integrated Gradients (Sundararajan et al., 2017) on an Inception-V3 (Szegedy et al., 2015) model pretrained on the ImageNet dataset (ILSVRC2012) (Deng et al., 2009) , in an objective manner (i.e., without the need of a human-in-the-loop).", "Moreover, our proposed metrics are general and computationally inexpensive.", "Our main contributions are:", "1. Identifying and formulating the properties of a good explainer.", "2. Proposing a generic, computationally inexpensive suite of metrics to evaluate explainers.", "3. Comparing common explainers and discussing pros and cons of each.", "We find that while Grad-CAM seems to perform best overall, it does suffer from drawbacks not reported in prior works.", "On the other hand, LIME consistently underperforms in comparison to the other models." ]

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true

[ "We propose a suite of metrics that capture desired properties of explainability algorithms and use it to objectively compare and evaluate such methods" ]

[ "Neural networks are known to produce unexpected results on inputs that are far from the training distribution.", "One approach to tackle this problem is to detect the samples on which the trained network can not answer reliably.", "ODIN is a recently proposed method for out-of-distribution detection that does not modify the trained network and achieves good performance for various image classification tasks.", "In this paper we adapt ODIN for sentence classification and word tagging tasks.", "We show that the scores produced by ODIN can be used as a confidence measure for the predictions on both in-distribution and out-of-distribution datasets." ]

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false

[ "A recent out-of-distribution detection method helps to measure the confidence of RNN predictions for some NLP tasks" ]

[ "Some recent work has shown separation between the expressive power of depth-2 and depth-3 neural networks.", "These separation results are shown by constructing functions and input distributions, so that the function is well-approximable by a depth-3 neural network of polynomial size but it cannot be well-approximated under the chosen input distribution by any depth-2 neural network of polynomial size.", "These results are not robust and require carefully chosen functions as well as input distributions.\n\n", "We show a similar separation between the expressive power of depth-2 and depth-3 sigmoidal neural networks over a large class of input distributions, as long as the weights are polynomially bounded.", "While doing so, we also show that depth-2 sigmoidal neural networks with small width and small weights can be well-approximated by low-degree multivariate polynomials.", "Understanding the remarkable success of deep neural networks in many domains is an important problem at present (e.g., BID10 ).", "This problem has many facets such as understanding generalization, expressive power, optimization algorithms in deep learning.", "In this paper, we focus on the question of understanding the expressive power of neural networks.", "In other words, we study what functions can and cannot be represented and approximated by neural networks of bounded size, depth, width and weights.The early results on the expressive power of neural networks showed that the depth-2 neural networks are universal approximators; that is to say, with only mild restrictions on the activation functions or neurons, the depth-2 neural networks are powerful enough to uniformly approximate arbitrary continuous functions on bounded domains in R d ,", "e.g., BID2 ; BID9 ; BID0 .", "However, the bounds that they provide on the size or width of these neural networks are quite general, and therefore, weak.", "Understanding what functions can be represented or wellapproximated by neural networks with bounded parameters is a general direction in the study of expressive power of neural networks.", "Here the parameters could mean the number of neurons, the width of hidden layers, the depth, and the magnitude of its weights etc.Natural signals (images, speech etc.) tend to be representable as compositional hierarchies BID10 , and deeper networks can be thought of as representing deeper hierarchies.", "The power of depth has been a subject of investigation in deep learning,", "e.g., BID8 .", "We are interested in understanding the effect of depth on the expressive power.", "In particular, one may ask whether having more depth allows representation of more functions if the size bound remains the same.", "BID5 show a separation between depth-2 and depth-3 neural networks.", "More precisely, they exhibit a function g : R d → R and a probability distribution µ on R d such that g is bounded and supported on a ball of radius O( √ d) and expressible by a depth-3 network of size polynomially bounded in", "d. But any depth-2 network approximating g in L 2 -norm (or squared error) within a small constant under the distribution µ must be of size exponentially large in", "d. Their separation works for all reasonable activation functions including ReLUs (Rectified Linear Units) and sigmoids.", "The function and the input distribution in BID5 are carefully constructed and their proof techniques seem to crucially rely on the specifics of these constructions.", "Building upon this result, BID14 show that while the indicator function of the L 2 -ball can be well-approximated by depth-3 networks of polynomial size, any good approximation to it by depth-2 networks must require exponential size.", "Here, the notion of approximation in the lower bound is the same as in BID5 and a carefully constructed distribution that is arguably not quite natural.Daniely (2017) (see also BID12 ) also gave a separation between depth-2 and depth-3 networks by exhibiting a function g : S d−1 × S d−1 → R which can be well-approximated by a depth-3 ReLU neural network of polynomially bounded size and weights but cannot be approximated by any depth-2 (sigmoid, ReLU or more general) neural network of polynomial size with (exponentially) bounded weights.", "This separation holds under uniform distribution on S d−1 × S d−1 , which is more natural than the previous distributions.", "However, the proof technique crucially uses harmonic analysis on the unit sphere, and does not seems robust or applicable to other distributions.", "Telgarsky (2016) shows a separation between depth-2k 3 + 8 and depth-k ReLU neural networks, for any positive integer k, when the input is uniformly distributed over [−1, 1] d .", "BID11 (see also BID14 BID21 ) show that there are univariate functions on a bounded interval such that neural networks of constant depth require size at least Ω (poly(1/ )) for a uniform -approximation over the interval, whereas deep networks (the depth can depend on ) can have size O (polylog(1/ )).The", "above separation results all fit the following template: certain carefully constructed functions can be well approximated by deep networks, but are hard to approximate by shallow networks using a notion of error that uses a carefully defined distribution. (Only", "Liang & Srikant (2017) is distribution-independent as it deals with uniform approximation everywhere in the domain). Thus", "these results do not tell us the extent to which deeper networks are more expressive than the shallow ones. We would", "like to understand whether there are large classes of functions and distributions that witness the separation between deep and shallow networks. An answer", "to this question is also more likely to shed light on practical applications of neural networks. BID17 ; BID16", "; BID18 show that even functions computed by a depth-2 neural network of polynomial size can be hard to learn using gradient descent type of algorithms for a wide class of distributions. These results", "address questions about learnability rather than the expressive power of deep neural networks. BID7 shows that", "piecewise affine functions on [0, 1] d with N pieces can be exactly represented by a width (d + 3) network of depth at most N . Lower bound of", "Ω((N + d − 1)/(d + 1)) on the depth is proven for functions of the above type when the network has width at most (d + 1) and very closely approximates the function.Our depth separation results apply to neural networks with bounds on the magnitudes of the weights. While we would", "prefer to prove our results without any weight restrictions, we now argue that small weights are natural. In training neural", "networks, often weights are not allowed to be too large to avoid overfitting. Weight decay is a", "commonly used regularization heuristic in deep learning to control the weights. Early stopping can", "also achieve this effect. Another motivation", "to keep the weights low is to keep the Lipschitz constant of the function computed by the network (w.r.t. changes in the input, while keeping the network parameters fixed) small. BID6 contains many", "of these references. One of the surprising", "discoveries about neural networks has been the existence of adversarial examples BID19 ). These are examples obtained", "by adding a tiny perturbation to input from class so that the resulting input is misclassified by the network. The perturbations are imperceptible", "to humans. Existence of such examples for a network", "suggests that the Lipschitz constant of the network is high as noted in BID19 . This lead them to suggest regularizing training", "of neural nets by penalizing high Lipschitz constant to improve the generalization error and, in particular, eliminate adversarial examples. This is carried out in BID1 , who find a way to", "control the Lipschitz constant by enforcing an orthonormality constraint on the weight matrices along with other tricks. They report better resilience to adversarial examples", ". On the other hand, BID13 suggest that Lipschitz constant", "cannot tell the full story about generalization." ]

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true

[ "depth-2-vs-3 separation for sigmoidal neural networks over general distributions" ]

[ "The smallest eigenvectors of the graph Laplacian are well-known to provide a succinct representation of the geometry of a weighted graph.", "In reinforcement learning (RL), where the weighted graph may be interpreted as the state transition process induced by a behavior policy acting on the environment, approximating the eigenvectors of the Laplacian provides a promising approach to state representation learning.", "However, existing methods for performing this approximation are ill-suited in general RL settings for two main reasons: First, they are computationally expensive, often requiring operations on large matrices.", "Second, these methods lack adequate justification beyond simple, tabular, finite-state settings.", "In this paper, we present a fully general and scalable method for approximating the eigenvectors of the Laplacian in a model-free RL context.", "We systematically evaluate our approach and empirically show that it generalizes beyond the tabular, finite-state setting.", "Even in tabular, finite-state settings, its ability to approximate the eigenvectors outperforms previous proposals.", "Finally, we show the potential benefits of using a Laplacian representation learned using our method in goal-achieving RL tasks, providing evidence that our technique can be used to significantly improve the performance of an RL agent.", "The performance of machine learning methods generally depends on the choice of data representation BID2 .", "In reinforcement learning (RL), the choice of state representation may affect generalization (Rafols et al., 2005) , exploration (Tang et al., 2017; Pathak et al., 2017) , and speed of learning BID7 .", "As a motivating example, consider goal-achieving tasks, a class of RL tasks which has recently received significant attention BID1 Pong et al., 2018) .", "In such tasks, the agent's task is to achieve a certain configuration in state space; e.g. in FIG0 the environment is a two-room gridworld and the agent's task is to reach the red cell.", "A natural reward choice is the negative Euclidean (L2) distance from the goal (e.g., as used in Nachum et al. FORMULA4 ).", "The ability of an RL agent to quickly and successfully solve the task is thus heavily dependent on the representation of the states used to compute the L2 distance.", "Computing the distance on one-hot (i.e. tabular) representations of the states (equivalent to a sparse reward) is most closely aligned with the task's directive.", "However, such a representation can be disadvantageous for learning speed, as the agent receives the same reward signal for all non-goal cells.", "One may instead choose to compute the L2 distance on (x, y) representations of the grid cells.", "This allows the agent to receive a clear signal which encourages it to move to cells closer to the goal.", "Unfortunately, this representation is agnostic to the environment dynamics, and in cases where the agent's movement is obstructed (e.g. by a wall as in FIG0 ), this choice of reward is likely to cause premature convergence to sub-optimal policies unless sophisticated exploration strategies are used.", "The ideal reward structure would be defined on state representations whose distances roughly correspond to the ability of the agent to reach one state from another.", "Although there are many suitable such representations, in this paper, we focus on a specific approach based on the graph Laplacian, which is notable for this and several other desirable properties.", "For a symmetric weighted graph, the Laplacian is a symmetric matrix with a row and column for each vertex.", "The d smallest eigenvectors of the Laplacian provide an embedding of each vertex in R d which has been found to be especially useful in a variety of applications, such as graph visualization BID9 , clustering (Ng et al., 2002) , and more BID6 .Naturally", ", the use of the Laplacian in RL has also attracted attention. In an RL", "setting, the vertices of the graph are given by the states of the environment. For a specific", "behavior policy, edges between states are weighted by the probability of transitioning from one state to the other (and vice-versa) . Several previous", "works have proposed that approximating the eigenvectors of the graph Laplacian can be useful in RL. For example, Mahadevan", "(2005) shows that using the eigenvectors as basis functions can accelerate learning with policy iteration. Machado et al. (2017a;", "b) show that the eigenvectors can be used to construct options with exploratory behavior. The Laplacian eigenvectors", "are also a natural solution to the aforementioned reward-shaping problem. If we use a uniformly random", "behavior policy, the Laplacian state representations will be appropriately aware of the walls present in the gridworld and will induce an L2 distance as shown in FIG0 (right). This choice of representation", "accurately reflects the geometry of the problem, not only providing a strong learning signal at every state, but also avoiding spurious local optima.While the potential benefits of using Laplacian-based representations in RL are clear, current techniques for approximating or learning the representations are ill-suited for model-free RL. For one, current methods mostly", "require an eigendecomposition of a matrix. When this matrix is the actual", "Laplacian (Mahadevan, 2005) , the eigendecomposition can easily become prohibitively expensive. Even for methods which perform", "the eigendecomposition on a reduced matrix (Machado et al., 2017a; b) , the eigendecomposition step may be computationally expensive, and furthermore precludes the applicability of the method to stochastic or online settings, which are common in RL. Perhaps more crucially, the justification", "for many of these methods is made in the tabular setting. The applicability of these methods to more", "general settings is unclear.To resolve these limitations, we propose a computationally efficient approach to approximate the eigenvectors of the Laplacian with function approximation based on the spectral graph drawing objective, an objective whose optimum yields the desired eigenvector representations. We present the objective in a fully general", "RL setting and show how it may be stochastically optimized over minibatches of sampled experience. We empirically show that our method provides", "a better approximation to the Laplacian eigenvectors than previous proposals, especially when the raw representation is not tabular. We then apply our representation learning procedure", "to reward shaping in goal-achieving tasks, and show that our approach outperforms both sparse rewards and rewards based on L2 distance in the raw feature space. Results are shown under a set of gridworld maze environments", "and difficult continuous control navigation environments.", "We have presented an approach to learning a Laplacian-based state representation in RL settings.", "Our approach is both general -being applicable to any state space regardless of cardinality -and scalable -relying only on the ability to sample mini-batches of states and pairs of states.", "We have further provided an application of our method to reward shaping in both discrete spaces and continuous-control settings.", "With our scalable and general approach, many more potential applications of Laplacian-based representations are now within reach, and we encourage future work to continue investigating this promising direction.", "A EXISTENCE OF SMALLEST EIGENVALUES OF THE LAPLACIAN.Since the Hilbert space H may have infinitely many dimensions we need to make sure that the smallest d eigenvalues of the Laplacian operator is well defined.", "Since L = I − D if λ is an eigenvalue of D then 1 − λ is an eigenvalue of L. So we turn to discuss the existence of the largest d eigenvalues of D. According to our definition D is a compact self-adjoint linear operator on H. So it has the following properties according to the spectral theorem:• D has either", "(i) a finite set of eigenvalues or", "(ii) countably many eigenvalues {λ 1 , λ 2 , ...} and λ n → 0 if there are infinitely many.", "All eigenvalues are real.•", "Any eigenvalue λ satisfies − D ≤ λ ≤ D where · is the operator norm.If the operator D has a finite set of n eigenvalues its largest d eigenvalues exist when d is smaller than n.If D has a infinite but countable set of eigenvalues we first characterize what the eigenvalues look like: DISPLAYFORM0 Recall that the operator norm is defined as DISPLAYFORM1 Define q u be the probability measure such that DISPLAYFORM2 and DISPLAYFORM3 which hold for any f ∈ H. Hence D ≤ 1.So the absolute values of the eigenvalues of D can be written as a non-increasing sequence which converges to 0 with the largest eigenvalue to be 1. If", "d is smaller than the number of positive eigenvalues of D then the largest d eigenvalues are guaranteed to exist. Note", "that this condition for d is stricter than the condition when D has finitely many eigenvalues. We conjecture", "that this restriction is due to an artifact of the analysis and in practice using any value of d would be valid when H has infinite dimensions." ]

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[ "We propose a scalable method to approximate the eigenvectors of the Laplacian in the reinforcement learning context and we show that the learned representations can improve the performance of an RL agent." ]

[ "Our work offers a new method for domain translation from semantic label maps\n", "and Computer Graphic (CG) simulation edge map images to photo-realistic im-\n", "ages.", "We train a Generative Adversarial Network (GAN) in a conditional way to\n", "generate a photo-realistic version of a given CG scene.", "Existing architectures of\n", "GANs still lack the photo-realism capabilities needed to train DNNs for computer\n", "vision tasks, we address this issue by embedding edge maps, and training it in an\n", "adversarial mode.", "We also offer an extension to our model that uses our GAN\n", "architecture to create visually appealing and temporally coherent videos.", "The topic of image to image translation and more generally video to video translation is of major importance for training autonomous systems.", "It is beneficial to train an autonomous agent in real environments, but not practical, since enough data cannot be gathered Collins et al. (2018) .", "However, using simulated scenes for training might lack details since a synthetic image will not be photorealistic and will lack the variability and randomness of real images, causing training to succeed up to a certain point.", "This gap is also referred to as the reality gap Collins et al. (2018) .", "By combining a non photo-realistic, simulated model with an available dataset, we can generate diverse scenes containing numerous types of objects, lightning conditions, colorization etc.", "Chen & Koltun (2017) .", "In this paper, we depict a new approach to generate images from a semantic label map and a flexible Deep Convolution Neural Network (DCNN) we called Deep Neural Edge Detector (DNED) which embed edge maps.", "we combine embedded edge maps which act as a skeleton with a semantic map as input to our model (fig 2. 1), The model outputs a photo-realistic version of that scene.", "Using the skeleton by itself will generate images that lack variability as it restricts the representation to that specific skeleton itself.", "Instead, we learn to represent skeletons by a neural network and at test time, we sample the closest appropriate skeleton the network has seen at training.", "Moreover, we have extended this idea to generate photo-realistic videos (i.e. sequence of images) with a novel loss that uses the optical flow algorithm for pixel coherency between consecutive images.", "Figure 1: in this paper we propose a method for generating photo-realistic images from semantic labels of a simulator scene.", "This figure provides images related to the Synthia dataset Ros et al. (2016) .", "Left -semantic map of the scene.", "Middle -generated image from pix2pixHD Wang et al. (2018b) .", "Right -Our generated image.", "The texture and color space in our generated image is more natural giving the image the desired photo-realism.", "used as a super resolution generator.", "L1 loss for image generation is known to generate low quality images as the generated images are blurred and lack details Dosovitskiy & Brox (2016) .", "Instead, Gatys et al. (2016) , Johnson et al. (2016) are using a modified version of the perceptual loss, allowing generation of finer details in an image.", "Pix2pixHD Wang et al. (2018b) and CRN Chen & Koltun (2017) are using a perceptual loss as well for training their networks, e.g. VGGnet Simonyan & Zisserman (2014) .", "Moreover, pix2pixHD are using instance maps as well as label maps to enable the generator to separate several objects of the same semantics.", "This is of high importance when synthesizing images having many instances of the same semantics in a single frame.", "As for video generation the loss used by Wang et al. (2018a) , Shahar et al. (2011) tend to be computationally expensive while our approach is simpler.", "We are using two generators of the same architecture, and they are mutually trained using our new optical flow based loss that is fed by dense optical flow estimation.", "Our evaluation method is FID Heusel et al. (2017) and FVD Unterthiner et al. (2018) as it is a common metric being used for image and video generation schemes.", "We call this work s-Flow GAN since we embed Spatial information obtained from dense optical flow in a neural network as a prior for image generation and flow maps for video coherency.", "This optical flow is available since the simulated image is accessible at test time in the case of CG2real scheme.", "We make Three major contributions: First, our model can generate visually appealing photorealistic images from semantic maps having high definition details.", "Second, we incorporate a neural network to embed edge maps, thus allowing generation of diverse versions of the same scenes.", "Third, we offer a new loss function for generating natural looking videos using the above mentioned image generation scheme.", "please refer to this link for videos and comparison to related work." ]

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[ "Simulation to real images translation and video generation" ]

[ "Deep neural networks are widely used in various domains, but the prohibitive computational complexity prevents their deployment on mobile devices.", "Numerous model compression algorithms have been proposed, however, it is often difficult and time-consuming to choose proper hyper-parameters to obtain an efficient compressed model.", "In this paper, we propose an automated framework for model compression and acceleration, namely PocketFlow.", "This is an easy-to-use toolkit that integrates a series of model compression algorithms and embeds a hyper-parameter optimization module to automatically search for the optimal combination of hyper-parameters.", "Furthermore, the compressed model can be converted into the TensorFlow Lite format and easily deployed on mobile devices to speed-up the inference.", "PocketFlow is now open-source and publicly available at https://github.com/Tencent/PocketFlow.", "Deep learning has been widely used in various areas, such as computer vision, speech recognition, and natural language translation.", "However, deep learning models are often computational expensive, which limits further applications on mobile devices with limited computational resources.To address this dilemma between accuracy and computational complexity, numerous algorithms have been proposed to compress and accelerate deep networks with minimal performance degradation.", "Commonly-used approaches include low-rank decomposition BID15 BID14 , channel pruning (a.k.a. structured pruning) BID6 BID17 , weight sparsification (a.k.a. non-structured pruning) BID16 , and weight quantization BID1 BID2 .", "However, these algorithms usually involve several hyper-parameters that may have a large impact on the compressed model's performance.", "It can be quite difficult to efficiently choose proper hyper-parameter combinations for different models and learning tasks.", "Recently, some researches adopted reinforcement learning methods to automatically determine hyperparameters for channel pruning BID4 and weight sparsification BID5 algorithms.In this paper, we present an automated framework for compressing and accelerating deep neural networks, namely PocketFlow.", "We aim at providing an easy-to-use toolkit for developers to improve the inference efficiency with little or no performance degradation.", "PocketFlow has inte-grated a series of model compression algorithms, including structured/non-structured pruning and uniform/non-uniform quantization.", "A hyper-parameter optimizer is incorporated to automatically determine hyper-parameters for model compression components.", "After iteratively training candidate compressed models and adjusting hyper-parameters, a final compressed model is obtained to maximally satisfy user's requirements on compression and/or acceleration ratios.", "The resulting model can be exported as a TensorFlow-Lite file for efficient deployment on mobile devices.", "In this paper, we present the PocketFlow framework to boost the deployment of deep learning models on mobile devices.", "Various model compression algorithms are integrated and hyper-parameter optimizers are introduced into the training process to automatically generate highly-accurate compressed models with minimal human effort." ]

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[ "We propose PocketFlow, an automated framework for model compression and acceleration, to facilitate deep learning models' deployment on mobile devices." ]

[ "Generative models provide a way to model structure in complex distributions and have been shown to be useful for many tasks of practical interest.", "However, current techniques for training generative models require access to fully-observed samples.", "In many settings, it is expensive or even impossible to obtain fully-observed samples, but economical to obtain partial, noisy observations.", "We consider the task of learning an implicit generative model given only lossy measurements of samples from the distribution of interest.", "We show that the true underlying distribution can be provably recovered even in the presence of per-sample information loss for a class of measurement models.", "Based on this, we propose a new method of training Generative Adversarial Networks (GANs) which we call AmbientGAN.", "On three benchmark datasets, and for various measurement models, we demonstrate substantial qualitative and quantitative improvements.", "Generative models trained with our method can obtain $2$-$4$x higher inception scores than the baselines." ]

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[ "How to learn GANs from noisy, distorted, partial observations" ]

[ "Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. ", "Empirical and theoretical results clearly indicate that the empirical spectral density (ESD) of DNN layer matrices displays signatures of traditionally-regularized statistical models, even in the absence of exogenously specifying traditional forms of regularization, such as Dropout or Weight Norm constraints. ", "Building on recent results in RMT, most notably its extension to Universality classes of Heavy-Tailed matrices, we develop a theory to identify 5+1 Phases of Training, corresponding to increasing amounts of Implicit Self-Regularization. ", "For smaller and/or older DNNs, this Implicit Self-Regularization is like traditional Tikhonov regularization, in that there is a \"size scale\" separating signal from noise. ", "For state-of-the-art DNNs, however, we identify a novel form of Heavy-Tailed Self-Regularization, similar to the self-organization seen in the statistical physics of disordered systems. ", "This implicit Self-Regularization can depend strongly on the many knobs of the training process. ", "By exploiting the generalization gap phenomena, we demonstrate that we can cause a small model to exhibit all 5+1 phases of training simply by changing the batch size.", "The inability of optimization and learning theory to explain and predict the properties of NNs is not a new phenomenon.", "From the earliest days of DNNs, it was suspected that VC theory did not apply to these systems (1) .", "It was originally assumed that local minima in the energy/loss surface were responsible for the inability of VC theory to describe NNs (1) , and that the mechanism for this was that getting trapped in local minima during training limited the number of possible functions realizable by the network.", "However, it was very soon realized that the presence of local minima in the energy function was not a problem in practice (2; 3).", "Thus, another reason for the inapplicability of VC theory was needed.", "At the time, there did exist other theories of generalization based on statistical mechanics (4; 5; 6; 7), but for various technical and nontechnical reasons these fell out of favor in the ML/NN communities.", "Instead, VC theory and related techniques continued to remain popular, in spite of their obvious problems.More recently, theoretical results of Choromanska et al. (8) (which are related to (4; 5; 6; 7)) suggested that the Energy/optimization Landscape of modern DNNs resembles the Energy Landscape of a zero-temperature Gaussian Spin Glass; and empirical results of Zhang et al. (9) have again pointed out that VC theory does not describe the properties of DNNs.", "Martin and Mahoney then suggested that the Spin Glass analogy may be useful to understand severe overtraining versus the inability to overtrain in modern DNNs (10) .We", "should note that it is not even clear how to define DNN regularization. The", "challenge in applying these well-known ideas to DNNs is that DNNs have many adjustable \"knobs and switches,\" independent of the Energy Landscape itself, most of which can affect training accuracy, in addition to many model parameters. Indeed", ", nearly anything that improves generalization is called regularization (11) . Evaluating", "and comparing these methods is challenging, in part since there are so many, and in part since they are often constrained by systems or other not-traditionally-ML considerations.Motivated by this situation, we are interested here in two related questions.• Theoretical", "Question. Why is regularization", "in deep learning seemingly quite different than regularization in other areas on ML; and what is the right theoretical framework with which to investigate regularization for DNNs? • Practical Question.", "How can one control and", "adjust, in a theoretically-principled way, the many knobs and switches that exist in modern DNN systems, e.g., to train these models efficiently and effectively, to monitor their effects on the global Energy Landscape, etc.? That is, we seek a Practical", "Theory of Deep Learning, one that is prescriptive and not just descriptive. This theory would provide useful", "tools for practitioners wanting to know How to characterize and control the Energy Landscape to engineer larger and betters DNNs; and it would also provide theoretical answers to broad open questions as Why Deep Learning even works. Main Empirical Results. Our main", "empirical results consist", "in evaluating empirically the ESDs (and related RMT-based statistics) for weight matrices for a suite of DNN models, thereby probing the Energy Landscapes of these DNNs. For older and/or smaller models, these", "results are consistent with implicit Self-Regularization that is Tikhonov-like; and for modern state-of-the-art models, these results suggest novel forms of Heavy-Tailed Self-Regularization.• Self-Regularization in old/small models", ". The ESDs of older/smaller DNN models (like", "LeNet5 and a toy MLP3 model) exhibit weak Self-Regularization, well-modeled by a perturbative variant of MP theory, the Spiked-Covariance model. Here, a small number of eigenvalues pull out", "from the random bulk, and thus the MP Soft Rank and Stable Rank both decrease. This weak form of Self-Regularization is like", "Tikhonov regularization, in that there is a \"size scale\" that cleanly separates \"signal\" from \"noise,\" but it is different than explicit Tikhonov regularization in that it arises implicitly due to the DNN training process itself.• Heavy-Tailed Self-Regularization. The ESDs of", "larger, modern DNN models (including", "AlexNet and Inception and nearly every other large-scale model we have examined) deviate strongly from the common Gaussian-based MP model. Instead, they appear to lie in one of the very different", "Universality classes of Heavy-Tailed random matrix models. We call this HeavyTailed Self-Regularization. The ESD appears", "Heavy-Tailed, but with finite support. In this", "case, there is not a \"size scale\" (even in the theory)", "that cleanly separates \"signal\" from \"noise.\" Main Theoretical Results. Our main theoretical results consist", "in an operational theory", "for DNN Self-Regularization. Our theory uses ideas from RMT-both vanilla MP-based RMT as well", "as extensions to other Universality classes based on Heavy-Tailed distributions-to provide a visual taxonomy for 5 + 1 Phases of Training, corresponding to increasing amounts of Self-Regularization.• Modeling Noise and Signal. We assume that a weight matrix W can", "be modeled as W W rand + ∆ sig", ", where W rand is \"noise\" and where ∆ sig is \"signal.\" For small to medium sized signal, W is well-approximated by an MP distribution-with", "elements drawn from the Gaussian Universality class-perhaps after removing a few eigenvectors. For large and strongly-correlated signal, W rand gets progressively smaller, but we", "can model the non-random strongly-correlated signal ∆ sig by a Heavy-Tailed random matrix, i.e., a random matrix with elements drawn from a Heavy-Tailed (rather than Gaussian) Universality class.• 5+1 Phases of Regularization. Based on this, we construct a practical, visual taxonomy", "for 5+1 Phases of Training. Each", "phase is characterized by stronger, visually distinct signatures in the ESD of DNN weight", "matrices, and successive phases correspond to decreasing MP Soft Rank and increasing amounts of Self-Regularization. The 5+1 phases are: RANDOM-LIKE, BLEEDING-OUT, BULK+SPIKES, BULK-DECAY, HEAVY-TAILED, and RANK-COLLAPSE", ". Based on these results, we speculate that all well optimized, large DNNs will display Heavy-Tailed Self-Regularization", "in their weight matrices. Evaluating the Theory. We provide a detailed evaluation of our theory using a smaller MiniAlexNew model that we can train", "and retrain.• Effect of", "Explicit Regularization. We analyze ESDs of MiniAlexNet by removing all explicit regularization (Dropout, Weight", "Norm constraints, Batch Normalization", ", etc.) and characterizing how the ESD of weight matrices behave during and at the end of Backprop training, as we systematically add back in different forms of explicit regularization.• Exhibiting the 5+1 Phases. We demonstrate that we can exhibit all 5+1 phases by appropriate modification of the various knobs", "of the training process. In", "particular, by decreasing the batch size from 500 to 2, we can make the ESDs of the fully-connected layers of MiniAlexNet vary", "continuously from RANDOM-LIKE to HEAVY-TAILED, while increasing generalization accuracy along the way. These results illustrate the Generalization Gap pheneomena (12; 13; 14) , and they explain that pheneomena as being caused by the", "implicit Self-Regularization associated with models trained with smaller and smaller batch sizes.", "Clearly, our theory opens the door to address numerous very practical questions.", "One of the most obvious is whether our RMT-based theory is applicable to other types of layers such as convolutional layers.", "Initial results suggest yes, but the situation is more complex than the relatively simple picture we have described here.", "These and related directions are promising avenues to explore.", "This results from correlations arising at all size scales, which for DNNs arises implicitly due to the training process itself.", "This implicit Self-Regularization can depend strongly on the many knobs of the training process.", "In particular, by exploiting the generalization gap phenomena, we demonstrate that we can cause a small model to exhibit all 5+1 phases of training simply by changing the batch size.", "This demonstrates that-all else being equal-DNN optimization with larger batch sizes leads to less-well implicitly-regularized models, and it provides an explanation for the generalization gap phenomena.", "Our results suggest that large, welltrained DNN architectures should exhibit Heavy-Tailed Self-Regularization, and we discuss the theoretical and practical implications of this.", "Very large very deep neural networks (DNNs) have received attention as a general purpose tool for solving problems in machine learning (ML) and artificial intelligence (AI), and they perform remarkably well on a wide range of traditionally hard if not impossible problems, such as speech recognition, computer vision, and natural language processing.", "The conventional wisdom seems to be \"the bigger the better,\" \"the deeper the better,\" and \"the more hyper-parameters the better.\"", "Unfortunately, this usual modus operandi leads to large, complicated models that are extremely hard to train, that are extremely sensitive to the parameters settings, and that are extremely difficult to understand, reason about, and interpret.", "Relatedly, these models seem to violate what one would expect from the large body of theoretical work that is currently popular in ML, optimization, statistics, and related areas.", "This leads to theoretical results that fail to provide guidance to practice as well as to confusing and conflicting interpretations of empirical results.", "For example, current optimization theory fails to explain phenomena like the so-called Generalization Gap-the curious observation that DNNs generalize better when trained with smaller batches sizes-and it often does not provide even qualitative guidance as to how stochastic algorithms perform on non-convex landscapes of interest; and current statistical learning theory, e.g., VC-based methods, fails to provide even qualitative guidance as to the behavior of this class of learning methods that seems to have next to unlimited capacity and yet generalize without overtraining.", "There is a large body of related work, much of which either informed our approach or should be informed by our results.", "This includes: work on large-batch learning and the generalization gap BID195 BID119 BID111 BID104 BID114 BID178 BID113 BID193 BID141 BID198 BID199 ; work on Energy Landscape approaches to NN training BID117 BID196 44, BID170 30, 29, 27, BID112 47, 12, BID151 BID197 BID97 BID130 BID129 BID142 ; work on using weight matrices or properties of weight matrices [15, BID149 BID150 4, 14, BID200 BID148 3, BID133 BID145 ; work on different Heavy-Tailed Universality classes [46, 32, 18, 25, 20, 5, BID158 7, 38, 17, BID137 8, BID146 ; other work on RMT approaches BID180 BID167 BID161 BID159 BID134 BID134 BID184 BID132 BID173 ; other work on statistical physics approaches BID179 BID99 BID164 BID172 BID184 BID166 BID160 ; work on fitting to noisy versus reliable signal BID183 BID203 BID122 BID169 6] ; and several other related lines of work BID110 BID143 BID163 34, 1, BID153 BID154 BID144 BID131 .", "We conclude by discussing several aspects of our results in this broader context." ]

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[ "See the abstract. (For the revision, the paper is identical, except for a 59 page Supplementary Material, which can serve as a stand-along technical report version of the paper.)" ]

[ "We introduce an attention mechanism to improve feature extraction for deep active learning (AL) in the semi-supervised setting.", "The proposed attention mechanism is based on recent methods to visually explain predictions made by DNNs.", "We apply the proposed explanation-based attention to MNIST and SVHN classification.", "The conducted experiments show accuracy improvements for the original and class-imbalanced datasets with the same number of training examples and faster long-tail convergence compared to uncertainty-based methods.", "Deep active learning (AL) minimizes the number of expensive annotations needed to train DNNs by selecting a subset of relevant data points from a large unlabeled dataset BID7 .", "This subset is annotated and added to the training dataset in a single pool of data points or, more often, in an iterative fashion.", "The goal is to maximize prediction accuracy while minimizing the product of pool size × number of iterations.", "A proxy for this goal could be the task of matching feature distributions between the validation and the AL-selected training datasets.In density-based AL approaches, data selection is typically performed using a simple L 2 -distance metric BID10 .", "The image retrieval field BID17 has advanced much further in this area.", "For example, recent state-of-the-art image retrieval systems are based on DNNbased feature extraction BID0 with attention mechanisms BID8 .", "The latter estimates an attention mask to weight importance of the extracted features and it is trained along with the feature extraction.Inspired by this, we employ image retrieval techniques and propose a novel attention mechanism for deep AL.", "Unlike supervised self-attention in BID8 BID14 , our attention mechanism is not trained with the model.", "It relies on recent methods to generate visual explanations and to attribute feature importance values BID13 .", "We show the effectiveness of such explanation-based attention (EBA) mechanism for AL when combined with multi-scale feature extraction on a number of image classification datasets.", "We also conduct experiments for distorted class-imbalanced training data which is a more realistic assumption for unlabeled data.", "We applied recent image retrieval feature-extraction techniques to deep AL and introduced a novel EBA mechanism to improve feature-similarity matching.", "First feasibility experiments on MNIST and SVHN datasets showed advantages of EBA to improve density-based AL.", "Rather than performing AL for the well-picked training datasets, we also considered more realistic and challenging scenarios with class-imbalanced training collections where the proposed method emphasized the importance of additional feature supervision.", "In future research, EBA could be evaluated with other types of data distortions and biases: within-class bias, adversarial examples, etc.", "Furthermore, such applications as object detection and image segmentation may benefit more from EBA because multiscale attention can focus on spatially-important features." ]

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[ "We introduce an attention mechanism to improve feature extraction for deep active learning (AL) in the semi-supervised setting." ]

[ "We apply canonical forms of gradient complexes (barcodes) to explore neural networks loss surfaces.", "We present an algorithm for calculations of the objective function's barcodes of minima. ", "Our experiments confirm two principal observations: (1) the barcodes of minima are located in a small lower part of the range of values of objective function and (2) increase of the neural network's depth brings down the minima's barcodes.", "This has natural implications for the neural network learning and the ability to generalize.", "The learning via finding minima of objective functions is the principal strategy underlying majority of learning algorithms.", "For example, in Neural Network training, the objective function's input is model parameters (weights) and the objective function's output is the loss on training dataset.", "The graph of the loss function, often called loss surface, typically has complex structure (e.g. see loss surface visualisations by Li et al. (2018) ): non-convexity, many local minima, flat regions, steep slopes.", "These obstacles harm exploration of the loss surface and complicate searching for optimal network weights.", "The optimization of modern neural networks is based on the gradient descent algorithm.", "The global topological characteristics of the gradient vector field trajectories are captured by the Morse complex via decomposing the parameter space into cells of uniform flow, see Barannikov (1994) ; Le Roux et al. (2018) and references therein.", "The invariants of Morse complex called \"canonical forms\"(or barcodes) constitute the fundamental summary of the topology of the gradient vector field flow.", "The \"canonical forms\", or barcodes, in this context are decompositions of the change of topology of the sublevel sets of objective function into simple \"birth-death\" phenomena of topological feautures of different dimensions.", "The calculation of the barcodes for different functions constitutes the essence of the topological data analysis.", "The currently available software packages for the calculation of barcodes of functions, also called \"sublevel persistence\", are GUDHI, Dionysus, PHAT, and TDA package which incorporates all three previous packages B.T. Fasy et al. (2014) .", "They are based on the algorithm, described in Barannikov (1994) , see also appendix and e.g. Bauer et al. (2014) and references therein.", "This algorithm which has complexity of O(n 3 ).", "These packages can currently handle calculations of barcodes for functions defined on a grid of up to 10 6 points, and in dimensions two and three.", "Thus all current packages have the scalability issues.", "We describe a new algorithm for computations of the barcodes of functions in lowest degree.", "Our algorithm works with functions defined on randomly sampled or specifically chosen point clouds.", "Point cloud based methods are known to work better than grid based methods in optimization related problems (Bergstra and Bengio (2012) ).", "We also use the fact that the definition of the barcode of lowest degree can be reformulated in geometrical terms (see definition 1 in section 2).", "The previously known algorithms were based on the more algebraic approach as in definition 3.", "Our algorithm has complexity of O(n log(n)).", "It was tested in dimensions up to 16 and with number of points of up to 10 8 .", "In this work, we develop a methodology to describe the properties of the loss surface of the neural network via topological features of local minima.", "We emphasize that the value of the objective function at the minimum can be viewed as only a part of its topological characteristic from the \"canonical form\" (barcode).", "The second half can be described as the value of objective function at the index-one saddle, which can be naturally associated with each local minimum.", "The difference between the values of objective function at the associated index-one saddle and at the local minimum is a topological invariant of the minimum.", "For optimization algorithms this quantity measures, in particular, the obligatory penalty for moving from the given local minimum to a lower minimum.", "The main contributions of the paper are as follows:", "Applying the one-to-one correspondence between local minima and 1-saddles to exploration of loss surfaces.", "For each local minimum p there is canonically defined 1-saddle q (see Section 2).", "The 1-saddle associated with p can be described as follows.", "The 1-saddle q is precisely the point where the connected component of the sublevel set Θ f ≤c = {θ ∈ Θ | f (θ) ≤ c} containing the minimum p merges with another connected component of the sublevel set whose minimum is lower.", "This correspondence between the local minima and the 1-saddles, killing a connected component of Θ f ≤c , is one-to-one.", "The segment [f", "(p), f", "(q)] is then the \"canonical form\" invariant attached to the minimum p.", "The set of all such segments is the barcode (\"canonical form\") of minima invariant of f .", "It is a robust topological invariant of objective function.", "It is invariant in particular under the action of homeomorphisms of Θ.", "Full \"canonical form\" invariants give a concise summary of the topology of objective function and of the global structure of its gradient flow.", "Algorithm for calculations of the barcodes (canonical invariants) of minima.", "We describe an algorithm for calculation of the canonical invariants of minima.", "The algorithm works with function's values on a a randomly sampled or specifically chosen set of points.", "The local minima give birth to clusters of points in sublevel sets.", "The algorithm works by looking at neighbors of each point with lower value of the function and deciding if this point belongs to the existing clusters, gives birth to a new cluster (minimum), or merges two or more clusters (index one saddle).", "A variant of the algorithm has complexity of O(n log(n)), where n is the cardinality of the set of points.", "Calculations confirming observations on behaviour of neural networks loss functions barcodes.", "We calculate the canonical invariants (barcodes) of minima for small fully-connected neural networks of up to three hidden layers and verify that all segments of minima's barcode belong to a small lower part of the total range of loss function's values and that with the increase in the neural network depth the minima's barcodes descend lower.", "The usefulness of our approach and algorithms is clearly not limited to the optimization problems.", "Our algorithm permits really fast computation of the canonical form invariants (persistence barcodes) of many functions which were not accessible until now.", "These sublevel persistence barcodes have been successfully applied in different discipline, to mention just a few: cognitive science (M.", "K. Chung and Kim (2009) ), cosmology (Sousbie et al. (2011) ), see e.g. Pun et al. (2018) and references therein.", "Our viewpoint should also have applications in chemistry and material science where 1-saddle points on potential energy landscapes correspond to transition states and minima are stable states corresponding to different materials or protein foldings (see e.g. Dellago et al. (2003) , Oganov and Valle (2009) ).", "The article is structured as follows.", "First we describe three definitions of barcodes of minima.", "After that our algorithm for their calculation is described.", "In the last part we give examples of calculations, including the loss functions of simple neural nets.", "In this work we have introduced a methodology for analysing the plots of functions, in particular, loss surfaces of neural networks.", "The methodology is based on computing topological invariants called canonical forms or barcodes.", "To compute barcodes we used a graph-based construction which approximates the function plot.", "Then we apply the algorithm we developed to compute the barcodes of minima on the graph.", "Our experimental results of computing barcodes for small neural networks lead to two principal observations.", "First all barcodes sit in a tiny lower part of the total function's range.", "Secondly, with increase of the depth of neural network the barcodes descend lower.", "From the practical point of view, this means that gradient descent optimization cannot stuck in high local minima, and it is also not difficult to get from one local minimum to another (with smaller value) during learning.", "The method we developed has several further research directions.", "Although we tested the method on small neural networks, it is possible to apply it to large-scale modern neural networks such as convolutional networks (i.e. ResNet, VGG, AlexNet, U-Net, see Alom et al. (2018) ) for imageprocessing based tasks.", "However, in this case the graph-based approximation we use requires wise choice of representative graph vertices, which is a hardcore in high-dimensional spaces (dense filling of area by points is computationally intractable).", "Another direction is to study the connections between the barcode of local minima and the generalization properties of given minimum and of neural network.", "There are clearly also connections, deserving further investigation, between the barcodes of minima and results concerning the rate of convergency during learning of neural networks." ]

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[ "We apply canonical forms of gradient complexes (barcodes) to explore neural networks loss surfaces." ]

[ "\nNew types of compute hardware in development and entering the market hold the promise of revolutionizing deep learning in a manner as profound as GPUs.", "However, existing software frameworks and training algorithms for deep learning have yet to evolve to fully leverage the capability of the new wave of silicon.", "In particular, models that exploit structured input via complex and instance-dependent control flow are difficult to accelerate using existing algorithms and hardware that typically rely on minibatching.", "We present an asynchronous model-parallel (AMP) training algorithm that is specifically motivated by training on networks of interconnected devices.", "Through an implementation on multi-core CPUs, we show that AMP training converges to the same accuracy as conventional synchronous training algorithms in a similar number of epochs, but utilizes the available hardware more efficiently, even for small minibatch sizes, resulting in shorter overall training times.", "Our framework opens the door for scaling up a new class of deep learning models that cannot be efficiently trained today.", "An emerging category of neural networks show the common trait of reacting in dynamic and unique ways to properties of their input.", "Networks like tree-structured recursive neural networks BID35 BID36 and graph neural networks (GNNs) BID31 BID20 BID12 take structured data types as input and and execute a computation that depends on the input structure.", "This defies the moden GPU-driven paradigm of minibatch-based processing, and we refer to this new class of models with dynamic control flow as dynamic neural networks.The development of dynamic neural network frameworks -Chainer BID37 , DyNet BID24 , and PyTorch (PyTorch core team) -speaks to the importance of this class of models and highlights the challenge of how to make it easy for users to describe them.", "Yet there is another big challenge: how can we train these models efficiently?Managing", "minibatches to keep GPUs fully utilized is typically considered a user's responsibility in these dynamic frameworks (with the exception of DyNet's autobatching feature; see Sec. 7). This means", "that users have to think about how to change their data feeding pipeline or even the model itself to run efficiently on GPUs, rather spending time innovating to improve the model accuracy.What if we had a hypothetical device with low memory overhead that allows perfect scaling without batching; i.e., processing 1 item is simply 100x faster than processing 100 items? Recent work", "on FPGAs and other specialized hardware BID10 BID4 BID17 for deep learning encourages us to investigate this question. Our premises", "are 1. No batching", "is required for efficient processing.2. Each device", "may not have enough memory to hold the entire model (this is a realistic constraint for current memory systems that approach the perfect scaling we require)Based on these premises, we propose an asynchronous model-parallel (AMP) training algorithm. Our idea is", "illustrated in FIG0 . We need model", "parallelism because each device may be too small to hold the entire model (premise 2). However, if we", "perform synchronous parameter updates following the full forward and backward propagations, the only way to increase device utilization is by pipelining multiple instances into the system (see e.g., . Pipeline parallelism", "with synchronous updates is at odds with convergence speed due to a decreased parameter update frequency; compare FIG0 (a) and (b).To overcome", "this problem", ", we", "propose asynchronous parameter updates that occur without global synchronization whenever a pre-specified number of gradients have been accumulated; see Fig. 1 (c) . With this design we aim", "for both", "high device utilization and update frequency.In this setting, however, model parameters may be updated between the forward and the backward computation of an instance, introducing gradient \"staleness\". Despite staleness, we show that", "AMP training can converge fast with good hardware utilization. Specifically, our contributions", "are:• We present the asynchronous model parallel training algorithm for efficient distributed training of dynamic networks.• We present an intermediate representation", "(IR) with explicit constructs for branching and joining control flow that supports AMP training. Unlike previous work that considers static", "computation graphs for static control flow (e.g., Caffe), and dynamic computation graphs for dynamic control flow (e.g., Chainer), our IR encodes a static computation graph to execute dynamic control flow 1 . This makes training easy to distribute and", "parallelize.• We show that our IR can readily encode replicas", ", a form of data parallelism (see Sec. 5). In addition, our IR includes operators for data", "aggregation, which recover a form of batching, enabling our methods to be applied even on hardware where batching is beneficial.• We implement AMP training on a multi-core CPU", "and empirically demonstrate that AMP training converges to similar accuracies as synchronous algorithms on a variety of dynamic neural network models including Tree RNN and gated graph neural networks (GGNN).In summary, our work demonstrates the benefits of", "AMP training and gives a novel way to design and deploy neural network libraries with dynamic control flow. In addition, we use our implementation to estimate", "the performance on a hypothetical device satisfying premises 1 & 2, with 1TFLOPS compute capability (see Appendix C). Together, these contributions open up new ways to", "scale up dynamic networks on interconnected compute devices.", "We have presented an asynchronous model-parallel SGD algorithm for distributed neural network training.", "We have described an IR and multi-core CPU runtime for models with irregular and/or instance-dependent control flow.", "Looking forward, we aim to deploy our system on specialized hardware.", "Equally importantly, we plan to build a compiler that automatically deduces the information to be placed in the states and generates state keying functions from a higher-level description of the models.", "By unlocking scalable distributed training of dynamic models, we hope to enable exploration of this class of models that are currently only on the horizon but may become more mainstream in the future.A AMPNET RUNTIME IMPLEMENTATIONWe have implemented an AMPNet runtime for multi-core CPUs.", "Our runtime spawns multiple workers each associated with a hardware thread and hosting one or more IR nodes -in a more general setting each worker corresponds to a compute device.", "To remain faithful to a distributed environment communication is only through message passing.", "Each worker is equipped with a multiple-producer single-consumer queue that can accept messages for any IR node hosted on that worker.The main worker loop periodically offloads messages from the concurrent queue to a worker-local priority queue that assigns higher priority to backward messages.", "Backward prioritization is designed for situations when multiple IR nodes with a dependency on the IR graph end up hosted on the same worker.", "As a consequence, backpropagation can complete faster and new instances can be pumped in by the controller.", "We dequeue the top message and invoke the forward or backward method of the target IR node.", "These methods may update internal IR node state (such as cache the state of the incoming message and wait for more messages) or post new forward or backward messages.How to update the parameters using the gradients is a configuration option that selects amongst a range of optimization algorithms.", "We have implemented runtime configuration options for selecting several well-known schemes such as (momentum-)SGD and Adam BID18 , and for controlling the training hyper-parameters." ]

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[ "Using asynchronous gradient updates to accelerate dynamic neural network training" ]

[ "In cooperative multi-agent reinforcement learning (MARL), how to design a suitable reward signal to accelerate learning and stabilize convergence is a critical problem.", "The global reward signal assigns the same global reward to all agents without distinguishing their contributions, while the local reward signal provides different local rewards to each agent based solely on individual behavior.", "Both of the two reward assignment approaches have some shortcomings: the former might encourage lazy agents, while the latter might produce selfish agents.\n\n", "In this paper, we study reward design problem in cooperative MARL based on packet routing environments.", "Firstly, we show that the above two reward signals are prone to produce suboptimal policies.", "Then, inspired by some observations and considerations, we design some mixed reward signals, which are off-the-shelf to learn better policies.", "Finally, we turn the mixed reward signals into the adaptive counterparts, which achieve best results in our experiments.", "Other reward signals are also discussed in this paper.", "As reward design is a very fundamental problem in RL and especially in MARL, we hope that MARL researchers can rethink the rewards used in their systems.", "In reinforcement learning (RL), the goal of the agent is formalized in terms of a special signal, i.e., reward, coming from the environment.", "The agent tries to maximize the total amount of reward it receives in the long run.", "Formally, we express this idea as the Reward Hypothesis BID31 : the goal of RL agent can be exactly described as the maximization of the expected value of the cumulative sum of a received scalar reward signal.It is thus critical that the rewards truly indicate what we want to accomplish.", "One reward design principle is that the rewards must reflect what the goal is, instead of how to achieve the goal 1 .", "For example, in AlphaGo , the agent is only rewarded for actually winning.", "If we also reward the agent for achieving subgoals such as taking its opponent's pieces, the agent might find a way to achieve them even at the cost of losing the game.", "A similar example of faulty reward function is provided by BID26 : if we reward the action of cleaning up dirt, the optimal policy causes the robot to repeatedly dump and clean up the same dirt.", "In fact, the how reward encodes human experience, which is heuristic in some extent.", "Based on the heuristic how reward, it is really easy to deviate from the ultimate goal.However, as BID35 point out, the exact what reward that encodes the performance objective might be awful to use as a training objective.", "It will result in slow and unstable learning occasionally.", "At the same time, a training objective that differs from the performance objective can still do well with respect to it.", "For example, the Intrinsically Motivated Reinforcement Learning (IMRL) BID6 BID27 ) combines a domain-specific intrinsic reward with the reward coming from the environment to improve learning especially in sparse-reward domains.Although reward design problem in single-agent RL is relatively tractable, it becomes more thorny in multi-agent reinforcement learning (MARL), as MARL is naturally more complex than singleagent RL.", "As we know, the global reward and local reward have long been proved to be defective: the former might encourage lazy agents, while the latter might produce selfish agents.Inspired by the success of intrinsic reward in single-agent RL, we hypothesize that similar methods may be useful in MARL too.", "Naturally, in this paper, we ask and try to answer a question:Can we formulate some special rewards (such as intrinsic reward) based on the meta what rewards to accelerate learning and stabilize convergence of MARL systems?", "Specifically, in this paper, we propose several new MARL environments modified from the well known Packet Routing Domain.", "In those environments, the goal is to figure out some good flow splitting policies for all routers (i.e., agents) to minimize the maximum link utilization ratio in the whole network.", "We set the meta reward signals as 1 -max(U l ).", "We argue that the meta reward signals are some kinds of what rewards because they tell the agents that we want to minimize max(U l ), i.e., minimize the maximum of all link utilization ratios.", "For detailed discussions, we refer the readers to the proposed environments and rewards in Section 3 and 4.Based on those environments and the meta what rewards, we can focus on our reward design research purpose.", "Specifically, we firstly show that both of the widely adopted global and local reward signals are prone to produce suboptimal policies.", "Then, inspired by some observations and considerations, we design some mixed reward signals, which are off-the-shelf to learn better policies.", "Finally, we turn the mixed reward signals into the adaptive counterparts, which achieve best results in our experiments.", "Besides, we also discuss other reward signals in this paper.In summary, our contributions are two-fold.", "(1) We propose some new MARL environments to advance the study of MARL.", "As many applications in the real world can be modeled using similar methods, we expect that other fields can also benefit from this work.", "(2) We propose and evaluate several reward signals in these MARL environments.", "Our studies generalize the following thesis BID6 BID35 in single-agent RL to MARL: agents can learn better policies even when the training objective differs from the performance objective.", "This remind us to be careful to design the rewards, as they are really important to guide the agent behavior.The rest of this paper is organized as follows.", "Section 2 introduces background briefly, followed by the proposed environments and rewards in Section 3 and 4, respectively.", "We then present the experiments and discussions in Section 5 and 6, respectively.", "Section 7 concludes this work.", "Why the convergence rate of Complex Topology is low?", "In this paper, we only focus on designing special reward signals, rather than applying other sophisticated technologies, to solve the packet routing problem.", "In fact, the convergence rate can be improved to almost 100% for all topologies if we combine the proposed rewards with other methods.", "To make this paper easy to read, we do not introduce irrelevant methods.Can the proposed rewards generalize successfully in other environments?", "In fact, not all environments can directly calculate the local reward or global reward, as BID24 point out.", "In such environments, the proposed rewards might be only useful at high computation cost.", "However, the calculation of the rewards is not the research purpose of this paper.", "We argue that although the proposed rewards have limitations, they can be easily applied to many real-world applications such as internet packet routing and traffic flow allocation, as mentioned in Section 3.Can the designed rewards be seen as a kind of auxiliary task?", "Yes, they are some auxiliary reward signals indeed.", "But please note that the auxiliary reward signals are different from the auxiliary task used in UNREAL BID15 , where the auxiliary task is used for improving the feature extraction ability of neural networks, while our auxiliary reward signals directly guide the learned policies.", "In fact, the mixed rewards are similar with VIME (Houthooft et al., 2016) as analyzed in Section 2.1.", "And the adaptive rewards are similar with curriculum learning BID38 , as both of them train the agents progressively from easy to the final difficult environment.", "In this paper, we study reward design problem in cooperative MARL based on packet routing environments.", "Firstly, we show that both of the widely adopted global and local reward signals are prone to produce suboptimal policies.", "Then, inspired by some observations and considerations, we design some mixed reward signals, which are off-the-shelf to learn better policies.", "Finally, we turn the mixed reward signals into the adaptive counterparts, which achieve best results in our experiments.Our study generalizes the following thesis BID6 BID35 in singleagent RL to MARL: the training objective that differs from the performance objective can still do well with respect to it.", "As reward design is a very fundamental problem in RL and especially in MARL, we hope that MARL researchers can rethink the rewards used in their systems.For future work, we would like to use Evolutionary Algorithm BID11 to search the best weight of local reward, and verify whether the learned weight has the same decay property.", "We also expect to test the proposed reward signals in other application domains.", "Real flow trajectories from the American Abilene Network are shown in FIG5 .", "Note that we normalize the flow demands so that they can be consistent with link capacities.To test the learned policies, we randomly change the flow demands of each IE-pair." ]

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[ "We study reward design problem in cooperative MARL based on packet routing environments. The experimental results remind us to be careful to design the rewards, as they are really important to guide the agent behavior." ]

[ "Recent advances have illustrated that it is often possible to learn to solve linear inverse problems in imaging using training data that can outperform more traditional regularized least squares solutions.", "Along these lines, we present some extensions of the Neumann network, a recently introduced end-to-end learned architecture inspired by a truncated Neumann series expansion of the solution map to a regularized least squares problem.", "Here we summarize the Neumann network approach, and show that it has a form compatible with the optimal reconstruction function for a given inverse problem.", "We also investigate an extension of the Neumann network that incorporates a more sample efficient patch-based regularization approach.", "This work explores the Neumann network architecture to solve linear inverse problems, which can be interpreted as an approximation of the MSE optimal reconstruction according to our Proposition 1.", "The Neumann network architecture also permits a learned patchwise regularizer, which learns the low-dimensional conditional distributions over image patches instead of the whole image.", "The Neumann network is empirically competitive with other state-of-the-art methods for inverse problems in imaging, and we demonstrate the ability to learn to regularize from a single training pair." ]

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true

[ "Neumann networks are an end-to-end, sample-efficient learning approach to solving linear inverse problems in imaging that are compatible with the MSE optimal approach and admit an extension to patch-based learning." ]

[ "End-to-end task-oriented dialogue is challenging since knowledge bases are usually large, dynamic and hard to incorporate into a learning framework.", "We propose the global-to-local memory pointer (GLMP) networks to address this issue.", "In our model, a global memory encoder and a local memory decoder are proposed to share external knowledge.", "The encoder encodes dialogue history, modifies global contextual representation, and generates a global memory pointer.", "The decoder first generates a sketch response with unfilled slots.", "Next, it passes the global memory pointer to filter the external knowledge for relevant information, then instantiates the slots via the local memory pointers.", "We empirically show that our model can improve copy accuracy and mitigate the common out-of-vocabulary problem.", "As a result, GLMP is able to improve over the previous state-of-the-art models in both simulated bAbI Dialogue dataset and human-human Stanford Multi-domain Dialogue dataset on automatic and human evaluation.", "Task-oriented dialogue systems aim to achieve specific user goals such as restaurant reservation or navigation inquiry within a limited dialogue turns via natural language.", "Traditional pipeline solutions are composed of natural language understanding, dialogue management and natural language generation BID32 BID28 , where each module is designed separately and expensively.", "In order to reduce human effort and scale up between domains, end-to-end dialogue systems, which input plain text and directly output system responses, have shown promising results based on recurrent neural networks BID10 BID14 and memory networks BID24 .", "These approaches have the advantages that the dialogue states are latent without hand-crafted labels and eliminate the needs to model the dependencies between modules and interpret knowledge bases (KB) manually.However, despite the improvement by modeling KB with memory network BID0 , end-to-end systems usually suffer from effectively incorporating external KB into the system response generation.", "The main reason is that a large, dynamic KB is equal to a noisy input and hard to encode and decode, which makes the generation unstable.", "Different from chit-chat scenario, this problem is especially harmful in task-oriented one, since the information in KB is usually the expected entities in the response.", "For example, in TAB0 the driver will expect to get the correct address to the gas station other than a random place such as a hospital.", "Therefore, pointer networks BID26 or copy mechanism BID8 ) is crucial to successfully generate system responses because directly copying essential words from the input source to the output not only reduces the generation difficulty, but it is also more like a human behavior.", "For example, in TAB0 , when human want to reply others the Valero's address, they will need to \"copy\" the information from the table to their response as well.Therefore, in the paper, we propose the global-to-local memory pointer (GLMP) networks, which is composed of a global memory encoder, a local memory decoder, and a shared external knowledge.", "Unlike existing approaches with copy ability BID9 BID8 , which the only information passed to decoder is the encoder hidden states, our model shares the external knowledge and leverages the encoder and the external knowledge to learn a global memory pointer and global contextual representation.", "Global memory pointer modifies the external knowledge by softly filtering words that are not necessary for copying.", "Afterward, instead of generating system responses directly, the local memory decoder first uses a sketch RNN to obtain sketch responses without slot values but sketch tags, which can be considered as learning a latent dialogue management to generate dialogue action template.", "Then the decoder generates local memory pointers to copy words from external knowledge and instantiate sketch tags.We empirically show that GLMP can achieve superior performance using the combination of global and local memory pointers.", "In simulated out-of-vocabulary (OOV) tasks in the bAbI dialogue dataset BID0 , GLMP achieves 92.0% per-response accuracy and surpasses existing end-to-end approaches by 7.5% in full dialogue.", "In the human-human dialogue dataset , GLMP is able to surpass the previous state of the art on both automatic and human evaluation, which further confirms the effectiveness of our double pointers usage.", "In the work, we present an end-to-end trainable model called global-to-local memory pointer networks for task-oriented dialogues.", "The global memory encoder and the local memory decoder are designed to incorporate the shared external knowledge into the learning framework.", "We empirically show that the global and the local memory pointer are able to effectively produce system responses even in the out-of-vocabulary scenario, and visualize how global memory pointer helps as well.", "As a result, our model achieves state-of-the-art results in both the simulated and the human-human dialogue datasets, and holds potential for extending to other tasks such as question answering and text summarization.", "One of the reviewers suggested us to compare our work to some existing dialogue framework such as PyDial 5 .", "To the best of our knowledge, in the PyDial framework, it requires to have the dialogue acts labels for the NLU module and the belief states labels for the belief tracker module.", "The biggest challenge is we do not have such labels in the SMD and bAbI datasets.", "Moreover, the semi tracker in PyDial is rule-based, which need to re-write rules whenever it encounters a new domain or new datasets.", "Even its dialogue management module could be a learning solution like policy networks, the input of the policy network is still the hand-crafted state features and labels.", "Therefore, without the rules and labels predefined in the NLU and belief tracker modules, PyDial could not learn a good policy network.Truly speaking, based on the data we have (not very big size) and the current state-of-the-art machine learning algorithms and models, we believe that a well and carefully constructed task-oriented dialogue system using PyDial in a known domain using human rules (in NLU and Belief Tracker) with policy networks may outperform the end-to-end systems (more robust).", "However, in this paper, without additional human labels and human rules, we want to explore the potential and the advantage of end-to-end systems.", "Besides easy to train, for multi-domain cases, or even zero-shot domain cases, we believe end-to-end approaches will have better adaptability compared to any rule-based systems.", "Delexicalized Generation: the nearest @poi_type is @poi , @distance away at @address Final Generation: the nearest grocery_store is willows_market , 3_miles away at 409_bollard_st" ]

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[ "GLMP: Global memory encoder (context RNN, global pointer) and local memory decoder (sketch RNN, local pointer) that share external knowledge (MemNN) are proposed to strengthen response generation in task-oriented dialogue." ]

[ "The checkerboard phenomenon is one of the well-known visual artifacts in the computer vision field.", "The origins and solutions of checkerboard artifacts in the pixel space have been studied for a long time, but their effects on the gradient space have rarely been investigated.", "In this paper, we revisit the checkerboard artifacts in the gradient space which turn out to be the weak point of a network architecture.", "We explore image-agnostic property of gradient checkerboard artifacts and propose a simple yet effective defense method by utilizing the artifacts.", "We introduce our defense module, dubbed Artificial Checkerboard Enhancer (ACE), which induces adversarial attacks on designated pixels.", "This enables the model to deflect attacks by shifting only a single pixel in the image with a remarkable defense rate.", "We provide extensive experiments to support the effectiveness of our work for various attack scenarios using state-of-the-art attack methods.", "Furthermore, we show that ACE is even applicable to large-scale datasets including ImageNet dataset and can be easily transferred to various pretrained networks.", "The checkerboard phenomenon is one of the well-known artifacts that arise in various applications such as image super resolution, generation and segmentation BID29 BID27 .", "In general, the checkerboard artifacts indicate an uneven pattern on the output of deep neural networks (DNNs) that occurs during the feed-forward step.", "BID21 have investigated in-depth the origin of the phenomenon that the artifacts come from the uneven overlap of the deconvolution operations (i.e., transposed convolution, ) on pixels.", "Its solutions have been suggested in various studies BID35 BID0 .Interestingly", ", a possible relationship between the checkerboard artifacts and the robustness of neural networks has been noted by BID21 but not has it been seriously investigated. Moreover, while", "the previous works BID16 BID20 BID21 BID8 have concentrated on the artifacts in the pixel space, studies have been rare on the artifacts in the gradient space that occur during the backward pass of the convolution operation.To show that the gradient checkerboard artifacts phenomenon is crucial for investigating the network robustness and is indeed a weak point of a neural network, we focus on analyzing its effects on the gradient space in terms of adversarial attack and defense. By explicitly visualizing", "the gradients, we demonstrate that the phenomenon is inherent in many contemporary network architectures such as ResNet BID12 , which use strided convolutions with uneven overlap. It turns out that the gradient", "checkerboard artifacts substantially influence the shape of the loss surface, and the effect is image-agnostic.Based on the analysis, we propose an Artificial Checkerboard Enhancer module, dubbed ACE. This module further boosts or", "creates the checkerboard artifacts in the target network and manipulates the gradients to be caged in the designated area. Because ACE guides the attacks", "to the intended environment, the defender can easily dodge the attack by shifting a single pixel (Figure 1 ) with a negligible accuracy loss. Moreover, we demonstrate that", "our module is scalable to large-scale datasets such as ImageNet BID6 ) and also transferable to other models in a plug and play fashion without additional fine-tuning of pretrained networks. Therefore, our module is highly", "practical in general scenarios in that we can easily plug any pretrained ACE module into the target architecture.Base Network (e.g. ResNet, VGG) ACE Module", "In this paper, we have investigated the gradient checkerboard artifacts (GCA) which turned out to be a potential threat to the network robustness.", "Based on our observations, we proposed a novel Artificial Checkerboard Enhancer (ACE) which attracts the attack to the pre-specified domain.", "ACE is a module that can be plugged in front of any pretrained model with a negligible performance drop.", "Exploiting its favorable characteristics, we provide a simple yet effective defense method that is even scalable to a large-scale dataset such as ImageNet.", "Our extensive experiments show that the proposed method can deflect various attack scenarios with remarkable defense rates compared with several existing adversarial defense methods." ]

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[ "We propose a novel aritificial checkerboard enhancer (ACE) module which guides attacks to a pre-specified pixel space and successfully defends it with a simple padding operation." ]

[ "Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, and understanding the dynamics of (stochastic) gradient algorithms for solving such formulations has been a grand challenge.", "As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions.", "We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates.", "In particular, our results offer formal evidence that alternating updates converge \"better\" than simultaneous ones.", "Min-max optimization has received significant attention recently due to the popularity of generative adversarial networks (GANs) (Goodfellow et al., 2014) and adversarial training (Madry et al., 2018) , just to name some examples.", "Formally, given a bivariate function f (x, y), we aim to find a saddle point (x * , y * ) such that f (x * , y) ≤ f (x * , y * ) ≤ f (x, y * ), ∀x ∈ R n , ∀y ∈ R n .", "(1.1)", "Since the beginning of game theory, various algorithms have been proposed for finding saddle points (Arrow et al., 1958; Dem'yanov & Pevnyi, 1972; Gol'shtein, 1972; Korpelevich, 1976; Rockafellar, 1976; Bruck, 1977; Lions, 1978; Nemirovski & Yudin, 1983; Freund & Schapire, 1999) .", "Due to its recent resurgence in ML, new algorithms specifically designed for training GANs were proposed (Daskalakis et al., 2018; Kingma & Ba, 2015; Gidel et al., 2019b; Mescheder et al., 2017) .", "However, due to the inherent non-convexity in deep learning formulations, our current understanding of the convergence behaviour of new and classic gradient algorithms is still quite limited, and existing analysis mostly focused on bilinear games or strongly-convex-strongly-concave games (Tseng, 1995; Daskalakis et al., 2018; Gidel et al., 2019b; Liang & Stokes, 2019; Mokhtari et al., 2019b) .", "Nonzero-sum bilinear games, on the other hand, are known to be PPAD-complete (Chen et al., 2009 ) (for finding approximate Nash equilibria, see e.g. Deligkas et al. (2017) ).", "In this work, we study bilinear zero-sum games as a first step towards understanding general min-max optimization, although our results apply to some simple GAN settings (Gidel et al., 2019a) .", "It is well-known that certain gradient algorithms converge linearly on bilinear zero-sum games (Liang & Stokes, 2019; Mokhtari et al., 2019b; Rockafellar, 1976; Korpelevich, 1976) .", "These iterative algorithms usually come with two versions: Jacobi style updates or Gauss-Seidel (GS) style.", "In a Jacobi style, we update the two sets of parameters (i.e., x and y) simultaneously whereas in a GS style we update them alternatingly (i.e., one after the other).", "Thus, Jacobi style updates are naturally amenable to parallelization while GS style updates have to be sequential, although the latter is usually found to converge faster (and more stable).", "In numerical linear algebra, the celebrated Stein-Rosenberg theorem (Stein & Rosenberg, 1948) formally proves that in solving certain linear systems, GS updates converge strictly faster than their Jacobi counterparts, and often with a larger set of convergent instances.", "However, this result does not readily apply to bilinear zero-sum games.", "Our main goal here is to answer the following questions about solving bilinear zero-sum games:", "• When exactly does a gradient-type algorithm converge?", "• What is the optimal convergence rate by tuning the step size or other parameters?", "• Can we prove something similar to the Stein-Rosenberg theorem for Jacobi and GS updates?", "Table 2 : Optimal convergence rates.", "In the second column, β * denotes a specific parameter that depends on σ 1 and σ n (see equation 4.2).", "In the third column, the linear rates are for large κ.", "The optimal parameters for both Jacobi and Gauss-Seidel EG algorithms are the same.", "α denotes the step size (α 1 = α 2 = α), and β 1 and β 2 are hyper-parameters for EG and OGD, as given in §2.", "Algorithm α β 1 β 2 rate exponent Comment", "Jacobi and Gauss-Seidel Jacobi OGD 2β 1 β * β 1 ∼ 1 − 1/(6κ 2 ) β 1 = β 2 = α/2 GS OGD √ 2/σ 1 √ 2σ 1 /(σ Contributions We summarize our main results from §3 and §4 in Table 1 and 2 respectively, with supporting experiments given in §5.", "We use σ 1 and σ n to denote the largest and the smallest singular values of matrix E (see equation 2.1), and κ := σ 1 /σ n denotes the condition number.", "The algorithms will be introduced in §2.", "Note that we generalize gradient-type algorithms but retain the same names.", "Table 1 shows that in most cases that we study, whenever Jacobi updates converge, the corresponding GS updates converge as well (usually with a faster rate), but the converse is not true ( §3).", "This extends the well-known Stein-Rosenberg theorem to bilinear games.", "Furthermore, Table 2 tells us that by generalizing existing gradient algorithms, we can obtain faster convergence rates.", "In this work we focus on the convergence behaviour of gradient-based algorithms for solving bilinear games.", "By drawing a connection to discrete linear dynamical systems ( §2) and using Schur's theorem, we provide necessary and sufficient conditions for a variety of gradient algorithms, for both simultaneous (Jacobi) and alternating (Gauss-Seidel) updates.", "Our results show that Gauss-Seidel updates converge more easily than Jacobi updates.", "Furthermore, we find the optimal exponents of linear convergence for EG and OGD, and provide a numerical method for searching that exponent.", "We performed a number of experiments to validate our theoretical findings and suggest further analysis.", "There are many future directions to explore.", "For example, our preliminary experiments on GANs suggest that similar (local) results might be obtained for more general games.", "Indeed, the local convergence behaviour of min-max nonlinear optimization can be studied through analyzing the spectrum of the Jacobian matrix of the update operator (see, e.g., Nagarajan & Kolter (2017); Gidel et al. (2019b) ).", "We believe our framework that draws the connection to linear discrete dynamic systems and Schur's theorem is a powerful machinery that can be applied in such problems and beyond.", "It would be interesting to generalize our results to the constrained case (even for bilinear games), initiated in the recent work of Daskalakis & Panageas (2019) .", "Extending our results to account for stochastic noise (as empirically tested in our experiments) is another interesting direction, with some initial results in Gidel et al. (2019a A PROXIMAL POINT (PP) ALGORITHM PP was originally proposed by Martinet (1970) with α 1 = α 2 and then carefully studied by Rockafellar (1976) .", "The linear convergence for bilinear games was also proved in the same reference.", "Note that we do not consider Gauss-Seidel PP since we do not get a meaningful solution after a shift of steps 2 .", "where x (t+1) and y (t+1) are given implicitly by solving the equations above.", "For bilinear games, one can derive that:", "We can compute the exact form of the inverse matrix, but perhaps an easier way is just to compute the spectrum of the original matrix (the same as Jacobi GD except that we flip the signs of α i ) and perform λ → 1/λ.", "Using the fact that the eigenvalues of a matrix are reciprocals of the eigenvalues of its inverse, the characteristic equation is:", "With the scaling symmetry (α 1 , α 2 ) → (tα 1 , α 2 /t), we can take α 1 = α 2 = α > 0.", "With the notations in Corollary 2.1, we have a = −2/(1 + α 2 σ 2 ) and b = 1/(1 + α 2 σ 2 ), and it is easy to check |a| < 1 + b and b < 1 are always satisfied, which means linear convergence is always guaranteed.", "Hence, we have the following theorem: Theorem A.1.", "For bilinear games, the proximal point algorithm always converges linearly.", "Although the proximal point algorithm behaves well, it is rarely used in practice since it is an implicit method, i.e., one needs to solve (x (t+1) , y In this section we apply Theorem 2.1 to prove Theorem 2.3, an interesting connection between Jacobi and Gauss-Seidel updates:", "and L i is strictly lower block triangular.", "Then, the characteristic polynomial of Jacobi updates is p(λ, 1) while that of Gauss-Seidel updates is p(λ, λ).", "Let us first consider the block linear iterative process in the sense of Jacobi (i.e., all blocks are updated simultaneously):", ". . .", ". . .", "where A i,j is the j-th column block of A i .", "For each matrix A i , we decompose it into the sum", "where L i is the strictly lower block triangular part and U i is the upper (including diagonal) block triangular part.", "Theorem 2.1 indicates that the convergence behaviour of equation B.1 is governed by the largest modulus of the roots of the characteristic polynomial:", "Alternatively, we can also consider the updates in the sense of Gauss-Seidel (i.e., blocks are updated sequentially):", "We can rewrite the Gauss-Seidel update elegantly 3 as:", "i.e.,", "where L k+1 := 0.", "Applying Theorem 2.1 again we know the convergence behaviour of the GaussSeidel update is governed by the largest modulus of roots of the characteristic polynomial:", "Note that A 0 = −I and the factor det(I − L 1 ) −1 can be discarded since multiplying a characteristic polynomial by a non-zero constant factor does not change its roots.", "B.2", "PROOF OF COROLLARY 2.1 Corollary 2.1 (e.g. Mansour (2011)) .", "A real quadratic polynomial λ 2 + aλ + b is Schur stable iff b < 1, |a| < 1 + b; A real cubic polynomial λ 3 + aλ 2 + bλ + c is Schur stable iff |c| < 1,", "Proof.", "It suffices to prove the result for quartic polynomials.", "We write down the matrices:", "We require det(", "2 and thus |c − ad| < 1 − d 2 due to the first condition.", "δ 4 > 0 simplifies to:", "14)", "which yields |a + c| < |b + d + 1|.", "Finally, δ 3 > 0 reduces to:", "Denote p(λ) := λ 4 + aλ 3 + bλ 2 + cλ + d, we must have p(1) > 0 and p(−1) > 0, as otherwise there is a real root λ 0 with |λ 0 | ≥ 1.", "Hence we obtain b + d + 1 > |a + c| > 0.", "Also, from |c − ad| < 1 − d 2 , we know that:", "So, the second factor in B.15 is negative and the positivity of the first factor reduces to:", "To obtain the Schur condition for cubic polynomials, we take d = 0, and the quartic Schur condition becomes:", "To obtain the Schur condition for quadratic polynomials, we take c = 0 in the above and write:", "The proof is now complete." ]

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[ "We systematically analyze the convergence behaviour of popular gradient algorithms for solving bilinear games, with both simultaneous and alternating updates." ]

[ "Most approaches in generalized zero-shot learning rely on cross-modal mapping between an image feature space and a class embedding space or on generating artificial image features.", "However, learning a shared cross-modal embedding by aligning the latent spaces of modality-specific autoencoders is shown to be promising in (generalized) zero-shot learning.", "While following the same direction, we also take artificial feature generation one step further and propose a model where a shared latent space of image features and class embeddings is learned by aligned variational autoencoders, for the purpose of generating latent features to train a softmax classifier.", "We evaluate our learned latent features on conventional benchmark datasets and establish a new state of the art on generalized zero-shot as well as on few-shot learning.", "Moreover, our results on ImageNet with various zero-shot splits show that our latent features generalize well in large-scale settings.", "Generalized zero-shot learning (GZSL) is a classification task where no labeled training examples are available from some of the classes.", "Many approaches learn a mapping between images and their class embeddings BID11 BID19 BID0 .", "For instance, ALE maps CNN features of images to a perclass attribute space.", "An orthogonal approach to GZSL is to augment data by generating artificial image features, such as BID21 who proposed to generate image features via a conditional WGAN.", "As a third approach, BID16 proposed to learn a latent space embedding by transforming both modalities to the latent spaces of autoencoders and match the corresponding distributions by minimizing the Maximum Mean Discrepancy (MMD).", "Learning such cross-modal embeddings can be beneficial for potential downstream tasks that require multimodal fusion.", "In this regard, BID13 recently used a cross-modal autoencoder to extend visual question answering to previously unseen objects.Although recent cross-modal autoencoder architectures represent class prototypes in a latent space BID10 BID16 , better generalization can be achieved if the shared representation space is more amenable to interpolation between different classes.", "Variational Autoencoders (VAEs) are known for their capability in accurate interpolation between representations in their latent space, i.e. as demonstrated for sentence interpolation BID2 and image interpolation BID6 .", "Hence, in this work, we train VAEs to encode and decode features from different modalities, and align their latent spaces by matching the parametrized latent distributions and by enforcing a cross-modal reconstruction criterion.", "Since we learn representations that are oblivious to their origin, a zero-shot visual classifier can be trained using latent space features from semantic data.Our contributions in this work are as follows.", "FORMULA1 Generalized Zero-shot Learning Let S = {(x, y, c(y))|", "x ∈ X, y ∈ Y S , c(y) ∈", "C} be a set of training examples, consisting of image-features x, e.g. extracted by a CNN, class labels y available during training and class-embeddings c(y). Typical", "class-embeddings", "are vectors of continuous attributes or Word2Vec features . In addition, an set U =", "{(u, c(u))| u ∈ Y u , c(u) ∈ C} is used, where u denote unseen classes from a set Y u , which is disjoint from Y S . Here, C(U ) = {c(u 1 ),", "..., c(u L )} is the set of class-embeddings of unseen classes. In the legacy challenge", "of ZSL, the task is to learn a classifier f ZSL : X → Y U . However, in this work,", "we focus on the more realistic and challenging setup of generalized zero-shot learning (GZSL) where the aim is to learn a classifier DISPLAYFORM0 The Objective Function CADA-VAE is trained with pairs of image features and attribute vectors of seen classes. The data of each pair", "has to belong to the same class. In this process, an image", "feature encoder and an attribute encoder learn to transform the training data into the shared latent space. The encoders belong to two", "VAEs with a common latent space. Once the VAEs are trained,", "a softmax classifier is trained on both seen image data and unseen attributes, after they are transformed into the latent representation. As the VAE encoding is non-deterministic", ", many latent features are sampled for each datapoint. Since we only have one attribute vector", "per class, we oversample latent-space encoded features of unseen classes. To test the classifier, the visual test", "data is first transformed into the latent space, using only the predicted means µ of the latent representation. The Objective function for training the", "VAEs is derived as follows. For every modality i (image features, attributes", "), a VAE is trained. The basic VAE loss for a feature x of modality", "i ∈ 1, 2, ..M is: DISPLAYFORM1 where D KL represents the Kullback-Leibler", "Divergence, β is a weight, q(z|x (i) ) = N (µ, Σ) is the VAE encoder consisting of a multilayer perceptron, and p(z) is a Gaussian prior. Additionally, each encoded datapoint is decoded into every available modality, e.g. encoded image features are decoded into attributes and vice versa. Consequently, we minimize the L1 cross-reconstruction loss: DISPLAYFORM2 where γ is a weight. The L1 loss empirically proved to provide slighthly better results than L2. Furthermore, the 2-Wasserstein W distance between the multivariate Gaussian latent distribution of image features and attributes is minimized: DISPLAYFORM3 The VAE is trained using the final objective L = L basic +L CA +L DA . We refer to the Cross-Aligned and Distribution-Aligned VAE as CADA-VAE. In addition, we test the variant L = L basic + L CA , termed CA-VAE, and the variant L = L basic + L DA , referred to as DA-VAE. A latent size of 64 is used for all experiments, except 128 for ImageNet.", "In this work, we propose CADA-VAE, a cross-modal embedding framework for generalized zeroshot learning in which the modality-specific latent distributions are aligned by minimizing their Wasserstein distance and by using cross-reconstruction.", "This procedure leaves us with encoders that can encode features from different modalities into one cross-modal embedding space, in which a linear softmax classifier can be trained.", "We present different variants of cross-aligned and distribution aligned VAEs and establish new state-of-the-art results in generalized zero-shot learning for four medium-scale benchmark datasets as well as the large-scale ImageNet.", "We further show that a cross-modal embedding model for generalized zero-shot learning achieves better performance than data-generating methods, establishing the new state of the art." ]

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[ "We use VAEs to learn a shared latent space embedding between image features and attributes and thereby achieve state-of-the-art results in generalized zero-shot learning." ]

[ "Intuitively, image classification should profit from using spatial information.", "Recent work, however, suggests that this might be overrated in standard CNNs.", "In this paper, we are pushing the envelope and aim to further investigate the reliance on and necessity of spatial information.", "We propose and analyze three methods, namely Shuffle Conv, GAP+FC and 1x1 Conv, that destroy spatial information during both training and testing phases.", "We extensively evaluate these methods on several object recognition datasets (CIFAR100, Small-ImageNet, ImageNet) with a wide range of CNN architectures (VGG16, ResNet50, ResNet152, MobileNet, SqueezeNet).", "Interestingly, we consistently observe that spatial information can be completely deleted from a significant number of layers with no or only small performance drops.", "Despite the fantastic performances of convolutional neural networks (CNNs) on computer vision tasks, their inner workings remain mostly obfuscated to us and analyzing them results often in surprising results.", "Generally, the majority of modern CNNs for image classification learn spatial information across all the convolutional layers: every layer in AlexNet, VGG, Inception, and ResNet applies 3×3 or larger filters.", "Such design choice is based on the assumption that spatial information remains important at every convolutional layer to consecutively increase the access to a larger spatial context.", "This is based on the observations that single local features can be ambiguous and should be related to other features in the same scene to make accurate predictions Torralba et al. (2003) ; Hoiem et al. (2008) .", "Recent work on restricting the receptive field of CNN architectures, scrambling the inputs or using wavelet feature networks resulting in networks with shallow depth (Oyallon et al., 2017) have all found it to be possible to acquire competitive performances on the respective classification tasks.", "This raises doubts on whether common CNNs learn representations of global context as small local features appear to be sufficient for classification.", "We add to the list of surprising findings surrounding the inner workings of CNNs and present a rigorous investigation on the necessity of spatial information in standard CNNs by avoiding learning spatial information at multiple layers.", "To this end, we propose three methods i.e., shuffle conv, GAP+FC and 1x1Conv, to eliminate the spatial information.", "Surprisingly, we find that the modified CNNs i.e., without the ability to access any spatial information at last layers, can still achieve competitive results on several object recognition datasets.", "This indicates that the spatial information is overrated for standard CNNs and not necessary to reach competitive performances.", "In our experiments, the last layers of standard CNNs can be simplified by substituting them with our proposed GAP+FC or 1x1Conv layers which ignore spatial information, leading to a smaller model with less parameters.", "Moreover, our novel simplifications can be adapted to a wide range of CNN architectures and maintain state-of-the-art performance on various image classification datasets.", "The detail of the shuffle conv.", "Each feature map from the input tensor will be randomly and independently shuffled before being fed into an ordinary convolution.", "Our experiments in Table 2 left clearly show that ordinary models by default don't possess the invariance to the absence of the spatial information.", "In contrast to the common wisdom, we find that spatial information can be neglected from a significant number of last layers without any performance drop if the invariance is imposed at training, which suggests that spatial information at last layers is not necessary for a good performance.", "We should however notice that it doesn't indicate that models whose prediction is based on the spatial information can't generalize well.", "Besides, unlike the common design manner that layers at different depth inside the network are normally treated equally, e.g. the same module is always used throughout the architecture, our observation implies it is beneficial to have different designs for different layers since there is no necessity to encode spatial information in the last layers (see Appendix A.3 for discussion on first layers), therefore reducing the model complexity.", "Comparing our three methods, we observe that 1x1Conv is more robust to the absence of the spatial information while Shuffle Conv and GAP+FC perform similarly for both VGG-16 and ResNet-50.", "This implies that CNNs can still benefit from the larger size of activation maps even though its spatial information is not presented.", "To conclude, we empirically show that last layers of CNNs are robust to the absence of the spatial information, which is commonly assumed to be important for object recognition tasks.", "Our proposed methods, without accessing any spatial information at last layers of modern CNNs, are able to achieve competitive results on several object recognition datasets incuding CIFAR100, SmallImageNet and ImageNet.", "We suggest a good rule of thumb for CNN architectures: using 1x1 convolution or fully connected layers at last layers reduces the number of parameters without affecting the performance.", "An interesting future direction is to study whether our methods can generalize to other computer vision tasks, e.g., object detection and pose estimation where the spatial relationships are vital for localizing objects.", "A APPENDIX" ]

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[ "Spatial information at last layers is not necessary for a good classification accuracy." ]

[ "Disentangling underlying generative factors of a data distribution is important for interpretability and generalizable representations.", "In this paper, we introduce two novel disentangling methods.", "Our first method, Unlabeled Disentangling GAN (UD-GAN, unsupervised), decomposes the latent noise by generating similar/dissimilar image pairs and it learns a distance metric on these pairs with siamese networks and a contrastive loss.", "This pairwise approach provides consistent representations for similar data points.", "Our second method (UD-GAN-G, weakly supervised) modifies the UD-GAN with user-defined guidance functions, which restrict the information that goes into the siamese networks.", "This constraint helps UD-GAN-G to focus on the desired semantic variations in the data.", "We show that both our methods outperform existing unsupervised approaches in quantitative metrics that measure semantic accuracy of the learned representations.", "In addition, we illustrate that simple guidance functions we use in UD-GAN-G allow us to directly capture the desired variations in the data.", "Generative Adversarial Networks (GANs) are generative model estimators, where two neural networks (generator and discriminator) are trained in an adversarial setting, so that likelihood-based probabilistic modeling is not necessary.", "This works particularly well for sampling from a complex probability distribution, such as images.", "Although GANs yield realistic looking images BID18 , the original formulation in only allows for randomly sampling from the data distribution without disentangled structural or semantic control over the generated data points.One way to disentangle the generation process is to use conditional GANs BID16 BID17 .", "These models modify the generator by conditioning it with supervised labels.", "Then, they either take the same labels as input in the discriminator BID16 and measure the image-label compatibility, or classify the correct label at the output, given the generated image BID17 .", "Conditional GANs rely on a dataset with labels, which might not always be available or might be time-consuming to collect.In this paper, we propose two GAN-based methods that learns disentangled representations without using labeled data.", "Our first method, Unlabeled Disentangling GAN (UD-GAN), generates image pairs, then embeds them with Siamese Networks BID2 , and finally learns a distance metric on a disentangled representation space.", "Whereas our second method, UD-GAN-G, uses guidance functions to restrict the input to our siamese networks, so that they capture desired semantic variations.", "In this paper we introduced UD-GAN and UD-GAN-G, novel GAN formulations which employ Siamese networks with contrastive losses in order to make slices of the latent noise space disentangled and more semantically meaningful.", "Our experiments encompassed guided and unguided approaches for the embedding networks, and illustrated how our methods can be used for semantically meaningful image manipulation.", "Our qualitative and quantiative results confirm that our method can adjust well to the intrinsic factors of variation of the data and outperform the current state-of-the-art methods on the CelebA and 2D Shapes datasets.", "In future work, we plan to investigate more powerful forms of embedders, e.g. extracting information from pre-trained networks for semantic segmentation and landmark detection.", "This allows for even more powerful novel image manipulation techniques." ]

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[ "We use Siamese Networks to guide and disentangle the generation process in GANs without labeled data." ]

[ "We present Predicted Variables, an approach to making machine learning (ML) a first class citizen in programming languages.\n", "There is a growing divide in approaches to building systems: using human experts (e.g. programming) on the one hand, and using behavior learned from data (e.g. ML) on the other hand.", "PVars aim to make using ML in programming easier by hybridizing the two.", "We leverage the existing concept of variables and create a new type, a predicted variable.", "PVars are akin to native variables with one important distinction: PVars determine their value using ML when evaluated.", "We describe PVars and their interface, how they can be used in programming, and demonstrate the feasibility of our approach on three algorithmic problems: binary search, QuickSort, and caches.\n", "We show experimentally that PVars are able to improve over the commonly used heuristics and lead to a better performance than the original algorithms.\n", "As opposed to previous work applying ML to algorithmic problems, PVars have the advantage that they can be used within the existing frameworks and do not require the existing domain knowledge to be replaced.", "PVars allow for a seamless integration of ML into existing systems and algorithms.\n", "Our PVars implementation currently relies on standard Reinforcement Learning (RL) methods.", "To learn faster, PVars use the heuristic function, which they are replacing, as an initial function.", "We show that PVars quickly pick up the behavior of the initial function and then improve performance beyond that without ever performing substantially worse -- allowing for a safe deployment in critical applications.", "Machine Learning (ML) has had many successes in the past decade in terms of techniques and systems as well as in the number of areas in which it is successfully applied.", "However, using ML has some cost that comes from the additional complexity added to software systems BID24 .", "There is a fundamental impedance mismatch between the approaches to system building.", "Software systems have evolved from the idea that experts have full control over the behavior of the system and specify the exact steps to be followed.", "ML on the other hand has evolved from learning behavior by observing data.", "It allows for learning more complex but implicit programs leading to a loss of control for programmers since the behavior is now controlled by data.", "We believe it is very difficult to move from one to another of these approaches but that a hybrid between them needs to exist which allows to leverage both the developer's domain-specific knowledge and the adaptability of ML systems.We present Predicted Variables (PVars) as an approach to hybridize ML with programming.", "We leverage the existing concept of a variable which is universal across all programming modalities and add a new type, a predicted variable.", "PVars are akin to native variables with one important distinction: a PVar determines its value using ML when evaluated.", "A developer will be able to use a PVar just like any other variable, combine it with heuristics, domain specific knowledge, problem constraints, etc. in ways that are fully under the programmer's control.", "This represents an inversion of control compared to how ML systems are usually built.", "PVars allow to integrate ML tightly into algorithms whereas traditional ML systems are build around the model.", "PVars aim to make using ML in software development easier by avoiding the overhead of going through the traditional steps of building an ML system: (1) collecting and preparing training data, (2) defining a training loss, (3) training an initial model, (4) tweaking and optimizing the model, (5) integrating the model into their system, and (6) continuously updating and improving the model to adjust for drift in the distribution of the data processed.We show how these properties of PVars allow for applying ML in domains that have traditionally not been using ML.", "We demonstrate that ML can help improve the performance of \"classical\" algorithms that typically rely on a heuristic.", "The concrete implementation of PVars in this paper is based on standard deep reinforcement learning (RL).", "We emphasize that this is just one possible implementation.", "Other types of machine learning are in scope for PVars: supervised learning can be used when ground truth is available, or active learning is applicable when humans are in the loop to provide feedback.While in this paper we show PVars in the context of the Python programming language and use concepts from object oriented programming, everything described here applies directly to functional or procedural programming languages as well.", "We describe the framework around the central concept of a predicted variable but depending on the language the notion of a predicted function can be used interchangeably.We also introduce the notion of an initial function which can be the current heuristic that a PVar is replacing.", "It allows the PVar to minimize regret in critical applications and allow for safe deployment.", "This is a key strengths of our hybrid approach: it allows for better solutions while also providing better guarantees to the programmer.We demonstrate the feasibility of our approach on three algorithmic problems: binary search, QuickSort, and caches where we replace and enrich commonly used heuristics.", "We show improvements over common heuristics by injecting a predicted variable into an existing program, leaving much of the algorithm (including the domain-specific knowledge) untouched.", "We consider these problems the first applications of our newly defined interface and see the main contribution of this paper in the general applicability of the framework.", "The problem selection in this paper was driven by the desire for a self-contained setup and ease of reproducibility.", "PVars are applicable to more general problems across a large variety of domains from system optimization to user modelling.In our experiments we do not focus on the actual run time but rather on the effectiveness of the ML models.", "While for the algorithmic examples in this paper, in a practical scenario speed is the key metric, we see PVars as a more general interface that can be applied across a more diverse set of problems including user modelling, predicting user preference, or content recommendations.", "In many applications, speed is not a meaningful metric.", "Further, we believe that advances in specialized hardware will enable running machine learning models at insignificant cost (Kraska et al., 2018) .Our", "main contributions are:• we introduce the PVar API to smoothly integrate ML into software development;• we show how standard RL methods can be leveraged through the PVars interface;• we propose an approach to learn using the initial function, leveraging off-policy learning;• we demonstrate the feasibility of our approach on 3 standard algorithmic problems.The remainder of this paper is structured as follows: We describe how PVars can be used in software development in sec. 2 and how we make use of the heuristics that we are replacing to guide the training and avoid unstable behavior in sec. 3. Sec.", "4 describes our implementation and the application of PVars to three algorithmic applications. We also", "describe the experiments that we performed to demonstrate that PVars are an intuitive approach to bring ML closer to software development and are applicable to different problems. We describe", "related work in sec. 5.", "We have introduced a new programming concept called a predicted variable (PVar) aiming to make it easier for developers to use machine learning from their existing code.", "Contrary to other approaches, PVars can easily be integrated and hand full control to the developer over how ML models are used and trained.", "PVars bridge the chasm between the traditional approaches of software systems building and machine learning modeling and thus allow for the developer to focus on refining their algorithm and metrics rather than working on building pipelines to incorporate machine learning.", "PVars achieve this by reusing the existing concept of variables in programming in a novel way where the value of the variable is determined using machine learning.", "PVar observes information about its context and receives feedback about the quality of predictions instead of being assigned a value directly.We have studied the feasibility of PVars in three algorithmic problems.", "For each we show how easy PVars can be incorporated, how performance improves in comparison to not using a PVar at all.", "Specifically, through our experiments we highlight both advantages and disadvantages that reinforcement learning brings when used as a solution for a generic interface as PVars.Note that we do not claim to have the best possible machine learning model for each of these problems but our contribution lies in building a framework that allows for using ML easily, spreading its use, and improving the performance in places where machine learning would not have been used otherwise.", "PVars are applicable to more general problems across a large variety of domains from system optimization to user modelling.", "Our current implementation of PVars is built on standard RL methods but other ML methods such as supervised learning are in scope as well if the problem is appropriate." ]

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[ "We present Predicted Variables, an approach to making machine learning a first class citizen in programming languages." ]

[ "Much recent research has been devoted to video prediction and generation, but mostly for short-scale time horizons.", "The hierarchical video prediction method by Villegas et al. (2017) is an example of a state of the art method for long term video prediction. ", "However, their method has limited applicability in practical settings as it requires a ground truth pose (e.g., poses of joints of a human) at training time. ", "This paper presents a long term hierarchical video prediction model that does not have such a restriction.", "We show that the network learns its own higher-level structure (e.g., pose equivalent hidden variables) that works better in cases where the ground truth pose does not fully capture all of the information needed to predict the next frame. ", "This method gives sharper results than other video prediction methods which do not require a ground truth pose, and its efficiency is shown on the Humans 3.6M and Robot Pushing datasets.", "It is hypothesized that learning to predict the future and the effect of their actions is an important quality for intelligent agents that interact with their environment.", "This is a complicated task, as typical use cases require predicting the outcome of interactions between the agent and objects over multiple timesteps.In this work we are looking at the task of predicting the pixels of future video frames given the first few observed frames.", "We also consider the action conditional setting, in which we are given the action that the agent is taking and are tasked to predict the pixel level outcome of that action in the future.The method of BID20 is a novel way to generate long term video predictions, but requires ground truth human pose annotations.", "In this work we explore ways to generate videos using a hierarchical model without requiring a ground truth pose or other high level structure annotations for each frame.", "The method is hierarchical in the sense that it learns to generate a high level structure, then makes next frame predictions based on that structure.", "On datasets where the pose does not capture all of the information needed to predict future frames, letting the network define its own high level structure in addition to the pose is an improvement upon a BID20 .", "The EPEV method generates sharper images than BID3 on non deterministic datasets, and can generate further into the future on a toy dataset that we introduced.", "We posit an adversarial loss between the predictor and encoder would likely help with potentially uncertain scenarios and would fix the problem of the EPEV method sometimes generating blurry images,Under review as a conference paper at ICLR 2018 To see what the encoder has learned in the EPEV method, we can obtain results from the visual analogy network given the input from the encoder.", "The encoder is given the ground truth image.The results are shown in figure 9 .", "The results show that the encoder encodes where the person is Figure 9 : Results from the EPEV approach when the VAN is given the output of the encoder on the ground truth frame.in the image, as well as the orientation of the arms, legs and head to some extent.", "The results are not as good as one would expect from an autoencoder, since the encoder has the constraint that the encoding also has to be easy to predict." ]

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[ "We show ways to train a hierarchical video prediction model without needing pose labels." ]

[ "Combining information from different sensory modalities to execute goal directed actions is a key aspect of human intelligence.", "Specifically, human agents are very easily able to translate the task communicated in one sensory domain (say vision) into a representation that enables them to complete this task when they can only sense their environment using a separate sensory modality (say touch).", "In order to build agents with similar capabilities, in this work we consider the problem of a retrieving a target object from a drawer.", "The agent is provided with an image of a previously unseen object and it explores objects in the drawer using only tactile sensing to retrieve the object that was shown in the image without receiving any visual feedback.", "Success at this task requires close integration of visual and tactile sensing.", "We present a method for performing this task in a simulated environment using an anthropomorphic hand.", "We hope that future research in the direction of combining sensory signals for acting will find the object retrieval from a drawer to be a useful benchmark problem", "A core aspect of human intelligence is the ability to integrate and translate information between multiple sensory modalities to achieve an end goal.", "For example, we have no trouble discriminating between a set of keys, a wallet or a watch kept in our pocket by simply feeling them with our hands.", "Similarly, we can easily retrieve a desired object present inside a dark drawer even if we can't see the objects using touch sensation from our hands.", "Not only can we retrieve a previously known object, but if we are shown an image of a previously unseen object, we would still have no trouble retrieving this object using only tactile exploration inside the drawer even in absence of any visual feedback.", "Such translation of information between sensory modalities is not specific to tactile and vision, but is noticed between other modalities as well.", "For instance, it is easy to imagine someone walking down the stairs and opening the door by simply hearing the sound that was generated.", "These examples demonstrate how easily humans can translate information between sensory modalities.", "Different sensory modalities provide a different view of the same underlying reality.", "The ability to transform between sensory modalities therefore provides an interesting way to learn useful representations of sensory inputs.", "Recent work in self-supervised learning has made extensive use of this observation and shown that useful visual features can be learned by predicting, from images, corresponding sounds BID18 , ego-motion BID1 BID11 , depth or even predicting color values from grayscale images BID23 .In", "addition to learning feature representations, another and possibly more critical use of sensing from multiple modalities is performing goal directed actions in partially observable settings. In", "the running example of retrieving objects from a drawer, the agent receives only the image of the object as input and in absence of any light source in the drawer, the agent solely relies on its tactile sensing to find the object. Other", "examples are a pedestrian getting alerted when she hears the sound of a car coming from the back or animals in the jungle being alerted of a tiger behind the bushes by the sound of the movement. Yet another", "example showing close integration of two modalities (vision and touch) is a study that found it became almost impossible for human participants to perform the seemingly trivial task of picking up a matchstick and lighting it when their hands were anesthetized BID12 ). Figure 1 :", "(Left) Shows our experimental setup. p objects", "are in a drawer and a dexterous hand equipped with tactile sensing can explore novel objects using deterministic routines. In this case", ", p = 3 but we compared performance by varying the number of objects (Middle) We are presented with a query image as seen by the inset in the top right of the image. We explore", "the objects in the drawer using tactile sensing only to identify the object (Right) We then retrieve the object by applying a grasping routineIn this work we use the task of retrieving objects from a drawer as an experimental setup to investigate joint learning from two sensory modalities of vision and touch. Because the", "agent is provided only with a visual image of the object to be retrieved, it must translate into the representation space of tactile sensing to retrieve objects only by touching them. In the general", "case of retrieving the object, the agent must first explore spatially to locate where the objects are. Once it finds", "the object, it must move its fingers in an exploratory manner to collect information required to determine if the object is the one that needs to be retrieved. Solving this", "problem in its full generality requires not only good goal directed exploration strategies and also a method for translating between different sensory signals. We therefore", "think that object retrieval from a drawer is a good challenge problem for investigating different models that combine visual and tactile information for a target end task.In our setup the agent learns a mapping from visual to tactile signals using unsupervised exploration. This mapping", "enables the agent to determine the representation of the image in the representation space of tactile sensing (i.e. expected tactile response). The agent explores", "each object present in the drawer by touching it and compares the result of its exploration with the expected tactile response. Performing this comparisons", "requires a good representation of raw tactile signals. For learning such a representation", ", we leverage the results in image classification, where it was found that a network pre-trained to classify images from the Imagenet dataset into one thousand image categories learns features useful for many other visual tasks. Similar to image classification,", "we pose the task of classifying objects from tactile signals collected by touching eleven objects. We show that tactile representation", "learned by performing the task of classification, generalize and can be used to retrieve novel objects. We present results in a simulated environment", "and the agent explores the objects using an anthropomorphic hand.", "We present a model that when presented with a query image can identify a novel object from a set of p objects using tactile sensing only.", "As the number of novel objects presented in a single trial increased, this task quickly became more challenging.We show that a model with pre-determined exploration routine can identify the object but a richer exploration of the objects could allow us to answer more challenging inferences such as pose, texture, etc.", "One could imagine doing this by training a RL agent that uses the performance of { 2 as a reward while generating trajectories that explore an object for identification.Presently, we train our two networks F 1 and F 2 independently.", "Since, our larger goal is to identify objects it would be interesting to jointly optimize the network to maximize object identification.", "This can help smooth prediction errors that are not consequential to classification or identification.While the MuJoCo simulator provides fast physics solvers that can compute realistic contact forces they only compute normal contact forces.", "Research in neuroscience has shown BID15 ) that a variety of forces are applied and measured while employing tactile sensing.", "It would be interesting to perform similar experiments on robot grippers equipped with tactile sensors.Our current setup still trains network F 2 in a supervised fashion.", "This is biologically implausible and tedious for practical scalability on real robots.", "It would be interesting if we posed this problem as a self-supervised problem and explored learning to identify novel objects using tactile sensing." ]

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[ "In this work, we study the problem of learning representations to identify novel objects by exploring objects using tactile sensing. Key point here is that the query is provided in image domain." ]

[ "Locality sensitive hashing schemes such as \\simhash provide compact representations of multisets from which similarity can be estimated.", "However, in certain applications, we need to estimate the similarity of dynamically changing sets. ", "In this case, we need the representation to be a homomorphism so that the hash of unions and differences of sets can be computed directly from the hashes of operands. ", "We propose two representations that have this property for cosine similarity (an extension of \\simhash and angle-preserving random projections), and make substantial progress on a third representation for Jaccard similarity (an extension of \\minhash).", "We employ these hashes to compress the sufficient statistics of a conditional random field (CRF) coreference model and study how this compression affects our ability to compute similarities as entities are split and merged during inference.", "\\cut{We study these hashes in a conditional random field (CRF) hierarchical coreference model in order to compute the similarity of entities as they are merged and split during inference.}", "We also provide novel statistical analysis of \\simhash to help justify it as an estimator inside a CRF, showing that the bias and variance reduce quickly with the number of bits.", "On a problem of author coreference, we find that our \\simhash scheme allows scaling the hierarchical coreference algorithm by an order of magnitude without degrading its statistical performance or the model's coreference accuracy, as long as we employ at least 128 or 256 bits. ", "Angle-preserving random projections further improve the coreference quality, potentially allowing even fewer dimensions to be used.", "Probabilistic models in machine learning, such as conditional random fields (CRFs), are widely successful at modeling many problems at the heart of knowledge base construction, including those in natural language processing, information extraction and data integration.", "However, when dealing with natural language data, the underlying feature representations are often sparse, high-dimensional and dynamic (i.e., they change during inference).", "In this paper we consider the task of coreference resolution, in which the goal is to partition a set of mentions into the entities to which they refer.", "We might represent each mention with a feature vector in which each dimension corresponds to a word or n-gram.", "Since only a small subset of the vocabulary is observed per mention, most elements of the vector are zero.Given the model and these representations, inference entails making decisions about whether two entities should be coreferent.", "To make such decisions, the model estimates a probability that involves computing the similarities between the aggregate feature representations of the two entities' mentions.", "Since all the vectors are both sparse and high-dimensional, these similarity operations are computationally expensive because the sparse data structures supplant the dense arrays that would otherwise support fast look-ups.", "Moreover, as the inference algorithm makes decisions about whether or not two entities are coreferent, we may have to split or merge the entities and thus we must update the feature vector to reflect these changes.", "Maintaining such sparse-vector representations in the inner-loop of probabilistic inference is expensive, especially as the entities grow in size.In order to cope with the computational problems associated with sparse, high dimensional dynamic feature representations, we propose using homomorphic compression, in which the compressed representations of intermediate inference results can be computed directly from their operands, allowing inference to run directly on the compressed representations of the data even as they change.", "In this paper, we consider several such schemes to scale hierarchical coreference.", "First, we propose a novel homomorphic cosine-preserving hashing scheme based on simhash BID7 that also supports addition and subtraction to more efficiently represent the data and the evolving intermediate results of probabilistic inference.", "Second, because various linear norm-preserving random projections also preserve angles BID24 , we can directly compute cosine similarity on projected data -linearity of the projections means that they too can be updated dynamically.", "The resulting angle estimates are superior to the homomorphic simhash representation, at the cost of reduced efficiency for certain operations.", "Third, we develop a homomorphic version of minhash BID5 to support Jaccard similarity.", "Our current algorithm is biased, but the bias appears small in practice for the situations we have considered.", "Although the minhash based set representations are not currently employed in hierarchical coreference, they might be useful in other models or applications that involve binary features over changing sets BID9 .We", "provide error analysis for all three schemes, collating and extending known results, and in the case of simhash, we provide novel statistical analysis for its use as a direct estimator for cos(θ) that shows the bias and variance decrease rapidly with the number of bits, helping to justify its use in a CRF for a task like coreference. On", "a hierarchical model for coreference resolution, the proposed simhash scheme improves the speed of probabilistic inference by an order of magnitude while having little effect on model quality. Moreover", ", we find that the underlying random projection representation can provide even better cosine estimates than simhash, at the cost of not being able to use certain fast bitwise-operations to compute similarities. Finally", ", we briefly evaluate homomorphic minhash and show that even though there are possible pathological cases, as long as we employ enough hash functions, the estimates are reasonably close to the true Jaccard, albeit, biased.", "In this paper we presented several homomorphic compression schemes for representing the sparse, high dimensional features in a graphical model for coreference resolution, even as these features change during inference.", "Our primary concern was cosine similarity for which we investigated simhash and angle-preserving random projections.", "We also proposed a homomorphic version of minhash for Jaccard similarity.", "In the particular case of simhash, we presented a new variant of the original estimator and analyzed its statistical propertiesincluding variance, bias and consistency -to help justify its use in a probabilistic model.", "We found that both simhash and angle-preserving random projections were sufficiently accurate, given enough dimensions, to represent features for coreference, and that the random projections produce slightly better estimates.", "Moreover, these representations were an order of magnitude faster than conventional sparse data structures, laying the foundation for greater scalability." ]

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[ "We employ linear homomorphic compression schemes to represent the sufficient statistics of a conditional random field model of coreference and this allows us to scale inference and improve speed by an order of magnitude." ]

[ "Motivated by applications to unsupervised learning, we consider the problem of measuring mutual information.", "Recent analysis has shown that naive kNN estimators of mutual information have serious statistical limitations motivating more refined methods.", "In this paper we prove that serious statistical limitations are inherent to any measurement method.", "More specifically, we show that any distribution-free high-confidence lower bound on mutual information cannot be larger than $O(\\ln N)$ where $N$ is the size of the data sample.", "We also analyze the Donsker-Varadhan lower bound on KL divergence in particular and show that, when simple statistical considerations are taken into account, this bound can never produce a high-confidence value larger than $\\ln N$.", "While large high-confidence lower bounds are impossible, in practice one can use estimators without formal guarantees.", "We suggest expressing mutual information as a difference of entropies and using cross entropy as an entropy estimator.", " We observe that, although cross entropy is only an upper bound on entropy, cross-entropy estimates converge to the true cross entropy at the rate of $1/\\sqrt{N}$.", "Motivated by maximal mutual information (MMI) predictive coding BID11 BID16 BID13 , we consider the problem of measuring mutual information.", "A classical approach to this problem is based on estimating entropies by computing the average log of the distance to the kth nearest neighbor in a sample BID7 .", "It has recently been shown that the classical kNN methods have serious statistical limitations and more refined kNN methods have been proposed BID5 .", "Here we establish serious statistical limitations on any method of estimating mutual information.", "More specifically, we show that any distribution-free high-confidence lower bound on mutual information cannot be larger than O(ln N ) where N is the size of the data sample.Prior to proving the general case, we consider the particular case of the Donsker-Varadhan lower bound on KL divergence BID3 BID1 .", "We observe that when simple statistical considerations are taken into account, this bound can never produce a highconfidence value larger than ln N .", "Similar comments apply to lower bounds based on contrastive estimation.", "The contrastive estimation lower bound given in BID13 does not establish mutual information of more than ln k where k is number of negative samples used in the contrastive choice.The difficulties arise in cases where the mutual information I(x,", "y) is large.", "Since I(x,", "y) = H(y", ") − H(y|x) we are interested in cases where H(y", ") is large and H(y|x) is small. For", "example consider the mutual information between an English sentence and its French translation. Sampling", "English and French independently will (almost) never yield two sentences where one is a plausible translation of the other. In this", "case the DV bound is meaningless and contrastive estimation is trivial. In this", "example we need a language model for estimating H(y) and", "a translation model for estimating H(y|x). Language", "models and translation models are both typically trained with crossentropy loss. Cross-entropy", "loss can be used as an (upper bound) estimate of entropy and we get an estimate of mutual information as a difference of cross-entropy estimates. Note that the", "upper-bound guarantee for the cross-entropy estimator yields neither an upper bound nor a lower bound guarantee for a difference of entropies. Similar observations", "apply to measuring the mutual information for pairs of nearby frames of video or pairs of sound waves for utterances of the same sentence.We are motivated by the problem of maximum mutual information predictive coding BID11 BID16 BID13 . One can formally define", "a version of MMI predictive coding by considering a population distribution on pairs (x, y) where we think of x", "as past raw sensory signals (images or sound waves) and y as a future sensory signal. We consider the problem", "of learning stochastic coding functions C x and C y so as to maximize the mutual information I(C x (x), C y (y)) while limiting", "the entropies", "H(C x (x)) and H(C y (y)). The intuition", "is that we want", "to learn", "representations C x (x) and C y (y) that preserve \"signal\"", "while removing", "\"noise\". Here signal is simply defined to be a low", "entropy representation that preserves mutual information with the future. Forms of MMI predictive coding have been", "independently introduced in BID11 under the name \"information-theoretic cotraining\" and in BID13 under the name \"contrastive predictive coding\". It is also possible to interpret the local", "version of DIM (DIM(L)) as a variant of MMI predictive coding.A closely related framework is the information bottleneck BID17 . Here one again assumes a population distribution", "on pairs (x, y). The objective is to learn a stochastic coding", "function", "C x so as to maximize I(C x (x), y) while minimizing I(C x (x), x). Here one does", "not", "ask for a coding function", "on y", "and", "one does not limit H(C x (x)).Another related framework is INFOMAX BID8 BID2", ". Here", "we consider a population distribution on a single", "random variable x. The objective is to learn a stochastic coding function", "C x so as to maximize the mutual information I(x, C x (x)) subject to some constraint or additional objective", ".As mentioned above, in cases where I(C x (x), C y (y)) is large it seems best to train a model", "of the marginal", "distribution of P (C y ) and a model of the conditional distribution P (C y |C x ) where both models are trained with cross-entropy loss. Section 5 gives various high confidence upper bounds on cross-entropy", "loss for learned models. The main point is that, unlike lower bounds on entropy, high-confidence", "upper bounds on cross-entropy loss can be guaranteed to be close to the true cross entropy.Out theoretical analyses will assume discrete distributions. However, there is no loss of generality in this assumption. Rigorous treatments", "of probability (measure theory) treat integrals (either Riemann", "or Lebesgue) as limits of increasingly fine binnings. A continuous density can always be viewed as a limit of discrete distributions. Although", "our proofs are given for discrete case, all our formal limitations on the measurement", "of mutual information apply to continuous case as well. See BID9 for a discussion of continuous information theory. Additional comments on this point", "are given in section 4.", "Maximum mutual information (MMI) predictive coding seems well motivated as a method of unsupervised pretraining of representations that maintain semantic signal while dropping uninformative noise.", "However, the maximization of mutual information is a difficult training objective.", "We have given theoretical arguments that representing mutual information as a difference of entropies, and estimating those entropies by minimizing cross-entropy loss, is a more statistically justified approach than maximizing a lower bound on mutual information.Unfortunately cross-entropy upper bounds on entropy fail to provide either upper or lower bounds on mutual information -mutual information is a difference of entropies.", "We cannot rule out the possible existence of superintelligent models, models beyond current expressive power, that dramatically reduce cross-entropy loss.", "Lower bounds on entropy can be viewed as proofs of the non-existence of superintelligence.", "We should not surprised that such proofs are infeasible." ]

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[ "We give a theoretical analysis of the measurement and optimization of mutual information." ]

[ "In this paper, we propose a neural network framework called neuron hierarchical network (NHN), that evolves beyond the hierarchy in layers, and concentrates on the hierarchy of neurons.", "We observe mass redundancy in the weights of both handcrafted and randomly searched architectures.", "Inspired by the development of human brains, we prune low-sensitivity neurons in the model and add new neurons to the graph, and the relation between individual neurons are emphasized and the existence of layers weakened.", "We propose a process to discover the best base model by random architecture search, and discover the best locations and connections of the added neurons by evolutionary search.", "Experiment results show that the NHN achieves higher test accuracy on Cifar-10 than state-of-the-art handcrafted and randomly searched architectures, while requiring much fewer parameters and less searching time.", "Neural networks can be designed either by human experts or search algorithms, both of which have gained great success in image classification and language modeling BID45 BID33 .", "Network architectures designed by both means are mostly layer-based or block-based, which means that the fundamental components are either operation layers or blocks that consist of several layers.", "A clear tendency can be observed that models with more parameters generally have better performances.", "It is a well-established fact that redundancy of parameters exists widely in handcrafted neural networks BID16 BID41 BID25 .", "We find that such claim holds for architectures discovered by random search or evolutionary search as well.", "The pruning of unimportant neurons emphasizes the hierarchical relation between individual neurons.", "Additionally, the decrease in accuracy after parameter reduction is generally inevitable.", "Therefore, we propose a heuristic procedure to construct neuron-based network architectures by pruning redundant connections and neurons in layer-based models and adding new neurons to strengthen the neuron hierarchy while achieving competitive performances as layer-hierarchy models.", "Experiments show that NHN achieves higher test accuracy than DenseNet , SMASH BID4 and hierarchical representation with much fewer parameters.Handcrafted architectures.", "Successful convolutional neural networks (CNNs) designed by human experts can be sketchily categorized by the way data flow through the networks, i.e., plain networks and branching networks.", "A notable example of plain networks would be VGG nets BID37 , where there are only one input and output path in each hidden layer.", "However, in a branching network, the computation flow splits somewhere in the network and merges in a latter layer BID0 .", "The splitting and aggregation may occur multiple times in a single network.", "Many have discovered numerous branching network architectures whose performances surpass plain ones while requiring fewer parameters.", "Skip connections BID17 BID18 are increasingly popular in improving the performance of deep neural networks, and it becomes common to observe additional convolutions (or other forms of operations) stacked between large layers BID24 BID40 .", "In fact, the \"stacked-between\" operations can be considered as part of a generalized residual block.", "Multi-branching computation graphs benefit addressing the gradient vanishing problem during the gradient descent training BID18 .", "The distinguished techniques mentioned above (plus more listed in Table 1 ) share the same idea of weakening the hierarchy between layers by introducing complex paths to the data flow.", "The idea is further highlighted by architecture search algorithms.", "Random and evolutionary architectures.", "Machine learning algorithms evolve fast.", "Designing neural networks that perform remarkably on a given task requires ample experience.", "It has been found that neural networks are not only good at autonomically extracting useful features from raw data, but also capable of finding optimal network architectures to that end.", "Neural architecture search (NAS) has been attested to its ability to design network architectures for language modeling and image classification.", "However, candidate models have to be entirely randomly generated and fully trained, therefore NAS is extremely computation intensive, which dims its competitive performances to handcrafted architectures.", "Many efforts have been devoted to reducing the computational costs of NAS while ensuring sufficient capacity of search space BID47 BID5 .", "Two major ideas to achieve the purpose are to design individual reusable cells rather than the entire networks or to share trained weights between models.", "Recently, BID33 proposed to describe each candidate model as a subgraph of a single directed acyclic graph (DAG).", "By sharing weights between submodels, the searching time of NAS is reduced by 1000X in term of GPU-hours.", "Genetic algorithms are also applied in searching the optimal architectures of CNNs BID29 BID43 BID34 .", "BID35 proposed regularized evolution (RE) to remove the oldest models from the population, instead of removing the worst ones as in traditional tournament selection BID14 .", "The best CNN model discovered by RE achieves the state-of-the-art performance on Cifar-10, i.e., 2.13% test accuracy on average.", "However, the number of parameters it requires is as large as nearly 35 million.", "Convolutional neural fabrics (CNF) BID36 BID42 and other forms of random search methods BID2 BID4 BID10 have been investigated as well.Layer-wise to neuron-wise hierarchy.", "Take the best model discovered by macro search in ENAS BID33 for example.", "The 12-layer CNN model contains over 21 million parameters and achieves 4.23% test accuracy on Cifar-10.", "If we remove 75% − 90% parameters in all 3 × 3 and 5 × 5 convolutions, the test accuracy is hardly compromised after the same duration of retraining.", "Even though the architectures in all the search methods are described as directed graphs, each node in these graphs represents either an operation layer (e.g. convolution or pooling layer) or an operation block (e.g. residual block).", "None of the nodes stands for an actual individual neuron in the network.", "On one hand, random search and evolutionary search tend to discover architectures that contain complex branching paths.", "On the other hand, the pruned versions of such architectures work nearly as well as intact ones.", "These facts bring about the hypothesis that the hierarchy of neurons should work as well as the hierarchy of layers.", "Please note that we do not simply replace layers with individual neurons, considering layers are composed of abundant neurons.", "We need the sufficient number of neurons to meet the feature representation requirements.", "A good hierarchical architecture of neurons may be discovered by either random search or evolutionary search, or combined.", "The search process must be carefully designed.In this paper, we propose a three-step course to discover the optimal neuron hierarchy for image classification (see FIG1 , i.e., (1) discover the optimal layer hierarchy with ENAS, (2) prune unimportant neurons in the discovered layer-wise model, and (3) randomly add new neurons to the pruned model to enrich the expressive capacity of neuron hierarchy networks.", "It is worth pointing out that the three-step procedure is also an imitation of the natural development of human brains (Craik and Bialystok, 2006).", "For example, the creation and searching by ENAS correspond to the mass neurogenesis before birth.", "The pruning of unimportant neurons corresponds to the apoptosis before puberty BID11 .", "The addition of new neurons to the pruned model corresponds to the persisting neurogenesis during adulthood BID30 .", "Although the existence of neurogenesis in mature brains is being debated in the field of neuroscience BID38 BID3 , the software simulation of such process by our work indicates that it is helpful in improving the learning capability of neural networks.", "We did not choose fixed or handcrafted architectures as the base model because we believe that experiments conducted on a randomly searched model would be more compelling.", "There are also pruning-related issues with fixed models, for example, performances of ResNets and DenseNet are extremely sensitive to pruning.", "The training from scratch on the pruned architecture is crucial, because without it, the model only has a test accuracy of 15.7%.", "The NHN is not built upon the results by ENAS micro search even though it presents higher test accuracy while requiring fewer parameters than macro search.", "It is mainly due to the mass employment of depthwise separable convolution BID7 in which kernels are pairs of vectors and cannot be directly pruned.", "If we replace all the depthwise separable convolutions with normal convolutions, the micro model merely gains accuracy advantage of 0.3% over the macro model.", "However, it instead contains 67.8M parameters, which is more than 4 times of macro (16.3M).", "Also, it will consume more than 28GB of memory space to perform the layer-hierarchy search.", "LDS results FIG2 show that add-on neurons at lower layers work better, which indicates that rich representation of low-level features is crucial to the performance of NHN.", "When comparing the final test accuracy (96.52%) to the network without any add-on neuron (96.20%), we know that add-on neurons are helpful in increasing the performance of NHN.", "In fact, perturbation on the add-on genes discovered by LDS almost always leads to degradation of performance, and the total ablation of added neurons in the final model causes accuracy drop of 1.08%, which proves that the search results are optimal.The main goal of this paper is neither to comprehensively discuss the properties of neuron fields BID12 , nor to investigate a training method on an entirely randomly generated neuron graph.", "We'd like to point out that it is quite possible to directly generate a large number of free neurons with somewhat arbitrary connections and train this \"random neuron field\" to address the same task presented in this work.", "However, because modern GPUs, or to be more precise, the computation softwares that run on these GPUs are mainly designed for dense 4-d tensor calculation.", "It is hard to efficiently train such random neuron field at present.", "Therefore, as sophisticated as our approach may seem, it's an efficient method to construct network architectures that highlight the significance of individual neurons and perform competitively against other state-of-the-art methods.", "Neural networks that are designed by human experts and search algorithms perform outstandingly in image classification.", "However, redundancy in parameters exists widely in layer-based architectures.", "We propose a heuristic method to construct neuron-based architectures, namely, neuron hierarchical networks (NHN) , that obviate the redundancy in weights and emphasize the relation between individual neurons.", "Experiments show that the NHN discovered based on ENAS and by locationdirection search (LDS) outperforms the original ENAS architecture and many other handcrafted and randomly searched models in Cifar-10 classification, while requiring much fewer parameters.", "Also, the search time of NHN is very efficient compared to several state-of-the-art network architecture search methods, while achieving competitive performance." ]

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[ "By breaking the layer hierarchy, we propose a 3-step approach to the construction of neuron-hierarchy networks that outperform NAS, SMASH and hierarchical representation with fewer parameters and shorter searching time." ]

[ "Simulation is a useful tool in situations where training data for machine learning models is costly to annotate or even hard to acquire.", "In this work, we propose a reinforcement learning-based method for automatically adjusting the parameters of any (non-differentiable) simulator, thereby controlling the distribution of synthesized data in order to maximize the accuracy of a model trained on that data.", "In contrast to prior art that hand-crafts these simulation parameters or adjusts only parts of the available parameters, our approach fully controls the simulator with the actual underlying goal of maximizing accuracy, rather than mimicking the real data distribution or randomly generating a large volume of data.", "We find that our approach", "(i) quickly converges to the optimal simulation parameters in controlled experiments and", "(ii) can indeed discover good sets of parameters for an image rendering simulator in actual computer vision applications.", "In order to train deep neural networks, significant effort has been directed towards collecting largescale datasets for tasks such as machine translation BID16 , image recognition BID7 or semantic segmentation BID14 BID6 .", "It is, thus, natural for recent works to explore simulation as a cheaper alternative to human annotation BID11 BID19 BID18 .", "Besides, simulation is sometimes the most viable way to acquire data for rare events such as traffic accidents.", "However, while simulation makes data collection and annotation easier, it is still an open question what distribution should be used to synthesize data.", "Consequently, prior approaches have used human knowledge to shape the generating distribution of the simulator BID20 , or synthesized large-scale data with random parameters BID18 .", "In contrast, this paper proposes to automatically determine simulation parameters such that the performance of a model trained on synthesized data is maximized.Traditional approaches seek simulation parameters that try to model a distribution that resembles real data as closely as possible, or generate enough volume to be sufficiently representative.", "By learning the best set of simulation parameters to train a model, we depart from the above in three crucial ways.", "First, the need for laborious human expertise to create a diverse training dataset is eliminated.", "Second, learning to simulate may allow generating a smaller training dataset that achieves similar or better performances than random or human-synthesized datasets BID18 , thereby saving training resources.", "Third, it allows questioning whether mimicking real data is indeed the best use of simulation, since a different distribution might be optimal for maximizing a test-time metric (for example, in the case of events with a heavy-tailed distribution).More", "formally, a typical machine learning setup aims to learn a function h θ that is parameterized by θ and maps from domain X to range Y, given training samples (x, y) ∼ p(x, y). Data", "x usually arises from a real world process (for instance, someone takes a picture with a camera) and labels y are often annotated by humans (someone describing the content of that picture). The", "distribution p(x, y) is assumed unknown and only an empirical sample D = {(x i , y i )} N i=1 is available. The", "simulator attempts to model a distribution q(x, y; ψ). In", "prior works, the aim is to adjust the form of q and parameters ψ to mimic p as closely as possible. In", "this work, we attempt to automatically learn the parameters of the simulator ψ such that the loss L of a machine learning model h θ is minimized over some validation data set D val . This", "objective can be formulated as the bi-level optimization problem DISPLAYFORM0 where h θ is parameterized by model parameters θ, D q(x,y| ψ) describes a data set generated by the simulator and θ(ψ) denotes the implicit dependence of the model parameters θ on the model's training data and consequently, for synthetic data, the simulation parameters ψ. In contrast", "to BID10 , who propose a similar setup, we focus on the actual data generation process q(x, y; ψ) and are not limited to selecting subsets of existing data. In our formulation", ", the upper-level problem (equation 1a) can be seen as a meta-learner that learns how to generate data (by adjusting ψ) while the lower-level problem (equation 1b) is the main task model (MTM) that learns to solve the actual task at hand. In Section 2, we", "describe an approximate algorithm based on policy gradients BID24 to optimize the objective 1. For our algorithm", "to interact with a black-box simulator, we also present an interface between our model's output ψ and the simulator input.In various experiments on both toy data and real computer vision problems, Section 4 analyzes different variants of our approach and investigates interesting questions, such as: \"Can we train a model h θ with less but targeted high-quality data?\", or \"Are simulation parameters that approximate real data the optimal choice for training models?\". The experiments indicate", "that our approach is able to quickly identify good scene parameters ψ that compete and in some cases even outperform the actual validation set parameters for synthetic as well as real data, on computer vision problems such as object counting or semantic segmentation.", "The proposed approach can be seen as a meta-learner that alters the data a machine learning model is trained on to achieve high accuracy on a validation set.", "This concept is similar to recent papers that learn policies for neural network architectures BID25 and optimizers BID0 .", "In contrast to these works, we are focusing on the data generation parameters and actually create new, randomly sampled data in each iteration.", "While BID10 proposes a subset selection approach for altering the training data, we are actually creating new data.", "This difference is important because we are not limited to a fixed probability distribution at data acquisition time.", "We can thus generate or oversample unusual situations that would otherwise not be part of the training data.", "Similar to the above-mentioned papers, we also choose a variant of stochastic gradients (policy gradients BID24 ) to overcome the non-differentiable sampling and rendering and estimate the parameters of the policy π ω .", "While alternatives for black-box optimization exist, like evolutionary algorithms BID21 or sampling-based methods BID1 , we favor policy gradients in this work for their sample efficiency and success in prior art.", "BID13 train a policy to generate a program that creates a copy of an input image.", "Similar to us, they use policy gradients to train the policy, although they use an adversarial loss to construct their reward.", "Again, BID15 seek to tune parameters of a simulator such that the marginal distribution of the synthetic data matches the distribution of the observed data.", "In contrast to both works, we learn parameters of a simulator that maximize performance of a main task model on a specific task.", "The learned distribution need not match the distribution of the observed data.When relying on simulated data for training machine learning models, the issue of \"domain gap\" between real and synthetic data arises.", "Many recent works BID12 BID23 focus on bridging this domain gap, particularly for computer vision tasks.", "Even if we are able to tune parameters perfectly, there exists a simulation-to-real domain gap which needs to be addressed.", "Thus, we believe the contributions of our work are orthogonal.", "Learning to simulate can be seen as a meta-learning algorithm that adjusts parameters of a simulator to generate synthetic data such that a machine learning model trained on this data achieves high accuracies on validation and test sets, respectively.", "Given the need for large-scale data sets to feed deep learning models and the often high cost of annotation and acquisition, we believe our approach is a sensible avenue for practical applications to leverage synthetic data.", "Our experiments illustrate the concept and demonstrate the capability of learning to simulate on both synthetic and real data.", "For future work, we plan to expand the label space in our segmentation experiments, apply the algorithm to other tasks like object detection and to explore a dynamic memory of previously generated data for improving our learning to simulate procedure.", "A TRAFFIC SCENE MODEL Our model comprises the following elements:• A straight road of variable length.•", "Either an L, T or X intersection at the end of the road.•", "Cars of 5 different types which are spawned randomly on the straight road.•", "Houses of a unique type which are spawned randomly on the sides of the road.•", "Four different types of weather.All of these elements are tied to parameters: ρ k can be decomposed into parameters which regulate each of these objects. The", "scene is generated \"block\" by \"block\". A block", "consists of a unitary length of road with sidewalks. Buildings", "can be generated on both sides of the road and cars can be generated on the road. ρ k,car designates", "the probability of car presence in any road block. Cars are sampled block", "by block from a Bernouilli distribution X ∼ Bern (ρ k,car ). To determine which type", "of car is spawned (from our selection of 5 cars) we sample from a Categorical distribution which is determined by 5 parameters ρ k,cari where i is an integer representing the identity of the car and i ∈ [1, 5]. ρ k,house designates the", "probability of house presence in any road block. Houses are sampled block", "by block from a Bernouilli distribution X ∼ Bern (ρ k,house ).Length to intersection is", "sampled from a Categorical distribution determined by 10 parameters ρ k,lengthi with i ∈ [8, 18] where i denotes the length from the camera to the intersection in \"block\" units. Weather is sampled randomly", "from a Categorical distribution determined by 4 parameters φ k,weatheri where i is an integer representing the identity of the weather and i ∈ [1, 4]. L, T and X intersections are", "sampled randomly with equal probability." ]

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[ "We propose an algorithm that automatically adjusts parameters of a simulation engine to generate training data for a neural network such that validation accuracy is maximized." ]

[ "Modelling statistical relationships beyond the conditional mean is crucial in many settings.", "Conditional density estimation (CDE) aims to learn the full conditional probability density from data.", "Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum likelihood objective.", "Due to the inherent structure of such models, classical regularization approaches in the parameter space are rendered ineffective.", "To address this issue, we develop a model-agnostic noise regularization method for CDE that adds random perturbations to the data during training.", "We demonstrate that the proposed approach corresponds to a smoothness regularization and prove its asymptotic consistency.", "In our experiments, noise regularization significantly and consistently outperforms other regularization methods across seven data sets and three CDE models.", "The effectiveness of noise regularization makes neural network based CDE the preferable method over previous non- and semi-parametric approaches, even when training data is scarce.", "While regression analysis aims to describe the conditional mean E[y|x] of a response y given inputs x, many problems such as risk management and planning under uncertainty require gaining insight about deviations from the mean and their associated likelihood.", "The stochastic dependency of y on x can be captured by modeling the conditional probability density p(y|x).", "Inferring such a density function from a set of empirical observations {(x n , y n )} N n=1 is typically referred to as conditional density estimation (CDE) and is the focus of this paper.", "In the recent machine learning literature, there has been a resurgence of interest in high-capacity density models based on neural networks (Dinh et al., 2017; Ambrogioni et al., 2017; Kingma & Dhariwal, 2018) .", "Since this line of work mainly focuses on the modelling of images based on large scale data sets, over-fitting and noisy observations are of minor concern in this context.", "In contrast, we are interested in CDE in settings where data may be scarce and noisy.", "When combined with maximum likelihood estimation, the flexibility of such high-capacity models results in over-fitting and poor generalization.", "While regression typically assumes Gaussian conditional noise, CDE uses expressive distribution families to model deviations from the conditional mean.", "Hence, the overfitting problem tends to be even more severe in CDE than in regression.", "Classical regularization of the neural network weights such as weight decay (Pratt & Hanson, 1989) has been shown to be effective for regression and classification.", "However, in the context of CDE, the output of the neural network merely controls the parameters of a density model such as a Gaussian Mixture or Normalizing Flow.", "This makes the standard regularization methods in the parameter space less effective and harder to analyze.", "Aiming to address this issue, we propose and analyze noise regularization, a method well-studied in the context of regression and classification, for the purpose of conditional density estimation.", "In that, the paper attempts to close a gap in previous research.", "By adding small random perturbations to the data during training, the conditional density estimate is smoothed and tends to generalize better.", "In fact, we show that adding noise during maximum likelihood estimation is equivalent to penalizing the second derivatives of the conditional log-probability.", "Visually, the respective regularization term punishes very curved or even spiky density estimators in favor of smoother variants, which proves to be a favorable inductive bias in many applications.", "Moreover, under some regularity conditions, we show that the proposed regularization scheme is asymptotically consistent, converging to the unbiased maximum likelihood estimator.", "This does not only support the soundness of the proposed method but also endows us with useful insight in how to set the regularization intensity relative to the data dimensionality and training set size.", "Overall, the proposed noise regularization scheme is easy to implement and agnostic to the parameterization of the CDE model.", "We empirically demonstrate its effectiveness on three different neural network based models.", "The experimental results show that noise regularization outperforms other regularization methods significantly and consistently across various data sets.", "Finally, we demonstrate that, when properly regularized, neural network based CDE is able to improve upon state-of-the art non-parametric estimators, even when only 400 training observations are available.", "This paper addresses conditional density estimation with high-capacity models.", "In particular, we propose to add small random perturbations to the data during training.", "We demonstrate that the resulting noise regularization method corresponds to a smoothness regularization and prove its asymptotic consistency.", "The experimental results underline the effectiveness of the proposed method, demonstrating that it consistently outperforms other regularization methods across various conditional density models and data sets.", "This makes neural network based CDE the preferable method, even when only little training data is available.", "While we assess the estimator performance in terms of the test log-likelihood, an interesting question for future research is whether the noise regularization also improves the respective uncertainty estimates for downstream tasks such as safe control and decision making." ]

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[ "A model-agnostic regularization scheme for neural network-based conditional density estimation." ]

[ "Unsupervised representation learning holds the promise of exploiting large amount of available unlabeled data to learn general representations.", "A promising technique for unsupervised learning is the framework of Variational Auto-encoders (VAEs).", "However, unsupervised representations learned by VAEs are significantly outperformed by those learned by supervising for recognition.", "Our hypothesis is that to learn useful representations for recognition the model needs to be encouraged to learn about repeating and consistent patterns in data.", "Drawing inspiration from the mid-level representation discovery work, we propose PatchVAE, that reasons about images at patch level.", "Our key contribution is a bottleneck formulation in a VAE framework that encourages mid-level style representations.", "Our experiments demonstrate that representations learned by our method perform much better on the recognition tasks compared to those learned by vanilla VAEs.", "Due to the availability of large labeled visual datasets, supervised learning has become the dominant paradigm for visual recognition.", "That is, to learn about any new concept, the modus operandi is to collect thousands of labeled examples for that concept and train a powerful classifier, such as a deep neural network.", "This is necessary because the current generation of models based on deep neural networks require large amounts of labeled data (Sun et al., 2017) .", "This is in stark contrast to the insights that we have from developmental psychology on how infants develop perception and cognition without any explicit supervision (Smith & Gasser, 2005) .", "Moreover, the supervised learning paradigm is ill-suited for applications, such as health care and robotics, where annotated data is hard to obtain either due to privacy concerns or high cost of expert human annotators.", "In such cases, learning from very few labeled images or discovering underlying natural patterns in large amounts of unlabeled data can have a large number of potential applications.", "Discovering such patterns from unlabeled data is the standard setup of unsupervised learning.", "Over the past few years, the field of unsupervised learning in computer vision has followed two seemingly different tracks with different goals: generative modeling and self-supervised learning.", "The goal of generative modeling is to learn the probability distribution from which data was generated, given some training data.", "A learned model can draw samples from the same distribution or evaluate the likelihoods of new data.", "Generative models are also useful for learning compact representation of images.", "However, we argue that these representations are not as useful for visual recognition.", "This is not surprising since the task of reconstructing images does not require the bottleneck representation to sort out meaningful data useful for recognition and discard the rest; on the contrary, it encourages preserving as much information as possible for reconstruction.", "In comparison, the goal in selfsupervised learning is to learn representations that are useful for recognition.", "The standard paradigm is to establish proxy tasks that don't require human-supervision but can provide signals useful for recognition.", "Due to the mismatch in goals of unsupervised learning for visual recognition and the representations learned from generative modeling, self-supervised learning is a more popular way of learning representations from unlabeled data.", "However, fundamental limitation of this self-supervised paradigm is that we need to define a proxy-task that can mimic the desired recognition.", "It is not always possible to establish such a task, nor are these tasks generalizable across recognition tasks.", "In this paper, we take the first steps towards enabling the unsupervised generative modeling approach of VAEs to learn representations useful for recognition.", "Our key hypothesis is that for a representation to be useful, it should capture just the interesting parts of the images, as opposed to everything in the images.", "What constitutes an interesting image part has been defined and studied in earlier works that pre-date the end-to-end trained deep network methods Doersch et al., 2012; Juneja et al., 2013) .", "Taking inspiration from these works, we propose a novel representation that only encodes such few parts of an image that are repetitive across the dataset, i.e., the patches that occur often in images.", "By avoiding reconstruction of the entire image our method can focus on regions that are repeating and consistent across many images.", "In an encoder-decoder based generative model, we constrain the encoder architecture to learn such repetitive parts -both in terms of representations for appearance of these parts (or patches in an image) and where these parts occur.", "We formulate this using variational auto-encoder (β-VAEs) (Kingma & Welling, 2013; Matthey et al., 2017) , where we impose novel structure on the latent representations.", "We use discrete latents to model part presence or absence and continuous latents to model their appearance.", "We present this approach, PatchVAE, in Section 3 and demonstrate that it learns representations that are much better for recognition as compared to those learned by the standard β-VAEs (Kingma & Welling, 2013; Matthey et al., 2017) .", "In addition, we propose in Section 3.4 that losses that favor foreground, which is more likely to contain repetitive patterns, result in representations that are much better at recognition.", "In Section 4, we present results on CIFAR100 (Krizhevsky et al., 2009) , MIT Indoor Scene Recognition (Quattoni & Torralba, 2009) , Places (Zhou et al., 2017) , and ImageNet (Deng et al., 2009 ) datasets.", "Our contributions are as follows:", "• We propose a novel patch-based bottleneck in the VAE framework that learns representations that can encode repetitive parts across images.", "• We demonstrate that our method, PatchVAE, learns unsupervised representations that are better suited for recognition in comparison to traditional VAEs.", "• We show that losses that favor foreground are better for unsupervised learning of representations for recognition.", "• We perform extensive ablation analysis to understand the importance of different aspects of the proposed PatchVAE architecture.", "We presented a patch-based bottleneck in a VAE framework that encourages learning useful representations for recognition.", "Our method, PatchVAE, constrains the encoder architecture to only learn patches that are repetitive and consistent in images as opposed to learning everything, and therefore results in representations that perform much better for recognition tasks compared to vanilla VAEs.", "We also demonstrate that losses that favor high-energy foreground regions of an image are better for unsupervised learning of representations for recognition.", "6 APPENDIX 6.1 VISUALIZATION OF WEIGHTED LOSS Figure 3 shows an illustration of the reconstruction loss L w proposed in Section 3.4.", "Notice that in first column, guitar has more weight that rest of the image.", "Similarly in second, fourth and sixth columns that train, painting, and people are respectively weighed more heavily by L w than rest of the image; thus favoring capturing the foreground regions." ]

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[ "A patch-based bottleneck formulation in a VAE framework that learns unsupervised representations better suited for visual recognition." ]

[ "Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks (RNNs).", "In this paper, we present an efficient parametrization of the transition matrix of an RNN that allows us to stabilize the gradients that arise in its training.", "Specifically, we parameterize the transition matrix by its singular value decomposition (SVD), which allows us to explicitly track and control its singular values.", "We attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD.", "By explicitly controlling the singular values, our proposed svdRNN method allows us to easily solve the exploding gradient problem and we observe that it empirically solves the vanishing gradient issue to a large extent.", "We note that the SVD parameterization can be used for any rectangular weight matrix, hence it can be easily extended to any deep neural network, such as a multi-layer perceptron.", "Theoretically, we demonstrate that our parameterization does not lose any expressive power, and show how it potentially makes the optimization process easier.", "Our extensive experimental results also demonstrate that the proposed framework converges faster, and has good generalization, especially when the depth is large. \n", "Deep neural networks have achieved great success in various fields, including computer vision, speech recognition, natural language processing, etc.", "Despite their tremendous capacity to fit complex functions, optimizing deep neural networks remains a contemporary challenge.", "Two main obstacles are vanishing and exploding gradients, that become particularly problematic in Recurrent Neural Networks (RNNs) since the transition matrix is identical at each layer, and any slight change to it is amplified through recurrent layers BID3 ).Several", "methods have been proposed to solve the issue, for example, Long Short Term Memory (LSTM) BID8 ) and residual networks BID7 ). Another", "recently proposed class of methods is designed to enforce orthogonality of the square transition matrices, such as unitary and orthogonal RNNs (oRNN) BID1 ; BID13 ). However", ", while these methods solve the exploding gradient problem, they limit the expressivity of the network.In this paper, we present an efficient parametrization of weight matrices that arise in a deep neural network, thus allowing us to stabilize the gradients that arise in its training, while retaining the desired expressive power of the network. In more", "detail we make the following contributions:• We propose a method to parameterize weight matrices through their singular value decomposition (SVD). Inspired", "by BID13 ), we attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD. The SVD", "parametrization allows us to retain the desired expressive power of the network, while enabling us to explicitly track and control singular values.• We apply", "our SVD parameterization to recurrent neural networks to exert spectral constraints on the RNN transition matrix. Our proposed", "svdRNN method enjoys similar space and time complexity as the vanilla RNN. We empirically", "verify the superiority of svdRNN over RNN/oRNN, in some case even LSTMs, over an exhaustive collection of time series classification tasks and the synthetic addition and copying tasks, especially when the network depth is large.• Theoretically", ", we show how our proposed SVD parametrization can make the optimization process easier. Specifically,", "under a simple setting, we show that there are no spurious local minimum for the linear svdRNN in the population risk.• Our parameterization", "is general enough to eliminate the gradient vanishing/exploding problem not only in RNNs, but also in various deep networks. We illustrate this by", "applying SVD parametrization to problems with non-square weight matrices, specifically multi-layer perceptrons (MLPs) and residual networks.We now present the outline of our paper. In Section 2, we discuss", "related work, while in Section 3 we introduce our SVD parametrization and demonstrate how it spans the whole parameter space and does not limit expressivity. In Section 4 we propose", "the svdRNN model that is able to efficiently control and track the singular values of the transition matrices, and we extend our parameterization to non-square weight matrices and apply it to MLPs in Section 5. Section 6 provides the", "optimization landscape of svdRNN by showing that linear svdRNN has no spurious local minimum. Experimental results on", "MNIST and a popular time series archive are present in Section 7. Finally, we present our", "conclusions and future work in Section 8.", "In this paper, we have proposed an efficient SVD parametrization of various weight matrices in deep neural networks, which allows us to explicitly track and control their singular values.", "This parameterization does not restrict the network's expressive power, while simultaneously allowing fast forward as well as backward propagation.", "The method is easy to implement and has the same time and space complexity as compared to original methods like RNN and MLP.", "The ability to control singular values helps in avoiding the gradient vanishing and exploding problems, and as we have empirically shown, gives good performance.", "Although we only showed examples in the RNN and MLP framework, our method is applicable to many more deep networks, such as Convolutional Networks etc.", "However, further experimentation is required to fully understand the influence of using different number of reflectors in our SVD parameterization.", "Also, the underlying structures of the image of M k1,k2 when k 1 , k 2 = 1 is a subject worth investigating.", "DISPLAYFORM0 Proof of Proposition 1.", "For n = 1, note that H 1 1 (u 1 ) = ±1.", "By setting u 1 = 0 if B 1,1 > 0 and u 1 = 0 otherwise, we have the factorization desired.Assume that the result holds for n = k, then for n = k + 1 set u k+1 = B 1 − B 1 e 1 .", "Here B 1 is the first column of B and e 1 = (1, 0, ..., 0) .", "Thus we have DISPLAYFORM1 , whereB ∈ R k×k .", "Note that H k+1 k+1 (u k+1 ) = I k+1 when u k+1 = 0 and the above still holds.", "By DISPLAYFORM2 is an upper triangular matrix with positive diagonal elements.", "Thus the result holds for any n by the theory of mathematical induction.A.2", "PROOF OF THEOREM 1 Proof.", "Observe that the image of M 1 is a subset of O(n), and we now show that the converse is also true.", "Given A ∈ O(n), by Proposition 1, there exists an upper triangular matrix R with positive diagonal elements, and an orthogonal matrix Q expressed as DISPLAYFORM3 , such that A = QR.", "Since A is orthogonal, we have A A = AA = I n , thus:A A = R Q QR = R R = I n ; Q AA Q = Q QRR Q Q = RR = I n Thus R is orthogonal and upper triangular matrix with positive diagonal elements.", "So R = I n and DISPLAYFORM4" ]

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[ "To solve the gradient vanishing/exploding problems, we proprose an efficient parametrization of the transition matrix of RNN that loses no expressive power, converges faster and has good generalization." ]

[ "Recent image style transferring methods achieved arbitrary stylization with input content and style images.", "To transfer the style of an arbitrary image to a content image, these methods used a feed-forward network with a lowest-scaled feature transformer or a cascade of the networks with a feature transformer of a corresponding scale.", "However, their approaches did not consider either multi-scaled style in their single-scale feature transformer or dependency between the transformed feature statistics across the cascade networks.", "This shortcoming resulted in generating partially and inexactly transferred style in the generated images.\n", "To overcome this limitation of partial style transfer, we propose a total style transferring method which transfers multi-scaled feature statistics through a single feed-forward process.", "First, our method transforms multi-scaled feature maps of a content image into those of a target style image by considering both inter-channel correlations in each single scaled feature map and inter-scale correlations between multi-scaled feature maps.", "Second, each transformed feature map is inserted into the decoder layer of the corresponding scale using skip-connection.", "Finally, the skip-connected multi-scaled feature maps are decoded into a stylized image through our trained decoder network.", "Recent image style transferring methodsJohnson et al. (2016) ; BID18 improved image generating speed up to sub-realtime processing by learning a feed-forward network of a single style or several fixed stylesDumoulin et al. (2017) .", "Huang et al.Huang & Belongie (2017) proposed an adaptive instance normalization layer (AdaIN) that adaptively transforms the statistics of an encoded content feature into that of a target style feature and they achieved style transferring into arbitrary input target style.", "However, they did not consider multi-scaled style characteristics of an imageGatys et al. (2016) but only a single scale feature in differentiating styles inside AdaIN layer.", "Li et al.Li et al. (2017b) proposed to use cascade networks that cumulatively transfer the multi-scaled style characteristics by using a network per scale as shown in FIG0", "(a).", "They also transformed correlation between channels of feature map by using their whitening and coloring transformer (WCT).", "However, their cascade scheme requires multiple feed-forward passes to produce a stylized image and it is not guaranteed that the transferred style through a network is preserved after going through the subsequent networks because of inter-scale dependency in the multi-scaled styles of an image.", "Therefore, transferring multi-scaled style without interference between scales is still remained to study.In this paper, we propose an improved feed-forward network structure ( FIG0 ) and a multi-scaled style transferring method, called total style transfer, to efficiently perform style transfer in all scales of feature maps through a single feed-forward pass.", "Our work has the following contributions.•", "Transforming both intra-scale and inter-scale statistics of multi-scaled feature map: There exist both of inter and intra-correlations in the encoded multi-scaled feature map as shown in fig.2 (", "b).", "Therefore, we match the second-order statistics, i.e., mean and covariance, of the encoded multi-scaled feature map considering the correlations not only between channels in each scale (intra-scale correlation) but also between scales (inter-scale correlation).", "Our feature transformer makes the transformed feature map closer to the target style feature map and this results in an output style closer to the target style.", "Figure 2: Correlation between channels in the multi-scaled feature map of the input image", "(a) extracted from the pre-trained VGG16 BID16 .", "The area corresponding to each scale of feature map is divided into red lines.", "In case of intra-scale feature transform, the diagonal rectangles on the correlation matrix are used.", "In case of inter-scale feature transform, entire region of the correlation matrix is considered.•", "Decoder learning with multi-scaled style loss: we use a multi-scaled style loss consistent to the feature transformer, i.e., mean and covariance loss between the concatenated feature map ( FIG1 ). Using", "our multi-scaled style loss allows the decoder network to generate an output image of co-occurring multi-scale patterns which is better style expression than independently occurring scale patterns on the image that the existing methods generated.• Multi-scaled", "style transfer with a single feed-forward network: we use skip-connections for each decoder layer as shown in FIG0 (b) to consider", "the transformed feature map as well as the decoded feature map. By doing this,", "the style of scale corresponding to the layer and the transferred multi-scaled style so far are optimally merged into the next layer. Therefore, our", "method transfers multi-scaled style through a feed-forward pass in a single network instead of multiple feed-forward passes of cascade networks ( FIG0 ) without considering inter-scale correlation.In the remained of this paper, we review previous works closely related to this work in Sec. 2, our multi-scaled style transforming method is described in Sec. 3, the effectiveness of our method is tested and proven by a bundle of experiments in Sec. 4, and this work is concluded in Sec. 5.", "In this paper, we proposed a total style transfer network that generates an image through a single feed-forward network by utilizing multi-scale features of content and style images.", "Our intra-scale feature transformer transfers multi-scale style characteristics of the target style image and our inter-scale feature transformer transfers even more style characteristics of inter-scale correlation into the content image.", "By using our intra/inter scale feature transform, our total style transfer network achieved the lowest style loss among the existing feed-forward network methods.", "In addition, we modified the feed-forward network structure by using skip-connections which make our decoder network to utilize all transformed multi-scale features.", "This modification allowed a single feed-forward network to generate image of multi-scaled style without using multiple feedforward networks of cascade scheme, and resulted in the reduced test time by 31% and memory consumption by 4% compared to cascade network scheme." ]

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[ "A paper suggesting a method to transform the style of images using deep neural networks." ]

[ "Beyond understanding what is being discussed, human communication requires an awareness of what someone is feeling.", "One challenge for dialogue agents is recognizing feelings in the conversation partner and replying accordingly, a key communicative skill that is trivial for humans.", "Research in this area is made difficult by the paucity of suitable publicly available datasets both for emotion and dialogues.", "This work proposes a new task for empathetic dialogue generation and EmpatheticDialogues, a dataset of 25k conversations grounded in emotional situations to facilitate training and evaluating dialogue systems.", "Our experiments indicate that dialogue models that use our dataset are perceived to be more empathetic by human evaluators, while improving on other metrics as well (e.g. perceived relevance of responses, BLEU scores), compared to models merely trained on large-scale Internet conversation data.", "We also present empirical comparisons of several ways to improve the performance of a given model by leveraging existing models or datasets without requiring lengthy re-training of the full model.", "Natural communication is frequently prompted by people sharing their feelings or circumstances.", "As examples, a recent study found that 80% of Twitter users seem to post mostly about themselves BID28 , and ELIZA BID44 , one of the earliest chatbots developed, focused on asking its conversational partners why they were feeling a certain way.", "Interacting in these conversations requires reacting to what people share with an understanding of others' implied feelings.", "For instance, while the crossed-out response in FIG0 is topically relevant, \"Congrats! That's great!\" is more natural because it acknowledges the underlying feelings of accomplishment.", "Responding to people in a way that is empathetic or that acknowledges how the other person feels is a desirable trait for a dialogue agent, but still a nontrivial communicative skill.", "It is also currently difficult to measure.", "Although recent work has used large-scale corpora to train reasonably fluent and engaging dialogue agents (e.g. BID24 ), existing chitchat dialogue benchmarks are not designed to capture whether those agents are responding in an empathetic way to implicit emotional cues.", "This may indeed be unlikely, given that the sources of Internet conversation data used for training are known to harbor aggressive and callous responses BID0 .This", "works aims to make it easier to evaluate machines' ability to respond in an empathetic way. We introduce", "a new task for dialogue systems to respond to people discussing everyday situations, based on EMPATHETICDIALOGUES, a novel dataset with 25k personal dialogues. Each dialogue", "is grounded in a specific situation where a speaker was feeling a given emotion, with a listener responding. The dataset is", "larger and contains a more extensive set of emotions than many similar emotion prediction datasets from other text domains such as BID34 , BID39 , BID26 , and BID11 . Previous dialogue", "datasets of a similar scale that include emotion labels BID19 BID11 come from crawled Table 1 : Two examples from EMPATHETICDIALOGUES training set. The first worker", "(the speaker) is given an emotion label and writes their own description of a situation when they've felt that way. Then, the speaker", "tells their story in a conversation with a second worker (the listener).Label: Afraid Situation", ": Speaker felt this when... \"I've been hearing noises around the house at night\" Conversation: Speaker: I've been hearing some strange noises around the house at night. Listener: oh no! That's", "scary! What do you", "think it is?", "Speaker: I don't know, that", "'s what's making me anxious. Listener: I'm sorry to hear", "that. I wish I could help you figure", "it out Label: Proud Situation: Speaker felt this when... \"I finally got that promotion at work! I have tried so hard for so long to get it!\" Conversation: Speaker: I finally", "got promoted today at work! Listener: Congrats! That's great", "! Speaker: Thank you", "! I've been trying", "to get it for a while", "now! Listener: That is quite an accomplishment", "and you should be proud! conversations extracted from settings that are quite different from a one-on-one conversation (educational dialogues for English learners for DAILYDIALOG, public social media content for BID11 ) and cover either a very limited or a very imbalanced set of emotions: only ≈ 5% of the DailyDialog utterances have a label other than 'none' or 'happy', and BID11 only labels 'happy', 'sad', and 'angry'. The open resource we propose consists of", "crowdsourced one-on-one conversations, and covers a large set of emotions in a balanced way.We then examine how to train a dialogue system that is more adept at responding to emotional cues. While a rule-based system can be built around", "mapping predicted emotions to responses, end-toend dialogue systems relying on neural networks and trained on conversation corpora BID36 BID42 BID35 BID3 BID24 BID48 offer the promise of better generalization to new contexts. Through an extensive set of experiments, we show", "that fine-tuning a dialogue agent on our dataset results in better performance on a novel empathetic dialogue task.The pretraining of the dialogue agent on Internet conversation data is the most time-consuming step of this pipeline, by an order of magnitude. To make it easier for practitioners to improve performance", "of a model on the empathetic task with minimal re-training while re-using existing resources, we compare various ways of supplementing a pretrained model with additional representations from external tasks, and show that even simplistic schemes can lead to better performance. The contributions of this work are thus threefold: 1) we release", "a novel empathetic dialogue dataset as a new benchmark", "; 2) we show that using this dataset for training can improve the performance", "of an end-to-end dialogue system on empathetic dialogue; and 3) we compare multiple ways to further improve performance with combined representations", "while not requiring onerous re-training.", "We introduce a new dataset of 25k dialogues grounded in situations prompted by specific emotion labels.", "Our experiments show that using this dataset to fine-tune conversation models leads to responses that are evaluated by humans as more empathetic, and that simple schemes to augment a fine-tuned model with an external pretrained classifier can lead to better performance without requiring onerous retraining.", "Future work will investigate how to use this dataset to model the Speaker, and how to integrate empathetic responding into more general dialogue when, for example, the needs for empathy have to be balanced with staying on topic or providing information (see Table 6 ).Other", "possible directions would be to see if this data can serve as additional weakly supervised data for more complex emotion-related tasks that look at emotion evolution or causality BID10 BID33 . We hope", "that our results and dataset will stimulate more research in the important direction of making dialog systems more empathetic. In TAB5", ", we include the exact percentage of emotion labels for the situation descriptions in our final dataset." ]

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[ "We improve existing dialogue systems for responding to people sharing personal stories, incorporating emotion prediction representations and also release a new benchmark and dataset of empathetic dialogues." ]

[ "Granger causality is a widely-used criterion for analyzing interactions in large-scale networks.", "As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality between nonlinearly interacting stochastic processes from their time series measurements.", "Our proposed approach relies on modeling the embedded nonlinearities in the measurements using a component-wise time series prediction model based on Statistical Recurrent Units (SRUs).", "We make a case that the network topology of Granger causal relations is directly inferrable from a structured sparse estimate of the internal parameters of the SRU networks trained to predict the processes’ time series measurements.", "We propose a variant of SRU, called economy-SRU, which, by design has considerably fewer trainable parameters, and therefore less prone to overfitting.", "The economy-SRU computes a low-dimensional sketch of its high-dimensional hidden state in the form of random projections to generate the feedback for its recurrent processing.", "Additionally, the internal weight parameters of the economy-SRU are strategically regularized in a group-wise manner to facilitate the proposed network in extracting meaningful predictive features that are highly time-localized to mimic real-world causal events.", "Extensive experiments are carried out to demonstrate that the proposed economy-SRU based time series prediction model outperforms the MLP, LSTM and attention-gated CNN-based time series models considered previously for inferring Granger causality.", "The physical mechanisms behind the functioning of any large-scale system can be understood in terms of the networked interactions between the underlying system processes.", "Granger causality is one widely-accepted criterion used in building network models of interactions between large ensembles of stochastic processes.", "While Granger causality may not necessarily imply true causality, it has proven effective in qualifying pairwise interactions between stochastic processes in a variety of system identification problems, e.g., gene regulatory network mapping (Fujita et al. (2007) ), and the mapping of human brain connectome (Seth et al. (2015) ).", "This perspective has given rise to the canonical problem of inferring pairwise Granger causal relationships between a set of stochastic processes from their time series measurements.", "At present, the vast majority of Granger causal inference methods adopt a model-based inference approach whereby the measured time series data is modeled using with a suitable parameterized data generative model whose inferred parameters ultimately reveal the true topology of pairwise Granger causal relationships.", "Such methods typically rely on using linear regression models for inference.", "However, as illustrated in the classical bivariate example by Baek & Brock (1992) , linear model-based Granger causality tests can fail catastrophically in the presence of even mild nonlinearities in the measurements, thus making a strong case for our work which tackles the nonlinearities in the measurements by exploring new generative models of the time series measurements based on recurrent neural networks.", "In this work, we addressed the problem of inferring pairwise Granger causal relationships between stochastic processes that interact nonlinearly.", "We showed that the such causality between the processes can be robustly inferred from the regularized internal parameters of the proposed eSRU-based recurrent models trained to predict the time series measurements of the individal processes.", "Future work includes:", "i Investigating the use of other loss functions besides the mean-square error loss which can capture the exogenous and instantaneous causal effects in a more realistic way.", "ii Incorporating unobserved confounding variables/processes in recurrent models.", "iii Inferring Granger causality from multi-rate time series measurements." ]

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[ "A new recurrent neural network architecture for detecting pairwise Granger causality between nonlinearly interacting time series. " ]

[ "Graph convolutional networks (GCNs) are powerful deep neural networks for graph-structured data.", "However, GCN computes nodes' representation recursively from their neighbors, making the receptive field size grow exponentially with the number of layers. ", "Previous attempts on reducing the receptive field size by subsampling neighbors do not have any convergence guarantee, and their receptive field size per node is still in the order of hundreds.", "In this paper, we develop a preprocessing strategy and two control variate based algorithms to further reduce the receptive field size.", "Our algorithms are guaranteed to converge to GCN's local optimum regardless of the neighbor sampling size.", "Empirical results show that our algorithms have a similar convergence speed per epoch with the exact algorithm even using only two neighbors per node.", "The time consumption of our algorithm on the Reddit dataset is only one fifth of previous neighbor sampling algorithms.", "Graph convolution networks (GCNs) BID1 generalize convolutional neural networks (CNNs) (LeCun et al., 1995) to graph structured data.", "The \"graph convolution\" operation applies same linear transformation to all the neighbors of a node, followed by mean pooling.", "By stacking multiple graph convolution layers, GCNs can learn nodes' representation by utilizing information from distant neighbors.", "GCNs have been applied to semi-supervised node classification BID1 , inductive node embedding (Hamilton et al., 2017a) , link prediction (Kipf & Welling, 2016; BID1 and knowledge graphs (Schlichtkrull et al., 2017) , outperforming multi-layer perceptron (MLP) models that do not use the graph structure and graph embedding approaches (Perozzi et al., 2014; Tang et al., 2015; Grover & Leskovec, 2016 ) that do not use node features.However, the graph convolution operation makes it difficult to train GCN efficiently.", "A node's representation at layer L is computed recursively by all its neighbors' representations at layer L − 1.", "Therefore, the receptive field of a single node grows exponentially with respect to the number of layers, as illustrated in FIG0 .", "Due to the large receptive field size, BID1 proposed training GCN by a batch algorithm, which computes the representation for all the nodes altogether.", "However, batch algorithms cannot handle large scale datasets because of their slow convergence and the requirement to fit the entire dataset in GPU memory.", "Hamilton et al. (2017a) made an initial attempt on developing stochastic algorithms to train GCNs, which is referred as neighbor sampling (NS) in this paper.", "Instead of considering all the neighbors, they randomly subsample D (l) neighbors at the l-th layer.", "Therefore, they reduce the receptive field size to l D (l) , as shown in FIG0 (b).", "They found that for two layer GCNs, keeping D (1) = 10 and D (2) = 25 neighbors can achieve comparable performance with the original model.", "However, there is no theoretical guarantee on the predictive performance of the model learnt by NS comparing with the original algorithm.", "Moreover, the time complexity of NS is still D(1) D (2) = 250 times larger than training an MLP, which is unsatisfactory.In this paper, we develop novel stochastic training algorithms for GCNs such that D (l) can be as low as two, so that the time complexity of training GCN is comparable with training MLPs.", "Our methods are built on two techniques.", "First, we propose a strategy which preprocesses the first graph convolution layer, so that we only need to consider all neighbors within L−1 hops instead of L hops.", "This is significant because most GCNs only have L = 2 layers BID1 ; Hamilton et al., 2017a) .", "Second, we develop two control variate (CV) based stochastic training algorithms.", "We show that our CV-based algorithms have lower variance than NS, and for GCNs without dropout, our algorithm provably converges to a local optimum of the model regardless of D (l) .We", "empirically test on six graph datasets, and show that our techniques significantly reduce the bias and variance of the gradient from NS with the same receptive field size. Our", "algorithm with D (l) = 2 achieves the same predictive performance with the exact algorithm in comparable number of epochs on all the datasets, while the training time is 5 times shorter on our largest dataset.", "The large receptive field size of GCN hinders its fast stochastic training.", "In this paper, we present a preprocessing strategy and two control variate based algorithms to reduce the receptive field size.", "Our algorithms can achieve comparable convergence speed with the exact algorithm even the neighbor sampling size D (l) = 2, so that the per-epoch cost of training GCN is comparable with training MLPs.", "We also present strong theoretical guarantees, including exact prediction and convergence to GCN's local optimum, for our control variate based algorithm.", "DISPLAYFORM0 H (l+1) DISPLAYFORM1 After one more epoch, all the activations h (l+1)CV,i,v are computed at least once for each v, soH DISPLAYFORM2 for all i > (l + 2)I.", "By induction, we know that after LI steps, we havē DISPLAYFORM3 2.", "We omit the time subscript i and denote DISPLAYFORM4 CV,v ).", "By back propagation, the approximated gradients by CV can be computed as follows DISPLAYFORM5 where • is the element wise product and σ (Z DISPLAYFORM6 CV ) is the element-wise derivative.", "Similarly, denote DISPLAYFORM7 v ), the exact gradients can be computed as follows DISPLAYFORM8 Applying EP = EP (1) ,...,P (L) to both sides of Eq. 8, and utilizing DISPLAYFORM9 we have DISPLAYFORM10 Comparing Eq. 10 and Eq. 9 we get DISPLAYFORM11" ]

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[ "A control variate based stochastic training algorithm for graph convolutional networks that the receptive field can be only two neighbors per node." ]

[ "Low bit-width integer weights and activations are very important for efficient inference, especially with respect to lower power consumption.", "We propose to apply Monte Carlo methods and importance sampling to sparsify and quantize pre-trained neural networks without any retraining.", "We obtain sparse, low bit-width integer representations that approximate the full precision weights and activations.", "The precision, sparsity, and complexity are easily configurable by the amount of sampling performed.", "Our approach, called Monte Carlo Quantization (MCQ), is linear in both time and space, while the resulting quantized sparse networks show minimal accuracy loss compared to the original full-precision networks.", "Our method either outperforms or achieves results competitive with methods that do require additional training on a variety of challenging tasks.", "Developing novel ways of increasing the efficiency of neural networks is of great importance due to their widespread usage in today's variety of applications.", "Reducing the network's footprint enables local processing on personal devices without the need for cloud services.", "In addition, such methods allow for reducing power consumption -also in data centers.", "Very compact models can be fully stored and executed on-chip in specialized hardware like for example ASICs or FPGAs.", "This reduces latency, increases inference speed, improves privacy concerns, and limits bandwidth cost.", "Quantization methods usually require re-training of the quantized model to achieve competitive results.", "This leads to an additional cost and complexity.", "The proposed method, Monte Carlo Quantization (MCQ), aims to avoid retraining by approximating the full-precision weight and activation distributions using importance sampling.", "The resulting quantized networks achieve close to the full-precision accuracy without any kind of additional training.", "Importantly, the complexity of the resulting networks is proportional to the number of samples taken.", "First, our algorithm normalizes the weights and activations of a given layer to treat them as probability distributions.", "Then, we randomly sample from the corresponding cumulative distributions and count the number of hits for every weight and activation.", "Finally, we quantize the weights and activations by their integer count values, which form a discrete approximation of the original continuous values.", "Since the quality of this approximation relies entirely on (quasi)random sampling, the accuracy of the quantized model is directly dependent on the amount of sampling performed.", "Thus, accuracy may be traded for higher sparsity and speed by adjusting the number of samples.", "On the challenging tasks of image classification, language modeling, speech recognition, and machine translation, our method outperforms or is competitive with existing quantization methods that do require additional training.", "The experimental results show the performance of MCQ on multiple models, datasets, and tasks, demonstrated by the minimal loss of accuracy compared to the full-precision counterparts.", "MCQ either outperforms or is competitive to other methods that require additional training of the quantized network.", "Moreover, the trade-off between accuracy, sparsity, and bit-width can be easily controlled by adjusting the number of samples.", "Note that the complexity of the resulting quantized network is proportional to the number of samples in both space and time.", "One limitation of MCQ, however, is that it often requires a higher number of bits to represent the quantized values.", "On the other hand, this sampling-based approach directly translates to a good approximation of the real full-precision values without any additional training.", "Recently Zhao et al. (2019) proposed to outlier channel splitting, which is orthogonal work to MCQ and could be used to reduce the bit-width required for the highest hit counts.", "There are several paths that could be worth following for future investigations.", "In the importance sampling stage, using more sophisticated metrics for importance ranking, e.g. approximation of the Hessian by Taylor expansion could be beneficial (Molchanov et al., 2016) .", "Automatically selecting optimal sampling levels on each layer could lead to a lower cost since later layers seem to tolerate more sparsity and noise.", "For efficient hardware implementation, it's important that the quantized Figure 4: Results of quantizing both weights and activations on ImageNet using different sampling amounts.", "All quantized models reach close to full-precision accuracy at K = 3.", "Table 4 : Evaluation of MCQ on language modeling, speech recognition, and machine translation.", "All quantized models reach close to full precision performance.", "Note that, as opposed to the image classification task, we did not study different sampling amounts nor the effect of quantization on specific network layers.", "A more in-depth analysis could then help to achieve close to full-precision accuracy at a lower bit-width on these additional models.", "network can be executed using integer operations only.", "Bias quantization and rescaling, activation rescaling to prevent overflow or underflow, and quantization of errors and gradients for efficient training leave room for future work.", "In this work, we showed that Monte Carlo sampling is an effective technique to quickly and efficiently convert floating-point, full-precision models to integer, low bit-width models.", "Computational cost and sparsity can be traded for accuracy by adjusting the number of sampling accordingly.", "Our method is linear in both time and space in the number of weights and activations, and is shown to achieve similar results as the full-precision counterparts, for a variety of network architectures, datasets, and tasks.", "In addition, MCQ is very easy to use for quantizing and sparsifying any pre-trained model.", "It requires only a few additional lines of code and runs in a matter of seconds depending on the model size, and requires no additional training.", "The use of sparse, low-bitwidth integer weights and activations in the resulting quantized networks lends itself to efficient hardware implementations.", "A ALGORITHM An overview of the proposed method is given in Algorithm 1.", "Input: Pre-trained full-precision network Output: Quantized network with integer weights for K=0 to L-1 do", "// Update layer's precision B W K ← 1 + f loor(log 2 (max(abs(W K )))) + 1 ; end Algorithm 1: Monte Carlo Quantization (MCQ) on network weights.", "L represents the number of trainable layers, K indicates the percentage of samples to be sampled per weight.", "The process is performed equivalently for quantizing activations at inference time.", "Our algorithm is linear in both time and space in the number of weights and activations." ]

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[ "Monte Carlo methods for quantizing pre-trained models without any additional training." ]

[ "We propose the Information Maximization Autoencoder (IMAE), an information theoretic approach to simultaneously learn continuous and discrete representations in an unsupervised setting.", "Unlike the Variational Autoencoder framework, IMAE starts from a stochastic encoder that seeks to map each input data to a hybrid discrete and continuous representation with the objective of maximizing the mutual information between the data and their representations.", "A decoder is included to approximate the posterior distribution of the data given their representations, where a high fidelity approximation can be achieved by leveraging the informative representations. \n", "We show that the proposed objective is theoretically valid and provides a principled framework for understanding the tradeoffs regarding informativeness of each representation factor, disentanglement of representations, and decoding quality.", "A central tenet for designing and learning a model for data is that the resulting representation should be compact yet informative.", "Therefore, the goal of learning can be formulated as finding informative representations about the data under proper constraints.", "Generative latent variable models are a popular approach to this problem, where a model parameterized by θ of the form p θ (x) = p θ (x|z)p(z)dz is used to represent the relationship between the data x and the low dimensional latent variable z.", "The model is optimized by fitting the generative data distribution p θ (x) to the training data distribution p(x), which involves maximizing the likelihood for θ.", "Typically, this model is intractable even for moderately complicated functions p θ (x|z) with continuous z.", "To remedy this issue, variational autoencoder (VAE) BID13 BID19 proposes to maximize the evidence lower bound (ELBO) of the marginal likelihood objective.However, as was initially pointed out in BID10 , maximizing ELBO also penalizes the mutual information between data and their representations.", "This in turn makes the representation learning even harder.", "Many recent efforts have focused on resolving this problem by revising ELBO.", "Generally speaking, these works fall into two lines.", "One of them targets \"disentangled representations\" by encouraging the statistical independence between representation components BID9 BID12 BID8 BID4 BID7 , while the other line of work seeks to control or encourage the mutual information between data and their representations BID16 BID3 BID1 BID6 Zhao et al., 2017) .", "However, these approaches either result in an invalid lower bound for the VAE objective or cannot avoid sacrificing the mutual information.Instead of building upon the generative latent variable model, we start with a stochastic encoder p θ (z|x) and aim at maximizing the mutual information between the data x and its representations z.", "In this setting, a reconstruction or generating phase can be obtained as the variational inference of the true posterior p θ (x|z).", "By explicitly seeking for informative representations, the proposed model yields better decoding quality.", "Moreover, we show that the information maximization objective naturally induces a balance between the informativeness of each latent factor and the statistical independence between them, which gives a more principled way to learn semantically meaningful representations without invalidating ELBO or removing individual terms from it.Another contribution of this work is proposing a framework for simultaneously learning continuous and discrete representations for categorical data.", "Categorical data are ubiquitous in real-world tasks, where using a hybrid discrete and continuous representation to capture both categorical information and continuous variation in data is more consistent with the natural generation process.", "In this work, we focus on categorical data that are similar in nature, i.e., where different categories still share similar variations (features).", "We seek to learn semantically meaningful discrete representations while maintaining disentanglement of the continuous representations that capture the variations shared across categories.", "We show that, compared to the VAE based approaches, our proposed objective gives a more natural yet effective way for learning these hybrid representations.", "We have proposed IMAE, a novel approach for simultaneously learning the categorical information of data while uncovering latent continuous features shared across categories.", "Different from VAE, IMAE starts with a stochastic encoder that seeks to maximize the mutual information between data and their representations, where a decoder is used to approximate the true posterior distribution of the data given the representations.", "This model targets at informative representations directly, which in turn naturally yields an objective that is capable of simultaneously inducing semantically meaningful representations and maintaining good decoding quality, which is further demonstrated by the numerical results.Unsupervised joint learning of disentangled continuous and discrete representations is a challenging problem due to the lack of prior for semantic awareness and other inherent difficulties that arise in learning discrete representations.", "This work takes a step towards achieving this goal.", "A limitation of our model is that it pursues disentanglement by assuming or trying to encourage independent scalar latent factors, which may not always be sufficient for representing the real data.", "For example, data may exhibit category specific variation, or a subset of latent factors might be correlated.", "This motivates us to explore more structured disentangled representations; one possible direction is to encourage group independence.", "We leave this for future work.H.", "Xiao, K. Rasul, and R. Vollgraf.", "Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms, 2017.S.", "Zhao, J. Song, and S. Ermon.", "Infovae: Information maximizing variational autoencoders.", "arXiv preprint arXiv:1706.02262, 2017." ]

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[ "Information theoretical approach for unsupervised learning of unsupervised learning of a hybrid of discrete and continuous representations, " ]

[ "Learning rules for neural networks necessarily include some form of regularization.", "Most regularization techniques are conceptualized and implemented in the space of parameters.", "However, it is also possible to regularize in the space of functions.", "Here, we propose to measure networks in an $L^2$ Hilbert space, and test a learning rule that regularizes the distance a network can travel through $L^2$-space each update. ", "This approach is inspired by the slow movement of gradient descent through parameter space as well as by the natural gradient, which can be derived from a regularization term upon functional change.", "The resulting learning rule, which we call Hilbert-constrained gradient descent (HCGD), is thus closely related to the natural gradient but regularizes a different and more calculable metric over the space of functions.", "Experiments show that the HCGD is efficient and leads to considerably better generalization.", "Large neural networks can overfit to training data, but we desire networks that instead learn general aspects that apply to new data.", "A learning rule can encourage generalization through regularization, which may be implicit to the learning rule or explicitly added to the cost function.", "Many regularization techniques introduce penalties in the space of network parameters.", "Canonical examples include weight decay and the constraints upon parameter movement inherent to Stochastic Gradient Descent (SGD).", "Ultimately, however, it is the complexity of the parameterized function that we seek to regularize, not pf the parameters themselves.", "A well-known example of this more direct approach is the natural gradient, which constrains how much the output distribution of a network can change due to an update.Here, we introduce a new learning rule that, like the natural gradient, limits how much the output function can change during learning.", "However, we use a different and more calculable metric over function space: the expected L 2 norm.", "Since the L 2 -space is a Hilbert space, we term the rule Hilbert-constrained gradient descent (HCGD).The", "interpretation of the natural gradient as resulting from regularization competes in the literature with many other interpretations and justifications. In", "order to establish a foundation for the Hilbert constraint as analogous to the natural gradient, we begin by reviewing and discussing the natural gradient.", "Neural networks encode functions, and it is important to consider the behavior of optimizers through the space of possible functions.", "The L 2 Hilbert space defined over distribution of input examples is a tractable and useful space for analysis.", "In this paper we propose to regularize the change in L 2 space between successive updates.", "The idea is to limit the movement of the function, just as gradient descent limits movement of the parameters.", "Our resulting learning rule, Hilbert-constrained gradient descent (HCGD), increases test performance on standard image classification architectures.", "We hope that this work inspires more thought and analysis of behavior in L 2 -space.A alternative explanation of our algorithm is that it penalizes directions that are very sensitive controls of the outputs, similar to the natural gradient, while still allowing learning.", "In addition, since we evaluate the change in L 2 -space and the gradient on different data, HCGD asks the model to learn from current examples only in ways that will not affect what has already been learned from other examples.", "These intuitions are equivalent to the idea of limiting changes in L 2 -space.Given these empirical results, it would be desirable to theoretically prove better generalization bounds for a method regularized in L 2 -space.", "One promising framework is stability analysis, which has recently been applied to establish some bounds on the generalization error of SGD itself BID7 ).", "It can be shown that generalization error is bounded by the stability of an algorithm, defined as the expected difference of the loss when two networks are trained on datasets that are identical except for one example.", "BID7 analyzes the stability of SGD in parameter space, then uses a Lipschitz condition to move to function space and bound the stability of the error.", "We expect that bounding the movement through L 2 -space leads to increased error stability compared to bounding movement through parameter space (as is done by SGD), simply by removing reliance on the assumed Lipschitz condition.", "We leave a proof of this idea to later work.It interesting to ask if there is support in neuroscience for learning rules that diminish the size of changes when that change would have a large effect on other tasks.", "It is unlikely that the nervous system performs precisely the natural gradient or HCGD, but there is some evidence that some analog is in play.", "One otherwise perplexing finding is that behavioral learning rates in motor tasks are dependent on the direction of an error but independent of the magnitude of that error BID6 ).", "This result is not expected by most models of gradient descent, but would be expected if the size of the change in the output distribution (i.e. behavior) were regulated to be constant.", "Regularization upon behavior change (rather than synaptic change) would predict that neurons that are central to many actions, like neurons in motor pools of the spinal cord, would learn very slowly after early development, despite the fact that their gradient to the error on any one task (if indeed it is calculated) is likely to be quite large.", "Given our general resistance to overfitting during learning, and the great variety of roles of neurons, it is likely that some type of regularization of behavioral and perceptual change is at play." ]

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[ "It's important to consider optimization in function space, not just parameter space. We introduce a learning rule that reduces distance traveled in function space, just like SGD limits distance traveled in parameter space." ]

[ "Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization.", "Research on SGD resurged recently in machine learning for optimizing convex loss functions and training nonconvex deep neural networks.", "The theory assumes that one can easily compute an unbiased gradient estimator, which is usually the case due to the sample average nature of empirical risk minimization.", "There exist, however, many scenarios (e.g., graphs) where an unbiased estimator may be as expensive to compute as the full gradient because training examples are interconnected.", "Recently, Chen et al. (2018) proposed using a consistent gradient estimator as an economic alternative.", "Encouraged by empirical success, we show, in a general setting, that consistent estimators result in the same convergence behavior as do unbiased ones.", "Our analysis covers strongly convex, convex, and nonconvex objectives.", "We verify the results with illustrative experiments on synthetic and real-world data.", "This work opens several new research directions, including the development of more efficient SGD updates with consistent estimators and the design of efficient training algorithms for large-scale graphs.\n", "Consider the standard setting of supervised learning.", "There exists a joint probability distribution P (x, y) of data x and associated label y and the task is to train a predictive model, parameterized by w, that minimizes the expected loss between the prediction and the ground truth y.", "Let us organize the random variables as ξ = (x, y) and use the notation (w; ξ) for the loss.", "If ξ i = (x i , y i ), i = 1, . . . , n, are iid training examples drawn from P , then the objective function is either one of the following well-known forms: expected risk f (w) = E[ (w; ξ)]; empirical risk f (w) = 1 n n i=1 (w; ξ i ).", "Stochastic gradient descent (SGD), which dates back to the seminal work of Robbins & Monro (1951) , has become the de-facto optimization method for solving these problems in machine learning.", "In SGD, the model parameter is updated until convergence with the rule", "where γ k is a step size and g k is an unbiased estimator of the gradient ∇f (w k ).", "Compared with the full gradient (as is used in deterministic gradient descent), an unbiased estimator involves only one or a few training examples ξ i and is usually much more efficient to compute." ]

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[ "Convergence theory for biased (but consistent) gradient estimators in stochastic optimization and application to graph convolutional networks" ]

[ "We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification.", "In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the classification problem at hand.", "We demonstrate that such techniques tend to introduce biased estimates for instances whose predictions are supposed to be highly confident.", "We argue that this deficiency is an artifact of the dynamics of training with SGD-like optimizers, and it has some properties similar to overfitting.", "Based on this observation, we develop an uncertainty estimation algorithm that selectively estimates the uncertainty of highly confident points, using earlier snapshots of the trained model, before their estimates are jittered (and way before they are ready for actual classification).", "We present extensive experiments indicating that the proposed algorithm provides uncertainty estimates that are consistently better than all known methods.", "The deployment of deep learning models in applications with demanding decision-making components such as autonomous driving or medical diagnosis hinges on our ability to monitor and control their statistical uncertainties.", "Conceivably, the Bayesian framework offers a principled approach to infer uncertainties from a model; however, there are computational hurdles in implementing it for deep neural networks BID9 .", "Presently, practically feasible (say, for image classification) uncertainty estimation methods for deep learning are based on signals emerging from standard (non Bayesian) networks that were trained in a standard manner.", "The most common signals used for uncertainty estimation are the raw softmax response BID4 , some functions of softmax values (e.g., entropy), signals emerging from embedding layers BID20 , and the MC-dropout method BID9 ) that proxies a Bayesian inference using dropout sampling applied at test time.", "These methods can be quite effective, but no conclusive evidence on their relative performance has been reported.", "A recent NIPS paper provides documentation that an ensemble of softmax response values of several networks performs better than the other approaches BID17 .In", "this paper, we present a method of confidence estimation that can consistently improve all the above methods, including the ensemble approach of BID17 . Given", "a trained classifier and a confidence score function (e.g., generated by softmax response activations), our algorithm will learn an improved confidence score function for the same classifier. Our approach", "is based on the observation that confidence score functions extracted from ordinary deep classifiers tend to wrongly estimate confidence, especially for highly confident instances. Such erroneous", "estimates constitute a kind of artifact of the training process with an stochastic gradient descent (SGD) based optimizers. During this process", ", the confidence in \"easy\" instances (for which we expect prediction with high confidence) is quickly and reliably assessed during the early SGD epochs. Later on, when the", "optimization is focused on the \"hard\" points (whose loss is still large), the confidence estimates of the easy points become impaired.Uncertainty estimates are ultimately provided in terms of probabilities. Nevertheless, as previously", "suggested BID10 BID20 BID17 , in a non-Bayesian setting (as we consider here) it is productive to decouple uncertainty estimation into two separate tasks: ordinal ranking according to uncertainty, and probability calibration. Noting that calibration (of", "ordinal confidence ranking) already has many effective solutions BID21 BID23 BID27 BID11 , our main focus here is on the core task of ranking uncertainties. We thus adopt the setting of", "BID17 , and others BID10 BID20 , and consider uncertainty estimation for classification as the following problem. Given labeled data, the goal", "is to learn a pair (f, κ), where f (x) is a classifier and κ(x) is a confidence score function. Intuitively, κ should assign", "lower confidence values to points that are misclassified by f , relative to correct classifications (see Section 2 for details).We propose two methods that can", "boost known confidence scoring functions for deep neural networks (DNNs). Our first method devises a selection", "mechanism that assigns for each instance an appropriate early stopped model, which improves that instance's uncertainty estimation. The mechanism selects the early-stopped", "model for each individual instance from among snapshots of the network's weights that were saved during the training process. This method requires an auxiliary training", "set to train the selection mechanism, and is quite computationally intensive to train. The second method approximates the first without", "any additional examples. Since there is no consensus on the appropriate performance", "measure for scoring functions, we formulate such a measure based on concepts from selective prediction BID10 BID26 . We report on extensive experiments with four baseline methods", "(including all those mentioned above) and four image datasets. The proposed approach consistently improves all baselines, often", "by a wide margin. For completeness, we also validate our results using probably-calibrated", "uncertainty estimates of our method that are calibrated with the well-known Platt scaling technique BID23 and measured with the negative log-likelihood and Brier score Brier (1950)." ]

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[ "We use snapshots from the training process to improve any uncertainty estimation method of a DNN classifier." ]

[ "Existing public face image datasets are strongly biased toward Caucasian faces, and other races (e.g., Latino) are significantly underrepresented.", "The models trained from such datasets suffer from inconsistent classification accuracy, which limits the applicability of face analytic systems to non-White race groups.", "To mitigate the race bias problem in these datasets, we constructed a novel face image dataset containing 108,501 images which is balanced on race.", "We define 7 race groups: White, Black, Indian, East Asian, Southeast Asian, Middle Eastern, and Latino.", "Images were collected from the YFCC-100M Flickr dataset and labeled with race, gender, and age groups.", "Evaluations were performed on existing face attribute datasets as well as novel image datasets to measure the generalization performance.", "We find that the model trained from our dataset is substantially more accurate on novel datasets and the accuracy is consistent across race and gender groups.", "We also compare several commercial computer vision APIs and report their balanced accuracy across gender, race, and age groups.", "To date, numerous large scale face image datasets (Huang et al., 2007; Kumar et al., 2011; Escalera et al., 2016; Yi et al., 2014; Liu et al., 2015; Joo et al., 2015; Parkhi et al., 2015; Guo et al., 2016; Kemelmacher-Shlizerman et al., 2016; Rothe et al., 2016; Cao et al., 2018; Merler et al., 2019) have been proposed and fostered research and development for automated face detection (Li et al., 2015b; Hu & Ramanan, 2017) , alignment (Xiong & De la Torre, 2013; Ren et al., 2014) , recognition (Taigman et al., 2014; Schroff et al., 2015) , generation (Yan et al., 2016; Bao et al., 2017; Karras et al., 2018; Thomas & Kovashka, 2018) , modification (Antipov et al., 2017; Lample et al., 2017; He et al., 2017) , and attribute classification (Kumar et al., 2011; Liu et al., 2015) .", "These systems have been successfully translated into many areas including security, medicine, education, and social sciences.", "Despite the sheer amount of available data, existing public face datasets are strongly biased toward Caucasian faces, and other races (e.g., Latino) are significantly underrepresented.", "A recent study shows that most existing large scale face databases are biased towards \"lighter skin\" faces (around 80%), e.g. White, compared to \"darker\" faces, e.g. Black (Merler et al., 2019) .", "This means the model may not apply to some subpopulations and its results may not be compared across different groups without calibration.", "Biased data will produce biased models trained from it.", "This will raise ethical concerns about fairness of automated systems, which has emerged as a critical topic of study in the recent machine learning and AI literature (Hardt et al., 2016; Corbett-Davies et al., 2017) .", "For example, several commercial computer vision systems (Microsoft, IBM, Face++) have been criticized due to their asymmetric accuracy across sub-demographics in recent studies (Buolamwini & Gebru, 2018; Raji & Buolamwini, 2019) .", "These studies found that the commercial face gender classification systems all perform better on male and on light faces.", "This can be caused by the biases in their training data.", "Various unwanted biases in image datasets can easily occur due to biased selection, capture, and negative sets (Torralba & Efros, 2011) .", "Most public large scale face datasets have been collected from popular online media -newspapers, Wikipedia, or web search-and these platforms are more frequently used by or showing White people.", "To mitigate the race bias in the existing face datasets, we propose a novel face dataset with an emphasis on balanced race composition.", "Our dataset contains 108,501 facial images collected primarily from the YFCC-100M Flickr dataset (Thomee et al.) , which can be freely shared for a research purpose, and also includes examples from other sources such as Twitter and online newspaper outlets.", "We define 7 race groups: White, Black, Indian, East Asian, Southeast Asian, Middle Eastern, and Latino.", "Our dataset is well-balanced on these 7 groups (See Figures 1 and 2) Our paper makes three main contributions.", "First, we emprically show that existing face attribute datasets and models learned from them do not generalize well to unseen data in which more nonWhite faces are present.", "Second, we show that our new dataset performs better on novel data, not only on average, but also across racial groups, i.e. more consistently.", "Third, to the best of our knowledge, our dataset is the first large scale face attribute dataset in the wild which includes Latino and Middle Eastern and differentiates East Asian and Southeast Asian.", "Computer vision has been rapidly transferred into other fields such as economics or social sciences, where researchers want to analyze different demographics using image data.", "The inclusion of major racial groups, which have been missing in existing datasets, therefore significantly enlarges the applicability of computer vision methods to these fields.", "This paper proposes a novel face image dataset balanced on race, gender and age.", "Compared to existing large-scale in-the-wild datasets, our dataset achieves much better generalization classification performance for gender, race, and age on novel image datasets collected from Twitter, international online newspapers, and web search, which contain more non-White faces than typical face datasets.", "We show that the model trained from our dataset produces balanced accuracy across race, whereas other datasets often lead to asymmetric accuracy on different race groups.", "This dataset was derived from the Yahoo YFCC100m dataset (Thomee et al.) for the images with Creative Common Licenses by Attribution and Share Alike, which permit both academic and commercial usage.", "Our dataset can be used for training a new model and verifying balanced accuracy of existing classifiers.", "Algorithmic fairness is an important aspect to consider in designing and developing AI systems, especially because these systems are being translated into many areas in our society and affecting our decision making.", "Large scale image datasets have contributed to the recent success in computer vision by improving model accuracy; yet the public and media have doubts about its transparency.", "The novel dataset proposed in this paper will help us discover and mitigate race and gender bias present in computer vision systems such that such systems can be more easily accepted in society.", "A APPENDIX Figure 5: Individual Typology Angle (ITA), i.e. skin color, distribution of different races measured in our dataset." ]

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[ "A new face image dataset for balanced race, gender, and age which can be used for bias measurement and mitigation" ]

[ "Dramatic advances in generative models have resulted in near photographic quality for artificially rendered faces, animals and other objects in the natural world.", "In spite of such advances, a higher level understanding of vision and imagery does not arise from exhaustively modeling an object, but instead identifying higher-level attributes that best summarize the aspects of an object. ", "In this work we attempt to model the drawing process of fonts by building sequential generative models of vector graphics. ", "This model has the benefit of providing a scale-invariant representation for imagery whose latent representation may be systematically manipulated and exploited to perform style propagation.", "We demonstrate these results on a large dataset of fonts and highlight how such a model captures the statistical dependencies and richness of this dataset.", "We envision that our model can find use as a tool for designers to facilitate font design.", "moveTo (15, 25) lineTo (-2, 0.", "3) cubicBezier (-7.4, 0.", "2) (-14.5, 11.7), (-12.1, 23.4) ... (Ferraiolo, 2001 ) that enables such manipulations.", "All images are samples from this generative model.The last few years have witnessed dramatic advances in generative models of images that produce near photographic quality imagery of human faces, animals, and natural objects (Radford et al., 2015; Goodfellow et al., 2014; Brock et al., 2018; Karras et al., 2018; Kingma & Dhariwal, 2018) .", "These models provide an exhaustive characterization of natural image statistics (Simoncelli & Olshausen, 2001 ) and represent a significant advance in this domain.", "However, these advances in image synthesis ignore an important facet of how humans interpret raw visual information (Reisberg & Snavely, 2010) , namely that humans seem to exploit structured representations of visual concepts (Lake et al., 2017; Hofstadter, 1995) .", "Structured representations may be readily employed to aid generalization and efficient learning by identifying higher level primitives for conveying visual information (Lake et al., 2015) or provide building blocks for creative exploration (Hofstadter, 1995; Hofstadter & McGraw, 1993) .", "This may be best seen in human drawing, where techniques such as gesture drawing emphasize parsimony for capturing higher level semantics and actions with minimal graphical content (Stanchfield, 2007) .In", "this work, we focus on an subset of this domain where we think we can make progress and improve the generality of the approach. Font", "generation represents a 30 year old problem posited as a constrained but diverse domain for understanding high level perception and creativity (Hofstadter, 1995) . Early", "research attempted to heuristically systematize the creation of fonts for expressing the identity of characters (e.g. a, 2) as", "well as stylistic elements constituting the \"spirit\" of a font (Hofstadter & McGraw, 1993) . Despite", "providing great inspiration, the results were limited by a reliance on heuristics and a lack of a learned, structured representation (Rehling, 2001) . Subsequent", "work for learning font representations focused on models with simple parameterizations (Lau, 2009), template matching (Suveeranont & Igarashi, 2010) , example-based hints (Zongker et al., 2000) , or more recently, learning manifolds for geometric annotations (Campbell & Kautz, 2014) .We instead", "frame the problem of generating fonts by specifying it with Scalable Vector Graphics (SVG) -a common file format for fonts, human drawings, designs and illustrations (Ferraiolo, 2001) . SVGs are a", "compact, scale-invariant representation that may be rendered on most web browsers. SVGs specify", "an illustration as a sequence of a higher-level commands paired with numerical arguments FIG0 . We take inspiration", "from the literature on generative models of images in rasterized pixel space (Graves, 2013; Van den Oord et al., 2016) . Such models provide", "powerful auto-regressive formulations for discrete, sequential data (Hochreiter & Schmidhuber, 1997; Graves, 2013; Van den Oord et al., 2016) and may be applied to rasterized renderings of drawings (Ha & Eck, 2017) . We extend these approaches", "to the generation of sequences of SVG commands for the inference of individual font characters. The goal of this work is to", "build a tool to learn a representation for font characters and style that may be extended to other artistic domains (Clouâtre & Demers, 2019; Sangkloy et al., 2016; Ha & Eck, 2017) , or exploited as an intelligent assistant for font creation (Carter & Nielsen, 2017) .Our main contributions are:", "1) Build a generative model", "for scalable vector graphics (SVG) images and apply this to a large-scale dataset of 14 M font characters. 2) Demonstrate that the generative", "model provides a latent representation of font styles that captures a large amount of diversity and is consistent across individual characters. 3) Exploit the latent representation", "from the model to infer complete SVG fontsets from a single character. 4) Identify semantically meaningful", "directions in the latent representation to globally manipulate font style.", "In the work we presented a generative model for vector graphics.", "This model has the benefit of providing a scale-invariant representation for imagery whose latent representation may be systematically manipulated and exploited to perform style propagation.", "We demonstrate these results on a large dataset of fonts and highlight the limitations of a sequential, stochastic model for capturing the statistical dependencies and richness of this dataset.", "Even in its present form, the current model may be employed as an assistive agent for helping humans design fonts in a more time-efficient manner (Carter & Nielsen, 2017; Rehling, 2001 )." ]

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[ "We attempt to model the drawing process of fonts by building sequential generative models of vector graphics (SVGs), a highly structured representation of font characters." ]

[ "What can we learn about the functional organization of cortical microcircuits from large-scale recordings of neural activity? ", "To obtain an explicit and interpretable model of time-dependent functional connections between neurons and to establish the dynamics of the cortical information flow, we develop 'dynamic neural relational inference' (dNRI).", "We study both synthetic and real-world neural spiking data and demonstrate that the developed method is able to uncover the dynamic relations between neurons more reliably than existing baselines.", "Extraction of latent temporal dynamics in complex networks is important to understand their functional connectivity and to predict their behavior.", "Recently, various machine learning methods were used to encode/decode the behavior from recorded activity of large neuronal populations [2, 3] .", "However, in these mostly 'static' brain models the temporal dynamics of the firing activity as well as interactions between different neurons are often neglected.", "It is expected, however, that the dynamic interactions in neural networks might be the key to understanding the brain computations.", "Addressing this, several methods have been proposed to uncover low-dimensional latent representations of neural network activity and its dynamics, including dimensionality reduction-based techniques such as principal components analysis [1] and tensor components analysis [14] , pattern extraction techniques based on matrix factorization such as ConvNMF [11] and SeqNMF [7] , and autoencoder models such as LFADS [9] .", "However, temporal correlations between individual neurons in the network are often only modeled implicitly, hindering reconstruction of functional connectivity of the neural circuits.", "In contrast to these implicit techniques, here, we develop an extension to Neural Relational Inference [6] , which we call 'dynamic Neural Relational Inference' (dNRI).", "Specifically, we develop a new model to extract rapid dynamic changes of network activity in the form of a time-dependent adjacency matrix.", "We aim at extracting rapid (tens of milliseconds) correlations between recorded neurons that capture their functional relations across the network.", "Moreover, our method enables the tracking of the temporal evolution of this functional connectivity over the span of a trial.", "This means it can provide an interpretable approach to uncover hidden dynamical structure of brain information flows and to reconstruct the underlying functional brain circuitry.", "We demonstrate the applicability of our method on both synthetic spiking data and data recorded from the cortex of live and behaving mice.", "We develop a method to explicitly extract time-dependent functional relations from large-scale neural spiking data recordings of cortical networks.", "Using simulated data of spiking activity where ground truth is available, and real data, we demonstrate that the proposed approach is able to recover the implanted interactions more accurately than baselines which model relations implicitly." ]

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[ "We develop 'dynamic neural relational inference', a variational autoencoder model that can explicitly and interpretably represent the hidden dynamic relations between neurons." ]

[ "DeePa is a deep learning framework that explores parallelism in all parallelizable dimensions to accelerate the training process of convolutional neural networks.", "DeePa optimizes parallelism at the granularity of each individual layer in the network.", "We present an elimination-based algorithm that finds an optimal parallelism configuration for every layer.", "Our evaluation shows that DeePa achieves up to 6.5× speedup compared to state-of-the-art deep learning frameworks and reduces data transfers by up to 23×.", "Training convolutional neural networks (CNNs) is increasingly compute-intensive and timeconsuming.", "It takes days or even weeks to train deep CNNs from scratch BID10 BID12 BID9 BID11 .", "Existing deep learning frameworks such as TensorFlow, PyTorch, and Caffe2 parallelize the training process onto multiple processors (usually GPUs) using image parallelism 1 dividing the entire image dataset into batches with the same number of images and assigning each batch to a dedicated processor.The standard parallelization of CNN training only exploits image parallelism.", "However, other dimensions can also parallelize the training process.", "For example, in CNNs for 2D images, data is commonly organized as 4-dimensional tensors (i.e., image, height, width, channel).", "The image dimension includes an index for each image in the input dataset.", "The height and width dimensions specify a position in an image.", "For a particular position, the channel dimension 2 indexes different neurons for that position.", "Exploring these other parallelizable dimensions can potentially reduce the compute time and data transfer cost when training CNNs (see Section 2).", "Moreover, different layers in a CNN may prefer different parallelism configurations for achieving optimal performance.We propose DeePa, a deep learning framework that explores parallelism in all parallelizable dimensions to accelerate the training of CNNs.", "To the best of our knowledge, DeePa is the first system that models and exploits the parallelism of neural networks at the granularity of each individual layer.", "To generate a parallelism configuration for each layer, DeePa uses an elimination-based algorithm that automatically finds the configuration with the best estimated performance.The main contributions of this paper are:• We present DeePa, a deep learning framework that explores parallelism in all parallelizable dimensions to accelerate the training of CNNs.•", "The parallelization strategy is selected at the granularity of each individual layer.•", "We present an elimination-based algorithm for finding the parallelism configuration with optimal estimated performance for each layer.•", "Our evaluation shows that, compared to state-of-the-art deep learning frameworks (e.g., TensorFlow and PyTorch), DeePa achieves 6.5×, 1.9×, and 1.5× speedup for AlexNet, TAB0 Conv3x3 in an Inception-v3 module respectively . The", "performance improvement comes from reducing overall data transfers, automatically overlapping computation with data movement, and accelerating computation throughput.", "We have presented DeePa, a deep learning framework that explores parallelism in all parallelizable dimensions to accelerate the training of CNNs.", "DeePa optimizes the parallelism configuration chosen at the granularity of individual layers.", "DeePa achieves up to 6.5× for training CNNs and reduces overall data transfers by up to 23× compared to state-of-the-art deep learning frameworks.Proof.", "The Cost function is defined in Equation 1.", "Let g be any configuration.", "We first compute the difference between Cost(g, (V, E)) and Cost(g, (V , E )).", "DISPLAYFORM0 =w.compute(g(w", ")) + w.update(g(w", ")) DISPLAYFORM1 Now assume g is an optimal configuration for (V, E). Then", "we have w.compute(g(w))", "+ w.update(g(w))", "+ e 1 .xfer(g(u", "), g(w", ")) + e", "2 .xfer(g(w)", ", g(v)", ") = min", "cw {w.compute(c w ) + w.update(c w ) + e 1 .xfer(g(u),", "c w )", "+ e 2 .xfer(c w ,", "g(v))}Therefore", ", g is an optimal configuration of (V , E ). For the other", "direction, note that if g is an optimal configuration of (V , E ), then it can be extended to an optimal configuration of (V, E) by adding the node w with the same minimal assignment." ]

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[ "To the best of our knowledge, DeePa is the first deep learning framework that controls and optimizes the parallelism of CNNs in all parallelizable dimensions at the granularity of each layer." ]

[ "One can substitute each neuron in any neural network with a kernel machine and obtain a counterpart powered by kernel machines.", "The new network inherits the expressive power and architecture of the original but works in a more intuitive way since each node enjoys the simple interpretation as a hyperplane (in a reproducing kernel Hilbert space).", "Further, using the kernel multilayer perceptron as an example, we prove that in classification, an optimal representation that minimizes the risk of the network can be characterized for each hidden layer.", "This result removes the need of backpropagation in learning the model and can be generalized to any feedforward kernel network.", "Moreover, unlike backpropagation, which turns models into black boxes, the optimal hidden representation enjoys an intuitive geometric interpretation, making the dynamics of learning in a deep kernel network simple to understand.", "Empirical results are provided to validate our theory.", "Any neural network (NN) can be turned into a kernel network (KN) by replacing each artificial neuron (McCulloch & Pitts, 1943) , i.e., learning machine of the form f", "(x) = σ(w x + b), with a kernel machine, i.e., learning machine of the form f", "(x) = w, φ(x", ") + b with kernel function k(x, y", ") = φ(x", "), φ(y", ") . This", "combination of connectionism and kernel method enables the learning of hierarchical, distributed representations with kernels.In terms of training, similar to NN, KN can be trained with backpropagation (BP) (Rumelhart et al., 1986) . In the", "context of supervised learning, the need for BP in learning a deep architecture is caused by the fact that there is no explicit target information to tune the hidden layers (Rumelhart et al., 1986) . Moreover", ", BP is usually computationally intensive and can suffer from vanishing gradient. And most", "importantly, BP results in hidden representations that are notoriously difficult to interpret or assess, turning deep architectures into \"black boxes\".The main", "theoretical contribution of this paper is the following: Employing the simplest feedforward, fully-connected KN as an example, we prove that in classification and under certain losses, the optimal representation for each hidden layer that minimizes the risk of the network can be explicitly characterized. This result", "removes the need for BP and makes it possible to train the network in a feedforward, layer-wise fashion. And the same", "idea can be generalized to other feedforward KNs.The layer-wise learning algorithm gives the same optimality guarantee as BP in the sense that it minimizes the risk. But the former", "is much faster and evidently less susceptible to vanishing gradient. Moreover, the", "quality of learning in the hidden layers can be directly assessed during or after training, providing more information about the model to the user. For practitioners", ", this enables completely new model selection paradigms. For example, the", "bad performance of the network can now be traced to a certain layer, allowing the user to debug the layers individually. Most importantly", ", the optimal representation for each hidden layer enjoys an intuitive geometric interpretation, making the learning dynamics in a deep KN more transparent than that in a deep NN. A simple acceleration", "method that utilizes the \"sparse\" nature of the optimal hidden representations is proposed to further reduce computational complexity.Empirical results on several computer vision benchmarks are provided to demonstrate the competence of the model and the effectiveness of the greedy learning algorithm. Figure 1: (a) Any NN", "(left, presented in the usual weight-nonlinearity abstraction) can be abstracted as a \"graph\" (right) with each node representing a neuron and each edge the input-output relationship between neurons. If a node receives multiple", "inputs, we view its input as a vector in some Euclidean space, as indicated by the colored rectangles. Under this abstraction, each", "neuron (f (x) = σ(w x + b)) can be directly", "replaced by a kernel machine (f (x) = w, φ(x) + b with kernel k(x", ", y) = φ(x", "), φ(y) ) mapping from the", "same Euclidean", "space", "into the real line without altering the architecture and functionality of the model. (b) Illustration for layer-wise optimality", "drifting away from network-optimality. Consider a two-layer network and let T 1 ,", "T 2 be the target function of the first and second layer, respectively. If the first layer creates error, which is", "illustrated by F (1) (x) being far away from T 1 (x), the composed", "solution F (2) • F (1) on the", "right is better than that on the left and hence the F (2) on the right corresponds to the network-wise optimality of the second layer. But the F (2) on the left is clearly a better estimate", "to the layer-wise optimality T 2 if the quality of estimation is measured by the supremum distance." ]

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[ "We combine kernel method with connectionist models and show that the resulting deep architectures can be trained layer-wise and have more transparent learning dynamics. " ]

[ "Many notions of fairness may be expressed as linear constraints, and the resulting constrained objective is often optimized by transforming the problem into its Lagrangian dual with additive linear penalties.", "In non-convex settings, the resulting problem may be difficult to solve as the Lagrangian is not guaranteed to have a deterministic saddle-point equilibrium. ", "In this paper, we propose to modify the linear penalties to second-order ones, and we argue that this results in a more practical training procedure in non-convex, large-data settings.", "For one, the use of second-order penalties allows training the penalized objective with a fixed value of the penalty coefficient, thus avoiding the instability and potential lack of convergence associated with two-player min-max games.", "Secondly, we derive a method for efficiently computing the gradients associated with the second-order penalties in stochastic mini-batch settings.", "Our resulting algorithm performs well empirically, learning an appropriately fair classifier on a number of standard benchmarks.", "Machine learning systems are becoming increasingly prevalent in real-world applications, consequently affecting the decisions that determine a person's life and future, such as playing a role in parole conditions BID1 , loan applications BID12 , and airport screening BID13 .", "Recent work has shown that such machine learning models often have biases which can unfairly disadvantage certain groups.", "For example, learned word embeddings exhibit gender-specific biases in what should be gender neutral words BID4 .", "In another case, a machine learning model's predictions regarding convict recidivism were found to be unfairly biased against African-Americans ( BID1 .", "While it may seem at first that simply ignoring the features corresponding to these protected traits when training can alleviate this, previous work BID18 has shown that enforcing such blindness is largely ineffective due to redundant encodings in the data.", "In other words, while the learning algorithm used may not be biased, the data can be inherently biased in complex ways, and this leads to models which perpetuate these undesirable biases.Research into the challenging problem of machine learning fairness is therefore of great interest.", "To better specify this problem, previous work has elaborated on precise notions of fairness, such as demographic parity BID8 , equal opportunity BID14 , etc.", "These notions can often be expressed mathematically as a linear constraint on the output of a machine learning model, taken in expectation over the entire data distribution.", "Accordingly, a number of recent works have proposed to incorporate fairness during training by expressing the objective as a constrained optimization problem BID24 BID11 .", "If the original objective is convex, the addition of linear constraints results in a problem which may be readily solved by Lagrangian methods.However, modern machine learning models are often not in a convex form.", "Indeed, the success of deep neural networks over the past decade makes it clear that the most well-performing models are often highly non-convex and optimized via stochastic gradient methods over large amounts of data BID19 BID20 .", "It is unfortunate that much of the existing work on fairness in machine learning has provided methods which are either focused on the convex, small data-set setting BID24 BID11 , or otherwise require sophisticated and complex training methods BID6 .In", "this paper, we present a general method for imposing fairness conditions during training, such that it is practical in non-convex, large data settings. We", "take inspiration from the standard Lagrangian method of augmenting the original loss with linear penalties. In", "non-convex settings, this dual objective must be optimized with respect to both model parameters and penalty coefficients concurrently, and in general is not guaranteed to converge to a deterministic equilibrium.We propose to re-express the linear penalties associated with common fairness criteria as secondorder penalties. Second-order", "penalties are especially beneficial in non-convex settings, as they may be optimized using a fixed non-negative value for the penalty coefficient λ. When λ → 0 the", "optimization corresponds to an unconstrained objective, while as λ → ∞, the problem approaches that of a hard equality constraint. This allows us", "to avoid sophisticated optimization methods for potentially non-convergent two-player games. Instead, we only", "need to choose a fixed value for the penalty coefficient, which may be easily determined via standard hyperparameter optimization methods, such as cross-validation. As an additional", "benefit, by choosing the penalty coefficient on a separate validation set, we can improve generalization performance.Second-order penalties, however, potentially introduce a new problem: By squaring an expectation over the entire data distribution, the resulting penalized loss is no longer an expectation of loss functions on individual data points sampled from the distribution, and therefore not readily approachable by stochastic gradient methods. We solve this by", "presenting an equivalent form of the second-order penalty as an expectation of individual loss functions on pairs of independently sampled data points.Our resulting algorithm is thus not only more practical to optimize in non-convex settings, using a fixed value for the penalty coefficient, but is also easily optimized in large-data settings via standard stochastic gradient descent. We evaluate the", "performance of our algorithm in a number of different settings. In each setting", ", our algorithm is able to adequately optimize the desired constraints, such as encouraging feature orthonormality in deep image autoencoders and imposing predictive fairness across protected data groups." ]

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[ "We propose a method to stochastically optimize second-order penalties and show how this may apply to training fairness-aware classifiers." ]

[ "Training methods for deep networks are primarily variants on stochastic gradient descent. ", "Techniques that use (approximate) second-order information are rarely used because of the computational cost and noise associated with those approaches in deep learning contexts. ", "However, in this paper, we show how feedforward deep networks exhibit a low-rank derivative structure. ", "This low-rank structure makes it possible to use second-order information without needing approximations and without incurring a significantly greater computational cost than gradient descent. ", "To demonstrate this capability, we implement Cubic Regularization (CR) on a feedforward deep network with stochastic gradient descent and two of its variants. ", "There, we use CR to calculate learning rates on a per-iteration basis while training on the MNIST and CIFAR-10 datasets. ", "CR proved particularly successful in escaping plateau regions of the objective function. ", "We also found that this approach requires less problem-specific information (e.g. an optimal initial learning rate) than other first-order methods in order to perform well.", "We see this CR approach as an addition to, not a replacement for, existing training methods.", "It could potentially replace existing methods, but it does not have to in order to be used.", "Because of the low-rank structure of the Hessian, we can use CR to supplement existing optimizers that do not explicitly leverage second order information.", "The CR technique used here is most useful when the optimization is stuck on a plateau prior to convergence: CR makes it possible to determine whether the optimization has converged (perhaps to a local minimum) or is simply bogged down in a flat region.", "It may eventually be possible to calculate a search direction as well as a step length, which would likely be a significant advancement, but this would be a completely separate algorithm.We found that applying CR to Adagrad and Adadelta provided the same kinds of improvements that applying CR to SGD did.", "However, using CR with Adam BID6 did not provide gains as it did with the other methods.", "Adam generally demonstrates a greater degree of adaptivity than Adagrad or Adadelta; in our experiments, we found that Adam was better than Adagrad or Adadelta in escaping the plateau region.", "We suspect that trying to overlay an additional calculated learning rate on top of the variable-specific learning rate produced by Adam may create interference in both sets of learning rate calculations.", "Analyzing each algorithm's update scheme in conjunction with the CR calculations could provide insight into the nature and extent of this interference, and provide ways to further improve both algorithms.", "In future work, though, it would not be difficult to adapt the CR approach to calculate layer-or variable-specific learning rates, and doing that could address this problem.", "Calculating a variable-specific learning rate would essentially involve rescaling each variable's step by the corresponding diagonal entry in the Hessian; calculating a layer-specific learning rate would involve rescaling the step of each variable in that layer by some measure of the block diagonal component of the Hessian corresponding to those variables.", "The calculations for variable-specific learning rates with CR are given in Appendix B.There are two aspects of the computational cost to consider in evaluating the use of CR.", "The first aspect is storage cost.", "In this regard, the second-order calculations are relatively inexpensive (comparable to storing gradient information).", "The second aspect is the number of operations, and the second-order calculations circumvent the storage issue by increasing the number of operations.", "The number of matrix multiplications involved in calculating the components of Equation 9, for example, scales quadratically with the number of layers (see the derivations in Appendix B).", "Although the number of matrix multiplications will not change with an increase in width, the cost of naïve matrix multiplication scales cubically with matrix size.", "That being said, these calculations are parallelizable and as such, the effect of the computation cost will be implementation-dependent.A significant distinction between CR and methods like SGD has to do with the degree of knowledge about the problem required prior to optimization.", "SGD requires an initial learning rate and (usually) a learning rate decay scheme; an optimal value for the former can be very problem-dependent and may be different for other algorithms when applied to the same problem.", "For CR, it is necessary to specify σ, but optimization performance is relatively insensitive to this -order of magnitude estimates seem to be sufficient -and varying σ has a stronger affect on the variability of the learning rate than it does on the magnitude (though it does affect both).", "If the space is very curved, the choice of σ matters little because the step size determination is dominated by the curvature, and if the space if flat, it bounds the step length.", "It is also possible to employ an adaptive approach for updating σ BID7 ), but we did not pursue that here.", "Essentially, using CR is roughly equivalent to using the optimal learning rate (for SGD).", "In this paper, we showed that feedforward networks exhibit a low-rank derivative structure.", "We demonstrate that this structure provides a way to represent the Hessian efficiently; we can exploit this structure to obtain higher-order derivative information at relatively low computational cost and without massive storage requirements.", "We then used second-order derivative information to implement CR in calculating a learning rate when supplied with a search direction.", "The CR method has a higher per-iteration cost than SGD, for example, but it is also highly parallelizable.", "When SGD converged well, CR showed comparable optimization performance (on a per-iteration basis), but the adaptive learning rate that CR provided proved to be capable of driving the optimization away from plateaus that SGD would stagnate on.", "The results were similar with Adagrad and Adadelta, though not with Adam.", "CR also required less problem-specific knowledge (such as an optimal initial learning rate) to perform well.", "At this point, we see it as a valuable technique that can be incorporated into existing methods, but there is room for further work on exploiting the low-rank derivative structure to enable CR to calculate search directions as well as step sizes." ]

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[ "We show that deep learning network derivatives have a low-rank structure, and this structure allows us to use second-order derivative information to calculate learning rates adaptively and in a computationally feasible manner." ]

[ "The worst-case training principle that minimizes the maximal adversarial loss, also known as adversarial training (AT), has shown to be a state-of-the-art approach for enhancing adversarial robustness against norm-ball bounded input perturbations.", "Nonetheless, min-max optimization beyond the purpose of AT has not been rigorously explored in the research of adversarial attack and defense.", "In particular, given a set of risk sources (domains), minimizing the maximal loss induced from the domain set can be reformulated as a general min-max problem that is different from AT.", "Examples of this general formulation include attacking model ensembles, devising universal perturbation under multiple inputs or data transformations, and generalized AT over different types of attack models.", "We show that these problems can be solved under a unified and theoretically principled min-max optimization framework. ", "We also show that the self-adjusted domain weights learned from our method provides a means to explain the difficulty level of attack and defense over multiple domains.", "Extensive experiments show that our approach leads to substantial performance improvement over the conventional averaging strategy.", "Training a machine learning model that is capable of assuring its worst-case performance against all possible adversaries given a specified threat model is a fundamental yet challenging problem, especially for deep neural networks (DNNs) (Szegedy et al., 2013; Goodfellow et al., 2015; Carlini & Wagner, 2017) .", "A common practice to train an adversarially robust model is based on a specific form of min-max training, known as adversarial training (AT) (Goodfellow et al., 2015; Madry et al., 2017) , where the minimization step learns model weights under the adversarial loss constructed at the maximization step in an alternative training fashion.", "On datasets such as MNIST and CIFAR-10, AT has achieved the state-of-the-art defense performance against p -norm-ball input perturbations (Athalye et al., 2018b) .", "Motivated by the success of AT, one follow-up question that naturally arises is: Beyond AT, can other types of min-max formulation and optimization techniques advance the research in adversarial robustness?", "In this paper, we give an affirmative answer corroborated by the substantial performance gain and the ability of self-learned risk interpretation using our proposed min-max framework on several tasks for adversarial attack and defense.", "We demonstrate the utility of a general formulation for min-max optimization minimizing the maximal loss induced from a set of risk sources (domains).", "Our considered min-max formulation is fundamentally different from AT, as our maximization step is taken over the probability simplex of the set of domains.", "Moreover, we show that many problem setups in adversarial attacks and defenses can in fact be reformulated under this general min-max framework, including attacking model ensembles (Tramèr et al., 2018; Liu et al., 2018) , devising universal perturbation to input samples (Moosavi-Dezfooli et al., 2017) or data transformations (Athalye & Sutskever, 2018; Brown et al., 2017) , and generalized AT over multiple types of threat models (Tramèr & Boneh, 2019; Araujo et al., 2019 ).", "However, current methods for solving these tasks often rely on simple heuristics (e.g.,", "In this paper, we propose a general min-max framework applicable to both adversarial attack and defense settings.", "We show that many problem setups can be re-formulated under this general framework.", "Extensive experiments show that proposed algorithms lead to significant improvement on multiple attack and defense tasks compared with previous state-of-the-art approaches.", "In particular, we obtain 17.48%, 35.21% and 9.39% improvement on attacking model ensembles, devising universal perturbation to input samples, and data transformations under CIFAR-10, respectively.", "Our minmax scheme also generalizes adversarial training (AT) for multiple types of adversarial attacks, attaining faster convergence and better robustness compared to the vanilla AT and the average strategy.", "Moreover, our approach provides a holistic tool for self-risk assessment by learning domain weights.", "where w ∈ R K represent domain weights, and P has been defined in (1)." ]

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[ "A unified min-max optimization framework for adversarial attack and defense" ]

[ "Most deep learning models rely on expressive high-dimensional representations to achieve good performance on tasks such as classification.", "However, the high dimensionality of these representations makes them difficult to interpret and prone to over-fitting.", "We propose a simple, intuitive and scalable dimension reduction framework that takes into account the soft probabilistic interpretation of standard deep models for classification.", "When applying our framework to visualization, our representations more accurately reflect inter-class distances than standard visualization techniques such as t-SNE.", "We show experimentally that our framework improves generalization performance to unseen categories in zero-shot learning.", "We also provide a finite sample error upper bound guarantee for the method.", "Dimensionality reduction is an important problem in machine learning tasks to increase classification performance of learned models, improve computational efficiency, or perform visualization.", "In the context of visualization, high-dimensional representations are typically converted to two or threedimensional representations so that the underlying relations between data points can be observed and interpreted from a scatterplot.", "Currently, a major source of high-dimensional representations that machine learning practitioners have trouble understanding are those generated by deep neural networks.", "Techniques such as PCA or t-SNE ( BID11 are typically used to visualize them, e.g., in Law et al. (2017) ; BID5 .", "Moreover, BID4 proposed a visualization technique that represents examples based on their predicted category only.", "However, none of these techniques exploit the fact that deep models have soft probabilistic interpretations.", "For instance, the output of deep classifiers typically employs softmax regression, which optimizes classification scores across categories by minimizing cross entropy.", "This results in soft probabilistic representations that reflect the confidence of the model in assigning examples to the different categories.", "Many other deep learning tasks such as semantic segmentation (Long et al., 2015) or boundary/skeleton detection BID16 also optimize for probability distributions.", "In this paper, we experimentally demonstrate that the soft probability representations learned by a neural network reveal key structure about the learned model.", "To this end, we propose a dimensionality reduction framework that transforms probability representations into a low-dimensional space for easy visualization.Furthermore, our approach improves generalization.", "In the context of zero-shot learning where novel categories are added at test time, deep learning approaches often learn high-dimensional representations that over-fit to training categories.", "By learning low-dimensional representations that match the classification scores of a high-dimensional pre-trained model, our approach takes into account inter-class similarities and generalizes better to unseen categories than standard approaches.Proposed approach: We propose to exploit as input representations the probability scores generated by a high-dimensional pre-trained model, called the teacher model or target, in order to train a lower-dimensional representation, called the student.", "In detail, our approach learns low-dimensional student representations of examples such that, when applying a specific soft clustering algorithm on the student representations, the predicted clustering scores are similar to the target probability scores.Contributions: This paper makes the following contributions: (1) We propose the first dimensionality reduction approach optimized to consider some soft target probabilistic representations as input.", "(2) By exploiting the probability representations generated by a pre-trained model, our approach reflects the learned semantic structure better than standard visualization approaches.", "(3) We experimentally show that our approach improves generalization performance in zero-shot learning.(4", ") We theoretically analyze the statistical properties of the approach and provide a finite sample error upper bound guarantee for it.", "We have proposed a dimensionality reduction approach such that the soft clustering scores obtained in the low-dimensional space are similar to those given as input.", "We experimentally show that our approach improves generalization performance in zero-shot learning on challenging datasets.", "It can also be used to complement t-SNE, as a visualization tool to better understand learned models.", "In particular, we show that we can give a soft clustering interpretation to models that have probabilistic interpretations.", "Real-world applications that can be used with DRPR include distillation.", "For instance, when the teacher model is too large to store on a device with small memory (e.g., mobile phone), the student model which has a smaller memory footprint is used instead.", "Low-dimensional representations can also speed up retrieval tasks.", "Future work includes applying our approach to the task of distillation in the standard classification task where training categories are also test categories." ]

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[ "dimensionality reduction for cases where examples can be represented as soft probability distributions" ]

[ "Intrinsically motivated goal exploration algorithms enable machines to discover repertoires of policies that produce a diversity of effects in complex environments.", "These exploration algorithms have been shown to allow real world robots to acquire skills such as tool use in high-dimensional continuous state and action spaces.", "However, they have so far assumed that self-generated goals are sampled in a specifically engineered feature space, limiting their autonomy.", "In this work, we propose an approach using deep representation learning algorithms to learn an adequate goal space.", "This is a developmental 2-stage approach: first, in a perceptual learning stage, deep learning algorithms use passive raw sensor observations of world changes to learn a corresponding latent space; then goal exploration happens in a second stage by sampling goals in this latent space.", "We present experiments with a simulated robot arm interacting with an object, and we show that exploration algorithms using such learned representations can closely match, and even sometimes improve, the performance obtained using engineered representations.", "Spontaneous exploration plays a key role in the development of knowledge and skills in human children.", "For example, young children spend a large amount of time exploring what they can do with their body and external objects, independently of external objectives such as finding food or following instructions from adults.", "Such intrinsically motivated exploration BID6 BID17 BID31 ) leads them to make ratcheting discoveries, such as learning to locomote or climb in various styles and on various surfaces, or learning to stack and use objects as tools.", "Equipping machines with similar intrinsically motivated exploration capabilities should also be an essential dimension for lifelong open-ended learning and artificial intelligence.In the last two decades, several families of computational models have both contributed to a better understanding of such exploration processes in infants, and how to apply them efficiently for autonomous lifelong machine learning .", "One general approach taken by several research groups BID1 BID4 BID16 has been to model the child as intrinsically motivated to make sense of the world, exploring like a scientist that imagines, selects and runs experiments to gain knowledge and control over the world.", "These models have focused in particular on three kinds of mechanisms argued to be essential and complementary to enable machines and animals to efficiently explore and discover skill repertoires in the real world BID10 : embodiment 1 , intrinsic motivation and social guidance 3 .", "This article focuses on challenges related to learning goal representations for intrinsically motivated exploration, but also leverages models of embodiment, through the use of parameterized Dynamic Movement Primitives controllers BID20 and social guidance, through the use of observations of another agent.Given an embodiment, intrinsically motivated exploration 4 consists in automatically and spontaneously conducting experiments with the body to discover both the world dynamics and how it can be controlled through actions.", "Computational models have framed intrinsic motivation as a family of mechanisms that self-organize agents exploration curriculum, in particular through generating and selecting experiments that maximize measures such as novelty BID0 BID48 , predictive information gain BID25 , learning progress BID43 BID21 , compression progress BID44 , competence progress , predictive information BID26 or empowerment BID41 .", "When used in the Reinforcement Learning (RL) framework (e.g. BID48 BID43 BID21 BID4 ), these measures have been called intrinsic rewards, and they are often applied to reward the \"interestingness\" of actions or states that are explored.", "They have been consistently shown to enable artificial agents or robots to make discoveries and solve problems that would have been difficult to learn using a classical optimization or RL approach based only on the target reward (which is often rare or deceptive) BID11 BID47 .", "Recently, they have been similarly used to guide exploration in difficult deep RL problems with sparse rewards, e.g. BID5 BID19 BID49 BID35 .However", ", many of these computational approaches have considered intrinsically motivated exploration at the level of micro-actions and states (e.g. considering low-level actions and pixel level perception). Yet, children", "'s intrinsically motivated exploration leverages abstractions of the environments, such as objects and qualitative properties of the way they may move or sound, and explore by setting self-generated goals BID53 , ranging from objects to be reached, toy towers to be built, or paper planes to be flown. A computational", "framework proposed to address this higher-level form of exploration has been Intrinsically Motivated Goal Exploration Processes (IMGEPs) BID2 BID15 , which is closely related to the idea of goal babbling BID39 . Within this approach", ", agents are equipped with a mechanism enabling them to sample a goal in a space of parameterized goals 5 , before they try to reach it by executing an experiment. Each time they sample", "a goal, they dedicate a certain budget of experiments time to improve the solution to reach this goal, using lower-level optimization or RL methods for example. Most importantly, in", "the same time, they take advantage of information gathered during this exploration to discover other outcomes and improve solutions to other goals 6 .This property of cross-goal", "learning often enables efficient exploration even if goals are sampled randomly in goal spaces containing many unachievable goals. Indeed, generating random goals", "(including unachievable ones) will very often produce goals that are outside the convex hull of already discovered outcomes, which in turn leads to exploration of variants of known corresponding policies, pushing the convex hull further. Thus, this fosters exploration", "of policies that have a high probability to produce novel outcomes without the need to explicitly measure novelty. This explains why forms of random", "goal exploration are a form of intrinsically motivated exploration. However, more powerful goal sampling", "strategies exist. A particular one consists in using meta-learning", "algorithms to monitor the evolution of competences over the space of goals and to select the next goal to try, according to the expected competence progress resulting from practicing it . This enables to automate curriculum sequences of", "goals of progressively increasing complexity, which has been shown to allow high-dimensional real world robots to acquire efficiently repertoires of locomotion skills or soft object manipulation , or advanced forms of nested tool use BID15 Here a goal is not necessarily an end state to be reached, but can characterize certain parameterized properties of changes of the world, such as following a parameterized trajectory. 6 E.g. while learning how to move an object to the", "right, they may discover how to move it to the left.sampling them randomly BID9 BID27 or adaptively BID13 ).Yet, a current limit of existing algorithms within", "the family of Intrinsically Motivated Goal Exploration Processes is that they have assumed that the designer 7 provides a representation allowing the autonomous agent to generate goals, together with formal tools used to measure the achievement of these goals (e.g. cost functions). For example, the designer could provide a representation", "that enables the agent to imagine goals as potential continuous target trajectories of objects BID15 , or reach an end-state starting from various initial states defined in Euclidean space BID13 , or realize one of several discrete relative configurations of objects BID9 ), which are high-level abstractions from the pixels. While this has allowed to show the power of intrinsically", "motivated goal exploration architectures, designing IMGEPs that sample goals from a learned goal representation remains an open question. There are several difficulties. One concerns the question", "of how an agent can learn in an", "unsupervised manner a representation for hypothetical goals that are relevant to their world before knowing whether and how it is possible to achieve them with the agent's own action system. Another challenge is how to sample \"interesting\" goals using", "a learned goal representation, in order to remain in regions of the learned goal parameters that are not too exotic from the underlying physical possibilities of the world. Finally, a third challenge consists in understanding which properties", "of unsupervised representation learning methods enable an efficient use within an IMGEP architecture so as to lead to efficient discovery of controllable effects in the environment.In this paper, we present one possible approach named IMGEP-UGL where aspects of these difficulties are addressed within a 2-stage developmental approach, combining deep representation learning and goal exploration processes:Unsupervised Goal space Learning stage (UGL): In the first phase, we assume the learner can passively observe a distribution of world changes (e.g. different ways in which objects can move), perceived through raw sensors (e.g. camera pixels or other forms of low-level sensors in other modalities). Then, an unsupervised representation learning algorithm is used to learn", "a lower-dimensional latent space representation (also called embedding) of these world configurations. After training, a Kernel Density Estimator (KDE) is used to estimate the", "distribution of these observations in the latent space.", "In this paper, we proposed a new Intrinsically Motivated Goal Exploration architecture with Unsupervised Learning of Goal spaces (IMGEP-UGL).", "Here, the Outcome Space (also used as Goal Space) representation is learned using passive observations of world changes through low-level raw sensors (e.g. movements of objects caused by another agent and perceived at the pixel level).Within", "the perspective of research on Intrinsically Motivated Goal Exploration started a decade ago , and considering the fundamental problem of how AI agents can autonomously explore environments and skills by setting their own goals, this new architecture constitutes a milestone as it is to our knowledge the first goal exploration architecture where the goal space representation is learned, as opposed to hand-crafted.Furthermore, we have shown in two simulated environments (involving a high-dimensional continuous action arm) that this new architecture can be successfully implemented using multiple kinds of unsupervised learning algorithms, including recent advanced deep neural network algorithms like Variational Auto-Encoders. This flexibility", "opens the possibility to benefit from future advances in unsupervised representation learning research. Yet, our experiments", "have shown that all algorithms we tried (except RGE-RFVAE) can compete with an IMGEP implementation using engineered feature representations. We also showed, in the", "context of our test environments, that providing to IMGEP-UGL algorithms a target embedding dimension larger than the true dimensionality of the phenomenon can be beneficial through leveraging exploration dynamics properties of IMGEPs. Though we must investigate", "more systematically the extent of this effect, this is encouraging from an autonomous learning perspective, as one should not assume that the learner initially knows the target dimensionality.Limits and future work. The experiments presented", "here were limited to a fairly restricted set of environments. Experimenting over a larger", "set of environments would improve our understanding of IMGEP-UGL algorithms in general. In particular, a potential", "challenge is to consider environments where multiple objects/entities can be independently controlled, or where some objects/entities are not controllable (e.g. animate entities). In these cases, previous work", "on IMGEPs has shown that random Goal Policies should be either replaced by modular Goal Policies (considering a modular goal space representation, see BID15 ), or by active Goal Policies which adaptively focus the sampling of goals in subregions of the Goal Space where the competence progress is maximal . For learning modular representations", "of Goal Spaces, an interesting avenue of investigations could be the use of the Independently Controllable Factors approach proposed in BID51 .Finally, in this paper, we only studied", "a learning scenario where representation learning happens first in a passive perceptual learning stage, and is then fixed during a second stage of autonomous goal exploration. While this was here motivated both by analogies", "to infant development and to facilitate evaluation, the ability to incrementally and jointly learn an outcome space representation and explore the world is a stimulating topic for future work.Bernouilli distribution of ξ parameters 13 , and the log likelihood of the dataset D is expressed as: DISPLAYFORM0 with DISPLAYFORM1 . For a binary valued input vector x (i) , the unitary", "Cost Function to minimize is: DISPLAYFORM2 provided that f θ is the encoder part of the architecture and g φ is the decoding part of the architecture. This Cost Function can be minimized using Stochastic", "Gradient Descent BID7 , or more advanced optimizers such as Adagrad BID12 ) or Adam (Kingma & Ba, 2015 .Depending on the depth of the network 14 , those architectures", "can prove difficult to train using vanilla Stochastic Gradient Descent. A particularly successful procedure to overcome this difficulty", "is to greedily train each pairs of encoding-decoding layers and stacking those to sequentially form the complete network. This procedure, known as stacked AEs, accelerates convergence.", "But it has shown bad results with our problem, and thus was discarded", "for the sake of clarity.Variational Auto-Encoders (VAEs) If we assume that the observed data are realizations of a random variable x ∼ p(x|ψ), we can hypothesize that they are conditioned by a random vector of independent factors z ∼ p(z|ψ). In this setting, learning the model would amount to searching the parameters", "ψ of both distributions. We might use the same principle of maximum likelihood as before to find the", "best parameters by computing the likelihood log L(D) = N i=1 log p(x (i) |ψ) by using the fact that p(x|ψ) = p(x, z|ψ)dz = p(x|z, ψ)p(z|ψ)dz. Unfortunately, in most cases, this integral is intractable and cannot be approximated", "by Monte-Carlo sampling in reasonable time.To overcome this problem, we can introduce an arbitrary distribution q(z|x, χ) and remark that the following holds: DISPLAYFORM3 with the Evidence Lower Bound being: DISPLAYFORM4 Looking at Equation FORMULA10 , we can see that since the KL divergence is non-negative, L(q, ψ) ≤ log p(x|ψ) − D KL ([q(z|x, χ) p(z|x, ψ)] whatever the q distribution, hence the name of Evidence Lower Bound (ELBO). Consequently, maximizing the ELBO have the effect to maximize the log likelihood, while", "minimizing the KL-Divergence between the approximate q(z|x) distribution, and the true unknown posterior p(z|x, ψ). The approach taken by VAEs is to learn the parameters of both conditional distributions", "p(x|z, ψ) and q(z|x, χ) as non-linear functions. Under some restricted conditions, Equation (6) can be turned into a valid cost function", "to train a neural network. First, we hypothesize that q(z|x, χ) and p(z|ψ) follow Multivariate Gaussian distributions", "with diagonal covariances, which allows us to compute the b term in closed form. Second, using the Gaussian assumption on q, we can reparameterize the inner sampling operation", "by z = µ + σ 2 with ∼ N (0, I). Using this trick, the Path-wise Derivative estimator can be used for the a member of the ELBO.", "Under those conditions, and assuming that p(x|ψ) follows a Multivariate Bernouilli distribution", ", we can write the cost function used to train the neural network as: DISPLAYFORM5 where f χ represents the encoding and sampling part of the architecture and g ψ represents the decoding part of the architecture. In essence, this derivation simplifies to the initial cost function used in AEs augmented by a", "term penalizing the divergence between q(z|x, χ) and the assumed prior that p(x|ψ) = N (0, I).Normalizing Flow overcomes the problem stated earlier, by permitting more expressive prior distributions", "(Rezende & Mohamed, 2015) . It is based on the classic rule of change of variables for random variables. Considering a random variable", "z 0 ∼ q(z 0 ), and an invertible transformation t : DISPLAYFORM6 We can then", "directly chain different invertible transformations t 1 , t 2 , . . . , t K to produce a new ran- DISPLAYFORM7 . In this case, we have: DISPLAYFORM8 This formulation is interesting because the Law Of The Unconscious Statistician", "allows us to compute expectations over q(z k ) without having a precise knowledge of it: DISPLAYFORM9 provided that h does not depends on q(z k ). Using this principle on the ELBO allows us to derive the following: DISPLAYFORM10 This is nothing more than the regular", "ELBO with an additional term concerning the log-determinant of the transformations. In practice, as before, we use p(z 0 ) = N (z 0 ; 0, I), and q(z 0 |x) = N (z 0 ; µ(x), diag(σ(x)2 )). We only have to", "find out parameterized transformations t, whose parameters can be learned and have a defined log-determinant", ". Using radial flow, which is expressed as: DISPLAYFORM11 where r = |z − c|, h(α, r) = 1 α+r and α, β, c are learnable parameters", "of the transformation, our cost function can be written as: DISPLAYFORM12 (1 + log(σ( DISPLAYFORM13 provided that f χ represents the encoding, sampling ad transforming part of the architecture, g ψ represents the decoding part of the architecture, and β k , α k , c k are the parameters of the different transformations. Other types of transformations have been proposed lately. The Householder flow BID52 ) is a volume preserving transformation, meaning that its log determinant equals 1, with the consequence that it can be used with no modifications of the loss function. A more convoluted type of transformations based on a masked autoregressive auto-encoder, the Inverse Autoregressive Flow, was proposed", "in BID23 . We did not explore those two last approaches." ]

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[ "We propose a novel Intrinsically Motivated Goal Exploration architecture with unsupervised learning of goal space representations, and evaluate how various implementations enable the discovery of a diversity of policies." ]

[ "One of the main challenges of deep learning methods is the choice of an appropriate training strategy.", "In particular, additional steps, such as unsupervised pre-training, have been shown to greatly improve the performances of deep structures.", "In this article, we propose an extra training step, called post-training, which only optimizes the last layer of the network.", "We show that this procedure can be analyzed in the context of kernel theory, with the first layers computing an embedding of the data and the last layer a statistical model to solve the task based on this embedding.", "This step makes sure that the embedding, or representation, of the data is used in the best possible way for the considered task.", "This idea is then tested on multiple architectures with various data sets, showing that it consistently provides a boost in performance.", "The experiments presented in Section 4 show that post-training improves the performances of all the networks considered -including recurrent, convolutional and fully connected networks.", "The gain is significant, regardless of the time at which the regular training is stopped and the posttraining is done.", "In both the CIFAR10 and the PTB experiment, the gap between the losses with and without post-training is more pronounced if the training is stopped early, and tends to be smaller as the network converges to a better solution (see Figure 4 and Figure 3 ).", "The reduction of the gap between the test performances with and without post-training is made clear in TAB0 .", "For the MNIST data set, with a small-size convolutional neural network, while the error rate drops by 1.5% when post-training is applied after 5000 iterations, this same error rate only drops by 0.2% when it is applied after 20000 iterations.", "This same observation can be done for the other results reported in TAB0 .", "However, while the improvement is larger when the network did not fully converge prior to the post-training, it is still significant when the network has reached its minimum: for example in PTB the final test perplexity is 81.7 with post-training and 82.4 without; in CIFAR10 the errors are respectively 0.147 and 0.154.If the networks are allowed to moderately overfit, for instance by training them with regular algorithm for a very large number of iterations, the advantage provided by post-training vanishes: for example in PTB the test perplexity after 2000 iterations (instead of 400) is 83.2 regardless of posttraining.", "This is coherent with the intuition behind the post-training: after overfitting, the features learned by the network become less appropriate to the general problem, therefore their optimal usage obtained by post-training no longer provide an advantage.It is important to note that the post-training computational cost is very low compared to the full training computations.", "For instance, in the CIFAR10 experiment, each iteration for post-training is 4× faster on the same GPU than an iteration using the full gradient.", "Also, in the different experiments, post-training produces a performance gap after using as little as 100 batches.", "There are multiple reasons behind this efficiency: first, the system reaches a local minimum relatively rapidly for post-training as the problem FORMULA3 has a small number of parameters compared to the dimensionality of the original optimization problem.", "Second, the iterations used for the resolution of (4) are computationally cheaper, as there is no need to chain high dimensional linear operations, contrarily to regular backpropagation used during the training phase.", "Finally, since the post-training optimization problem is generally convex, the optimization is guaranteed to converge rapidly to the optimal weights for the last layer.Another interesting point is that there is no evidence that the post-training step leads to overfitting.", "In CIFAR10, the test error is improved by the use of post-training, although the training loss is similar.", "The other experiments do not show signs of overfitting either as the test error is mostly improved by our additional step.", "This stems from the fact that the post-training optimization is much simpler than the original problem as it lies in a small-dimensional space -which, combined with the added 2 -regularization, efficiently prevents overfitting.", "The regularization parameter λ plays an important role in post-training.", "Setting λ to be very large reduces the explanatory capacity of the networks whereas if λ is too small, the capacity can become too large and lead to overfitting.", "Overall, our experiments highlighted that the post-training produces significant results for any choice of λ reasonably small (i.e 10 −5 ≤ λ ≤ 10 −2 ).", "This parameter is linked to the regularization parameter of the kernel methods, as stated in Section 3.Overall, these results show that the post-training step can be applied to most trained networks, without prerequisites about how optimized they are since post-training does not degrade their performances, providing a consistent gain in performances for a very low additional computational cost.In Subsection 4.3, numerical experiments highlight the link between post-training and kernel methods.", "As illustrated in TAB1 , using the optimal weights derived from kernel theory immediately a performance boost for the considered network.", "The post-training step estimate numerically this optimal layer with the gradient descent optimizer.", "However, computing the optimal weights for the last layer is only achievable for small data set due to the required matrix inversion.", "Moreover, the closed form solution is known only for specific problems, such as kernelized least square regression.", "But post-training approaches the same performance in these cases solving (4) with gradient-based methods.The post-training can be linked very naturally to the idea of pre-training, developed notably by BID12 , and BID5 .", "The unsupervised pre-training of a layer is designed to find a representation that captures enough information from the data to be able to reconstruct it from its embedding.", "The goal is thus to find suitable parametrization of the general layers to extract good features, summarizing the data.", "Conversely, the goal of the posttraining is, given a representation, to find the best parametrization of the last layer to discriminate the data.", "These two steps, in contrast with the usual training, focus on respectively the general or specific layers.", "In this work, we studied the concept of post-training, an additional step performed after the regular training, where only the last layer is trained.", "This step is intended to take fully advantage of the data representation learned by the network.", "We empirically shown that post-training is computationally inexpensive and provide a non negligible increase of performance on most neural network structures.", "While we chose to focus on post-training solely the last layer -as it is the most specific layer in the network and the resulting problem is strongly convex under reasonable prerequisites -the relationship between the number of layers frozen in the post-training and the resulting improvements might be an interesting direction for future works.Wojciech Zaremba, Ilya Sutskever, and Oriol Vinyals.", "Recurrent neural network regularization.arXiv preprint, arXiv:1409(2329), 2014." ]

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[ "We propose an additional training step, called post-training, which computes optimal weights for the last layer of the network." ]

[ "Natural language processing (NLP) models often require a massive number of parameters for word embeddings, resulting in a large storage or memory footprint.", "Deploying neural NLP models to mobile devices requires compressing the word embeddings without any significant sacrifices in performance.", "For this purpose, we propose to construct the embeddings with few basis vectors.", "For each word, the composition of basis vectors is determined by a hash code.", "To maximize the compression rate, we adopt the multi-codebook quantization approach instead of binary coding scheme.", "Each code is composed of multiple discrete numbers, such as (3, 2, 1, 8), where the value of each component is limited to a fixed range.", "We propose to directly learn the discrete codes in an end-to-end neural network by applying the Gumbel-softmax trick.", "Experiments show the compression rate achieves 98% in a sentiment analysis task and 94% ~ 99% in machine translation tasks without performance loss.", "In both tasks, the proposed method can improve the model performance by slightly lowering the compression rate.", "Compared to other approaches such as character-level segmentation, the proposed method is language-independent and does not require modifications to the network architecture.", "Word embeddings play an important role in neural-based natural language processing (NLP) models.", "Neural word embeddings encapsulate the linguistic information of words in continuous vectors.", "However, as each word is assigned an independent embedding vector, the number of parameters in the embedding matrix can be huge.", "For example, when each embedding has 500 dimensions, the network has to hold 100M embedding parameters to represent 200K words.", "In practice, for a simple sentiment analysis model, the word embedding parameters account for 98.8% of the total parameters.As only a small portion of the word embeddings is selected in the forward pass, the giant embedding matrix usually does not cause a speed issue.", "However, the massive number of parameters in the neural network results in a large storage or memory footprint.", "When other components of the neural network are also large, the model may fail to fit into GPU memory during training.", "Moreover, as the demand for low-latency neural computation for mobile platforms increases, some neural-based models are expected to run on mobile devices.", "Thus, it is becoming more important to compress the size of NLP models for deployment to devices with limited memory or storage capacity.In this study, we attempt to reduce the number of parameters used in word embeddings without hurting the model performance.", "Neural networks are known for the significant redundancy in the connections BID8 .", "In this work, we further hypothesize that learning independent embeddings causes more redundancy in the embedding vectors, as the inter-similarity among words is ignored.", "Some words are very similar regarding the semantics.", "For example, \"dog\" and \"dogs\" have almost the same meaning, except one is plural.", "To efficiently represent these two words, it is desirable to share information between the two embeddings.", "However, a small portion in both vectors still has to be trained independently to capture the syntactic difference.Following the intuition of creating partially shared embeddings, instead of assigning each word a unique ID, we represent each word w with a code C w = (C an integer number in [1, K] .", "Ideally, similar words should have similar codes.", "For example, we may desire C dog = (3, 2, 4, 1) and C dogs = (3, 2, 4, 2).", "Once we have obtained such compact codes for all words in the vocabulary, we use embedding vectors to represent the codes rather than the unique words.", "More specifically, we create M codebooks E 1 , E 2 , ..., E M , each containing K codeword vectors.", "The embedding of a word is computed by summing up the codewords corresponding to all the components in the code as DISPLAYFORM0 where DISPLAYFORM1 w -th codeword in the codebook E i .", "In this way, the number of vectors in the embedding matrix will be M × K, which is usually much smaller than the vocabulary size.", "FIG0 gives an intuitive comparison between the compositional approach and the conventional approach (assigning unique IDs).", "The codes of all the words can be stored in an integer matrix, denoted by C. Thus, the storage footprint of the embedding layer now depends on the total size of the combined codebook E and the code matrix C.Although the number of embedding vectors can be greatly reduced by using such coding approach, we want to prevent any serious degradation in performance compared to the models using normal embeddings.", "In other words, given a set of baseline word embeddingsẼ(w), we wish to find a set of codesĈ and combined codebookÊ that can produce the embeddings with the same effectiveness asẼ(w).", "A safe and straight-forward way is to minimize the squared distance between the baseline embeddings and the composed embeddings as DISPLAYFORM2 where |V | is the vocabulary size.", "The baseline embeddings can be a set of pre-trained vectors such as word2vec BID29 or GloVe BID34 embeddings.In Eq. 3, the baseline embedding matrixẼ is approximated by M codewords selected from M codebooks.", "The selection of codewords is controlled by the code C w .", "Such problem of learning compact codes with multiple codebooks is formalized and discussed in the research field of compressionbased source coding, known as product quantization BID16 and additive quantization BID1 BID28 .", "Previous works learn compositional codes so as to enable an efficient similarity search of vectors.", "In this work, we utilize such codes for a different purpose, that is, constructing word embeddings with drastically fewer parameters.Due to the discreteness in the hash codes, it is usually difficult to directly optimize the objective function in Eq. 3.", "In this paper, we propose a simple and straight-forward method to learn the codes in an end-to-end neural network.", "We utilize the Gumbel-softmax trick BID27 BID15 to find the best discrete codes that minimize the loss.", "Besides the simplicity, this approach also allows one to use any arbitrary differentiable loss function, such as cosine similarity.The contribution of this work can be summarized as follows:• We propose to utilize the compositional coding approach for constructing the word embeddings with significantly fewer parameters.", "In the experiments, we show that over 98% of the embedding parameters can be eliminated in sentiment analysis task without affecting performance.", "In machine translation tasks, the loss-free compression rate reaches 94% ∼ 99%.•", "We propose a direct learning approach for the codes in an end-to-end neural network, with a Gumbel-softmax layer to encourage the discreteness.•", "The neural network for learning codes will be packaged into a tool 1 . With", "the learned codes and basis vectors, the computation graph for composing embeddings is fairly easy to implement, and does not require modifications to other parts in the neural network.", "In this work, we propose a novel method for reducing the number of parameters required in word embeddings.", "Instead of assigning each unique word an embedding vector, we compose the embedding vectors using a small set of basis vectors.", "The selection of basis vectors is governed by the hash code of each word.", "We apply the compositional coding approach to maximize the storage efficiency.", "The proposed method works by eliminating the redundancy inherent in representing similar words with independent embeddings.", "In our work, we propose a simple way to directly learn the discrete codes in a neural network with Gumbel-softmax trick.", "The results show that the size of the embedding layer was reduced by 98% in IMDB sentiment analysis task and 94% ∼ 99% in machine translation tasks without affecting the performance.Our approach achieves a high loss-free compression rate by considering the semantic inter-similarity among different words.", "In qualitative analysis, we found the learned codes of similar words are very close in Hamming space.", "As our approach maintains a dense basis matrix, it has the potential to be further compressed by applying pruning techniques to the dense matrix.", "The advantage of compositional coding approach will be more significant if the size of embedding layer is dominated by the hash codes.A APPENDIX: SHARED CODESIn both tasks, when we use a small code decomposition, we found some hash codes are assigned to multiple words.", "Table 6 lists some samples of shared codes with their corresponding words from the sentiment analysis task.", "This phenomenon does not cause a problem in either task, as the words only have shared codes when they have almost the same sentiments or target translations.shared code words 4 7 7 0 4 7 1 1 homes cruises motel hotel resorts mall vacations hotels 6 6 7 1 4 0 2 0 basketball softball nfl nascar baseball defensive ncaa tackle nba 3 7 3 2 4 3 3 0 unfortunately hardly obviously enough supposed seem totally ... 4 6 7 0 4 7 5 0 toronto oakland phoenix miami sacramento denver minneapolis ... 7 7 6 6 7 3 0 0 yo ya dig lol dat lil bye Table 6 : Examples of words sharing same codes when using a 8 × 8 code decomposition B APPENDIX: SEMANTICS OF CODES In order to see whether each component captures semantic meaning.", "we learned a set of codes using a 3 x 256 coding scheme, this will force the model to decompose each embedding into 3 vectors.", "In order to maximize the compression rate, the model must make these 3 vectors as independent as possible.", "Table 7 : Some code examples using a 3 × 256 coding scheme.As we can see from Table 7 , we can transform \"man/king\" to \"woman/queen\" by change the subcode \"210\" in the first component to \"232\".", "So we can think \"210\" must be a \"male\" code, and \"232\" must be a \"female\" code.", "Such phenomenon can also be observed in other words such as city names." ]

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[ "Compressing the word embeddings over 94% without hurting the performance." ]

[ "It is important to detect anomalous inputs when deploying machine learning systems.", "The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples.", "At the same time, diverse image and text data are available in enormous quantities.", "We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE).", "This enables anomaly detectors to generalize and detect unseen anomalies.", "In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance.", "We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue.", "We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.", "Machine Learning systems in deployment often encounter data that is unlike the model's training data.", "This can occur in discovering novel astronomical phenomena, finding unknown diseases, or detecting sensor failure.", "In these situations, models that can detect anomalies (Liu et al., 2018; Emmott et al., 2013) are capable of correctly flagging unusual examples for human intervention, or carefully proceeding with a more conservative fallback policy.Behind many machine learning systems are deep learning models (Krizhevsky et al., 2012) which can provide high performance in a variety of applications, so long as the data seen at test time is similar to the training data.", "However, when there is a distribution mismatch, deep neural network classifiers tend to give high confidence predictions on anomalous test examples (Nguyen et al., 2015) .", "This can invalidate the use of prediction probabilities as calibrated confidence estimates (Guo et al., 2017) , and makes detecting anomalous examples doubly important.Several previous works seek to address these problems by giving deep neural network classifiers a means of assigning anomaly scores to inputs.", "These scores can then be used for detecting outof-distribution (OOD) examples (Hendrycks & Gimpel, 2017; Lee et al., 2018; Liu et al., 2018) .", "These approaches have been demonstrated to work surprisingly well for complex input spaces, such as images, text, and speech.", "Moreover, they do not require modeling the full data distribution, but instead can use heuristics for detecting unmodeled phenomena.", "Several of these methods detect unmodeled phenomena by using representations from only in-distribution data.In this paper, we investigate a complementary method where we train models to detect unmodeled data by learning cues for whether an input is unmodeled.", "While it is difficult to model the full data distribution, we can learn effective heuristics for detecting out-of-distribution inputs by exposing the model to OOD examples, thus learning a more conservative concept of the inliers and enabling the detection of novel forms of anomalies.", "We propose leveraging diverse, realistic datasets for this purpose, with a method we call Outlier Exposure (OE).", "OE provides a simple and effective way to consistently improve existing methods for OOD detection.Through numerous experiments, we extensively evaluate the broad applicability of Outlier Exposure.", "For multiclass neural networks, we provide thorough results on Computer Vision and Natural Language Processing tasks which show that Outlier Exposure can help anomaly detectors generalize to and perform well on unseen distributions of outliers, even on large-scale images.", "We also demonstrate that Outlier Exposure provides gains over several existing approaches to out-of-distribution detection.", "Our results also show the flexibility of Outlier Exposure, as we can train various models with different sources of outlier distributions.", "Additionally, we establish that Outlier Exposure can make density estimates of OOD samples significantly more useful for OOD detection.", "Finally, we demonstrate that Outlier Exposure improves the calibration of neural network classifiers in the realistic setting where a fraction of the data is OOD.", "Our code is made publicly available at https://github.com/hendrycks/outlier-exposure.", "Extensions to Multilabel Classifiers and the Reject Option.", "Outlier Exposure can work in more classification regimes than just those considered above.", "For example, a multilabel classifier trained on CIFAR-10 obtains an 88.8% mean AUROC when using the maximum prediction probability as the OOD score.", "By training with OE to decrease the classifier's output probabilities on OOD samples, the mean AUROC increases to 97.1%.", "This is slightly less than the AUROC for a multiclass model tuned with OE.", "An alternative OOD detection formulation is to give classifiers a \"reject class\" (Bartlett & Wegkamp, 2008) .", "Outlier Exposure is also flexible enough to improve performance in this setting, but we find that even with OE, classifiers with the reject option or multilabel outputs are not as competitive as OOD detectors with multiclass outputs.", "In addition to size and realism, we found diversity of D OE out to be an important factor.", "Concretely, a CIFAR-100 classifier with CIFAR-10 as D OE out hardly improves over the baseline.", "A CIFAR-10 classifier exposed to ten CIFAR-100 outlier classes corresponds to an average AUPR of 78.5%.", "Exposed to 30 such classes, the classifier's average AUPR becomes 85.1%.", "Next, 50 classes corresponds to 85.3%, and from thereon additional CIFAR-100 classes barely improve performance.", "This suggests that dataset diversity is important, not just size.", "In fact, experiments in this paper often used around 1% of the images in the 80 Million Tiny Images dataset since we only briefly fine-tuned the models.", "We also found that using only 50,000 examples from this dataset led to a negligible degradation in detection performance.", "Additionally, D OE Improves Calibration.", "When using classifiers for prediction, it is important that confidence estimates given for the predictions do not misrepresent empirical performance.", "A calibrated classifier gives confidence probabilities that match the empirical frequency of correctness.", "That is, if a calibrated model predicts an event with 30% probability, then 30% of the time the event transpires.", "In this paper, we proposed Outlier Exposure, a simple technique that enhances many current OOD detectors across various settings.", "It uses out-of-distribution samples to teach a network heuristics to detect new, unmodeled, out-of-distribution examples.", "We showed that this method is broadly applicable in vision and natural language settings, even for large-scale image tasks.", "OE can improve model calibration and several previous anomaly detection techniques.", "Further, OE can teach density estimation models to assign more plausible densities to out-of-distribution samples.", "Finally, Outlier Exposure is computationally inexpensive, and it can be applied with low overhead to existing systems.", "In summary, Outlier Exposure is an effective and complementary approach for enhancing out-of-distribution detection systems." ]

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[ "OE teaches anomaly detectors to learn heuristics for detecting unseen anomalies; experiments are in classification, density estimation, and calibration in NLP and vision settings; we do not tune on test distribution samples, unlike previous work" ]

[ "While generative neural networks can learn to transform a specific input dataset into a specific target dataset, they require having just such a paired set of input/output datasets.", "For instance, to fool the discriminator, a generative adversarial network (GAN) exclusively trained to transform images of black-haired *men* to blond-haired *men* would need to change gender-related characteristics as well as hair color when given images of black-haired *women* as input.", "This is problematic, as often it is possible to obtain *a* pair of (source, target) distributions but then have a second source distribution where the target distribution is unknown.", "The computational challenge is that generative models are good at generation within the manifold of the data that they are trained on.", "However, generating new samples outside of the manifold or extrapolating \"out-of-sample\" is a much harder problem that has been less well studied.", "To address this, we introduce a technique called *neuron editing* that learns how neurons encode an edit for a particular transformation in a latent space.", "We use an autoencoder to decompose the variation within the dataset into activations of different neurons and generate transformed data by defining an editing transformation on those neurons.", "By performing the transformation in a latent trained space, we encode fairly complex and non-linear transformations to the data with much simpler distribution shifts to the neuron's activations.", "Our technique is general and works on a wide variety of data domains and applications.", "We first demonstrate it on image transformations and then move to our two main biological applications: removal of batch artifacts representing unwanted noise and modeling the effect of drug treatments to predict synergy between drugs.", "A common situation arises when we have two datasets and seek to learn a transformation that is a mapping from one (the source) to the other (the target).", "While much existing work has been done on this, less studied is the case where we want to learn a transformation from this source/target pair of datasets and apply it to a second source dataset for which there is no known target.", "If the second source distribution differs from the first source distribution, any transformation naively learned with a neural network on only the first source/target pair will suffer from problems including domain shift (the second source distribution systematically differs from the first) and overfitting (which aspects of the target only exist because it started as the first source distribution, and shouldn't be part of the learned transformation?).", "This problem is important to address, as learning transformations is a common task in many different contexts, and often it is infeasible or impossible to obtain known source/target pairing information for every distribution needing to be transformed.", "For example, many experiments in biology are conducted to study the effect of a treatment on a set of samples, such as tissues from different patients.", "However, due to their expense and difficulty, clinical trials are often performed on only a small subset of the samples.", "The challenge is isolating treatment-induced variation from the confounding sample-specific variation.", "We propose a neural network-based method for learning a transformation that is general enough to be used across a wide range of data modalities and applications, from image-to-image translation to treatment in the biological setting.", "Popular neural network architectures like GANs pose the problem as one of learning to output data in the region of the space occupied by the target distribution, no matter where the input data is coming from.", "To fool the discriminator, the generator's output must end up in the same part of the space as the target distribution.", "The discriminator does not take into account the input points into the generator in any way.", "Instead, we reframe the problem as learning a transformation towards the target distribution that is more sensitive to where the input data starts.", "Thus, we could learn an edit between one source and target pair, and apply it to a second source without needing to assume it has no systematic differences from the first source.", "We propose to learn such an edit, which we term neuron editing, in the latent space of an autoencoder neural network with non-linear activations.", "First we train an autoencoder on the entire population of data which we are interested in transforming.", "This includes both the paired source/target data and the second source data.", "Neuron editing then involves extracting observed differences between the source/target activation distributions for neurons in this layer and then applying them to the second source data to generate a synthetic second target dataset.", "Performing the edit node-by-node in this space actually encodes complex multivariate edits in the ambient space, performed on denoised and meaningful features, owing to the fact that these features themselves are complex non-linear combinations of the input features.", "Neuron editing is a general technique that could be applied to the latent space of any neural network, even GANs themselves.", "We focus exclusively on the autoencoder in this work, however, to leverage its denoising ability, robustness to mode dropping, and superior training stability as compared to GANs.", "We demonstrate that neuron editing can work on a variety of architectures, while offering the advantages of introducing no new hyperparameters to tune and being stable across multiple runs.", "While latent space manipulation has been explored in previous work, ours differs in several ways.", "For example, Radford et al. (2015) represents a transformation between two distributions as a single constant shift in latent space.", "In addition to assuming the latent transformation is the same for all points in the distribution, Upchurch et al. (2017) also uses an off-the-shelf pre-trained Imagenet classifier network.", "Our work, on the other hand, does not require a richly supervised pre-trained model; also, we model the shift between two distributions as a complex, non-constant function that learns different shifts for different parts of the space.", "We compare to this \"constant-shift\" approach and demonstrate empirically why it is necessary to model the transformation more complexly.", "Some neurons are not heavily edited but still influence the output jointly with those neurons that are edited due to their integration in the decoding layers, propagating their effect into the output space.", "Thus, even a relatively simple transformation in the internal layer of an autoencoder allows for modeling complex transformations in the ambient data space.", "This aspect of neuron editing draws close connections with the field of domain adaptation, where the goal is to learn features on one labeled dataset that meaningfully separate points in another, unlabeled dataset (Tzeng et al., 2017) .", "Similarly to that task, we want to learn a transformation from the known source to the known target samples that will also apply to the second source dataset where the target is unknown.", "Thus, neuron editing represents an extension of domain adaptation, where instead of learning a classifier that can be used on the unlabeled data, we are learning a distribution transformation that can be used on the unlabeled data.", "Further differences include that while domain adaptation attempts to make features for the unlabeled dataset overlap with those of the labeled dataset, neuron editing transforms the second source dataset without first trying to align it to the first source dataset (Sankaranarayanan et al., 2018) .", "Also, different from many domain adaptation techniques, we do not need any sort of pre-trained classifier to yield an informative feature map for the data, as we learn our autoencoder de novo (Long et al., 2017) .", "Given the near exclusive focus of the domain adaptation community on learning classifiers on labeled data and applying it to unlabeled data, we are excited to expand the field to also learning transformations on data with known targets and applying it to data with unknown targets.", "We demonstrate that neuron editing extrapolates better than generative models on two important criteria.", "First, as to the original goal, the predicted change on the second source dataset more closely resembles the predicted change on the original source dataset.", "Second, the editing process produces more complex variation, since it simply preserves the existing variation in the data rather than needing a generator to learn to create it.", "We compare to standard GAN approaches, dedicated parametric statistical methods used by computational biologists, and alternative autoencoder frameworks.", "In Figure 1 :", "(a) Neuron editing interrupts the standard feedforward process, editing the neurons of a trained encoder/decoder to include the source-to-target variation, and letting the trained decoder cascade the resulting transformation back into the original data space.", "(b) The neuron editing process.", "The transformation is learned on the distribution of neuron activations for the source and applied to the distribution of neuron activations for the extrapolation data.", "each case, we see that they stumble on one or more of several hurdles: out-of-sample input, desired output that differs from the target of the training data, and data with complex variation.", "In the following section, we detail the neuron editing method.", "Then, we motivate the extrapolation problem by trying to perform natural image domain transfer on the canonical CelebA dataset .", "We then move to two biological applications where extrapolation is essential: correcting the artificial variability introduced by measuring instruments (batch effects), and predicting the combined effects of multiple drug treatments (combinatorial drug effects) (Anchang et al., 2018) .", ", and second source distributions with n S , n T , and n X observations, respectively.", "We seek a transformation such that:", "1. when applied to S it produces a distribution equivalent to", "T 2. when applied to T it is the identity function and", "3. when applied to X it does not necessarily produce T if S is different from X. While GANs learn a transformation with the first two properties, they fail at the third property due to the fact that T is the only target data we have for training, and thus the generator only learns to output data like T .", "Therefore, instead of learning such a transformation parameterized by a neural network, we learn a simpler transformation on a space learned by a neural network (summarized in Figure 1 ).", "We first train an encoder/decoder pair E/D to map the data into an abstract neuron space decomposed into high-level features such that it can also decode from that space, i.e., the standard autoencoder objective L:", "where MSE is the mean-squared error.", "The autoencoder is trained on all three data distributions S, T , and X and thus learns to model their joint manifold.", "Then, without further training, we separately extract the activations of an n-dimensional internal layer of the network for inputs from S and from T , denoted by a S : S → R n , a T : T → R n .", "We define a piecewise linear transformation, called N euronEdit, which we apply to these distributions of activations:", "where a ∈ R n consists of n activations for a single network input, p S j , p T j ∈ R n consist of the j th percentiles of activations (i.e., for each of the n neurons) over the distributions of a S , a T correspondingly, and all operations are taken pointwise, i.e., independently on each of the n neurons in the layer.", "Then, we define N euronEdit(a S ) : S → R n given by x → N euronEdit(a S (x)), and equivalently for a T and any other distribution (or collection) of activations over a set of network inputs.", "Therefore, the N euronEdit function operates on distributions, represented via activations over network input samples, and transforms the input activation distribution based on the difference between the source and target distributions (considered via their percentile disctretization).", "We note that the N euronEdit function has the three properties we stated above:", "This last property is crucial since learning to generate distributions like T , with a GAN for example, would produce a discriminator who encourages the output to be funneled as close to T as posssible no matter where in the support we start from.", "To apply the learned transformation to X, we first extract the activations of the internal layer computed by the encoder, a X .", "Then, we edit the activations with the neuron editing functionâ X .", "Finally, we cascade the transformations applied to the neuron activations through the decoder without any further training.", "Thus, the transformed outputX is obtained by:", "We emphasize that at this point, since we do no further training of the encoder and decoder, and since the neuron editing transformation has no weights to learn, there is no further objective term to minimize at this point and the transformation is fully defined.", "Crucially, the nomenclature of an autoencoder no longer strictly applies.", "If we allowed the encoder or decoder to train with the transformed neuron activations, the network could learn to undo these transformations and still produce the identity function.", "However, since we freeze training and apply these transformations exclusively on inference, we turn an autoencoder into a generative model that need not be close to the identity.", "Training a GAN in this setting could exclusively utilize the data in S and T , since we have no real examples of the output for X to feed to the discriminator.", "Neuron editing, on the other hand, is able to model the variation intrinsic to X in an unsupervised manner despite not having real posttransformation data for X. Since we know a priori that X will differ substantially from S, this provides significantly more information.", "Furthermore, GANs are notoriously tricky to train (Salimans et al., 2016; Gulrajani et al., 2017; Wei et al., 2018) .", "Adversarial discriminators suffer from oscillating optimization dynamics , uninterpretable losses (Barratt & Sharma, 2018; , and most debilitatingly, mode collapse (Srivastava et al., 2017; Kim et al., 2017; Nagarajan & Kolter, 2017) .", "Under mode collapse, significant diversity that should exist in the output of the generator is lost, instead producing synthetic data that is a severely degenerated version of the true target distribution.", "Neuron editing avoids all of these traps by learning an unsupervised model of the data space with the easier-to-train autoencoder.", "The essential step that facilitates generation is the isolation of the variation in the neuron activations that characterizes the difference between source and target distributions.", "There is a relationship between neuron editing and the well-known word2vec embeddings in natural language processing (Goldberg & Levy, 2014) .", "There, words are embedded in a latent space where a meaningful transformation such as changing the gender of a word is a constant vector in this space.", "This vector can be learned on one example, like transforming man to woman, and then extrapolated to another example, like king, to predict the location in the space of queen.", "Neuron editing is an extension in complexity of word2vec's vector arithmetic, because instead of transforming a single point into another single point, it transforms an entire distribution into another distribution.", "In this work, we have only consider learning from a single pair of distributions and applying it to another single distribution.", "We consider it an interesting direction for future work to extend this to multiple distributions, either for learning from and application to.", "Additional future work along these lines could include training parallel encoders with the same decoder, or training to generate conditionally." ]

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[ "A method for learning a transformation between one pair of source/target datasets and applying it a separate source dataset for which there is no target dataset" ]

[ "In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle.", "We study the effectiveness of the near- optimal cost-to-go oracle on the planning horizon and demonstrate that the cost- to-go oracle shortens the learner’s planning horizon as function of its accuracy: a globally optimal oracle can shorten the planning horizon to one, leading to a one- step greedy Markov Decision Process which is much easier to optimize, while an oracle that is far away from the optimality requires planning over a longer horizon to achieve near-optimal performance.", "Hence our new insight bridges the gap and interpolates between imitation learning and reinforcement learning.", "Motivated by the above mentioned insights, we propose Truncated HORizon Policy Search (THOR), a method that focuses on searching for policies that maximize the total reshaped reward over a finite planning horizon when the oracle is sub-optimal.", "We experimentally demonstrate that a gradient-based implementation of THOR can achieve superior performance compared to RL baselines and IL baselines even when the oracle is sub-optimal.", "Reinforcement Learning (RL), equipped with modern deep learning techniques, has dramatically advanced the state-of-the-art in challenging sequential decision problems including high-dimensional robotics control tasks as well as video and board games BID13 BID23 .", "However, these approaches typically require a large amount of training data and computational resources to succeed.", "In response to these challenges, researchers have explored strategies for making RL more efficient by leveraging additional information to guide the learning process.", "Imitation learning (IL) is one such approach.", "In IL, the learner can reference expert demonstrations BID0 , or can access a cost-to-go oracle BID19 , providing additional information about the long-term effects of learner decisions.", "Through these strategies, imitation learning lowers sample complexity by reducing random global exploration.", "For example, BID25 shows that, with access to an optimal expert, imitation learning can exponentially lower sample complexity compared to pure RL approaches.", "Experimentally, researchers also have demonstrated sample efficiency by leveraging expert demonstrations by adding demonstrations into a replay buffer BID28 BID14 , or mixing the policy gradient with a behavioral cloning-related gradient BID18 .Although", "imitating experts can speed up the learning process in RL tasks, the performance of the learned policies are generally limited to the performance of the expert, which is often sub-optimal in practice. Previous", "imitation learning approaches with strong theoretical guarantees such as Data Aggregation (DAgger) BID20 and Aggregation with Values (AGGREVATE) BID19 can only guarantee a policy which performs as well as the expert policy or a one-step deviation improvement over the expert policy.1 Unfortunately", ", this implies that imitation learning with a sub-optimal expert will often return a sub-optimal policy. Ideally, we", "want the best of both IL and RL: we want to use the expert to quickly learn a reasonable policy by imitation, while also exploring how to improve upon the expert with RL. This would", "allow the learner to overcome the sample inefficiencies inherent in a pure RL strategy while also allowing the learner to eventually surpass a potentially sub-optimal expert. Combining", "RL and IL is, in fact, not new. BID5 attempted", "to combine IL and RL by stochastically interleaving incremental RL and IL updates. By doing so, the", "learned policy will either perform as well as the expert policy-the property of IL BID19 , or eventually reach a local optimal policy-the property of policy iteration-based RL approaches. Although, when the", "expert policy is sub-optimal, the learned locally optimal policy could potentially perform better than the expert policy, it is still difficult to precisely quantify how much the learner can improve over the expert.In this work, we propose a novel way of combining IL and RL through the idea of Reward Shaping BID16 . Throughout our paper", "we use cost instead of reward, and we refer to the concept of reward shaping with costs as cost shaping. We assume access to", "a cost-to-go oracle that provides an estimate of expert cost-to-go during training. The key idea is that", "the cost-to-go oracle can serve as a potential function for cost shaping. For example, consider", "a task modeled by a Markov Decision Process (MDP). Cost shaping with the", "cost-to-go oracle produces a new MDP with an optimal policy that is equivalent to the optimal policy of the original MDP BID16 . The idea of cost shaping", "naturally suggests a strategy for IL: pick a favourite RL algorithm and run it on the new MDP reshaped using expert's cost-to-go oracle. In fact, BID16 demonstrated", "that running SARSA BID26 on an MDP reshaped with a potential function that approximates the optimal policy's value-to-go, is an effective strategy.We take this idea one step further and study the effectiveness of the cost shaping with the expert's cost-to-go oracle, with a focus on the setting where we only have an imperfect estimatorV e of the cost-to-go of some expert policy π e , i.e.,V e = V * , where V * is the optimal policy's cost-to-go in the original MDP. We show that cost shaping with", "the cost-to-go oracle shortens the learner's planning horizon as a function of the accuracy of the oracleV e compared to V * . Consider two extremes. On one", "hand, when we reshape", "the cost of the original MDP with V * (i.e.,V e = V * ), the reshaped MDP has an effective planning horizon of one: a policy that minimizes the one-step cost of the reshaped MDP is in fact the optimal policy (hence the optimal policy of the original MDP). On the other hand, when the", "cost-to-go oracle provides no information regarding V * , we have no choice but simply optimize the reshaped MDP (or just the original MDP) using RL over the entire planning horizon.With the above insight, we propose the high-level strategy for combining IL and RL, which we name Truncated HORizon Policy Search with cost-to-go oracle (THOR). The idea is to first shape", "the cost using the expert's cost-to-go oracleV e , and then truncate the planning horizon of the new MDP and search for a policy that optimizes over the truncated planning horizon. For discrete MDPs, we mathematically", "formulate this strategy and guarantee that we will find a policy that performs better than the expert with a gap that can be exactly quantified (which is missing in the previous work of BID5 ). In practice, we propose a gradient-based", "algorithm that is motivated from this insight. The practical algorithm allows us to leverage", "complex function approximators to represent policies and can be applied to continuous state and action spaces. We verify our approach on several MDPs with continuous", "state and action spaces and show that THOR can be much more sample efficient than strong RL baselines (we compared to Trust Region Policy Optimization with Generalized Advantage Estimation (TRPO-GAE) ), and can learn a significantly better policy than AGGREVATE (we compared to the policy gradient version of AGGREVATE from BID25 ) with access only to an imperfect cost-to-go oracle.", "We propose a novel way of combining IL and RL through the idea of cost shaping with an expert oracle.", "Our theory indicates that cost shaping with the oracle shortens the learner's planning horizon as a function of the accuracy of the oracle compared to the optimal policy's value function.", "Specifically, when the oracle is the optimal value function, we show that by setting k = 1 reveals previous imitation learning algorithm AGGREVATED.", "On the other hand, we show that when the oracle is imperfect, using planning horizon k > 1 can learn a policy that outperforms a policy that would been learned by AGGREVATE and AGGREVATED (i.e., k = 1).", "With this insight, we propose THOR (Truncated HORizon policy search), a gradient based policy search algorithm that explicitly focusing on minimizing the total cost over a finite planning horizon.", "Our formulation provides a natural half-way point between IL and RL, and experimentally we demonstrate that with a reasonably accurate oracle, our approach can outperform RL and IL baselines.", "We believe our high-level idea of shaping the cost with the oracle and then focusing on optimizing a shorter planning horizon is not limited to the practical algorithm we proposed in this work.", "In fact our idea can be combined with other RL techniques such as Deep Deterministic Policy Gradient (DDPG) BID12 , which has an extra potential advantage of storing extra information from the expert such as the offline demonstrations in its replay buffer BID28 ).", "Though in our experiments, we simply used some expert's demonstrations to pre-trainV e using TD learning, there are other possible ways to learn a more accurateV e .", "For instance, if an expert is available during training BID20 , one can online updateV e by querying expert's feedback.A PROOF OF THEOREM 3.1 Figure 3 : The special MDP we constructed for theorem 3.1Proof.", "We prove the theorem by constructing a special MDP shown in Fig 3, where H = ∞.", "The MDP has deterministic transition, 2H + 2 states, and each state has two actions a 1 and a 2 as shown in Fig. 3 .", "Every episode starts at state s 0 .", "For state s i (states on the top line), we have c(s i ) = 0 and for state s i (states at the bottom line) we have c(s i ) = 1.It is clear that for any state s i , we have Q * (s i , a 1 ) = 0, Q * (s i , a 2 ) = γ, Q * (s i , a 1 ) = 1 and Q * (s i , a 2 ) = 1 + γ, for i ≥ 1.", "Let us assume that we have an oracleV e such thatV e (s i ) = 0.5 + δ and V e (s i ) = 0.5 − δ, for some positive real number δ.", "Hence we can see that |V e (s) − V * (s)| = 0.5 + δ, for all s.", "DenoteQ e (s, a) = c(s, a) + γE s ∼Psa [V e (s )], we know thatQ e (s i , a 1 ) = γ(0.5 + δ),Q e (s i , a 2 ) = γ(0.5 − δ),Q e (s i , a 1 ) = 1 + γ(0.5 + δ) andQ e (s i , a 2 ) = 1 + γ(0.5 − δ).It", "is clear that the optimal policy π * has cost J(π * ) = 0. Now", "let us compute the cost of the induced policy from oracleQ e :π(s) = arg min aQ e (s, a). As", "we can seeπ makes a mistake at every state as arg min aQ e (s, a) = arg min a Q * (s, a). Hence", "we have J(π) = γ 1−γ . Recall", "that in our constructed example, we have = 0.5 + δ. Now let", "δ → 0 + (by δ → 0 + we mean δ approaches to zero from the right side), we have → 0.5, hence J(π) = Proof of Theorem 3.2. In this", "proof, for notation simplicity, we denote V π M0 as V π for any π. Using the", "definition of value function V π , for any state s 1 ∈ S we have: DISPLAYFORM0" ]

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[ "Combining Imitation Learning and Reinforcement Learning to learn to outperform the expert" ]

[ "Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions.", "Most of the existing works implicitly assume that the clean samples from the target distribution are easily available.", "However, in many applications, this assumption is violated.", "In this paper, we consider the observation setting in which the samples from a target distribution are given by the superposition of two structured components, and leverage GANs for learning of the structure of the components.", "We propose a novel framework, demixing-GAN, which learns the distribution of two components at the same time.", "Through extensive numerical experiments, we demonstrate that the proposed framework can generate clean samples from unknown distributions, which further can be used in demixing of the unseen test images.", "In this paper, we consider the classical problem of separating two structured signals observed under the following superposition model: DISPLAYFORM0 where X ∈ X and N ∈ N are the constituent signals/components, and X , N ⊆ R p denote the two structured sets.", "In general the separation problem is inherently ill-posed; however, with enough structural assumption on X and N , it has been established that separation is possible.", "Depending on the application one might be interested in estimating only X (in this case, N is considered as the corruption), which is referred to as denoising, or in recovering (estimating) both X and N which is referred to as demixing.", "Both denoising and demixing arise in a variety of important practical applications in the areas of signal/image processing, computer vision, machine learning, and statistics BID7 BID11 BID3 BID6 .", "Most of the existing demixing techniques assume some prior knowledge on the structures of X and N in order to recover the desired component signals.", "Prior knowledge about the structure of X and N can only be obtained if one has access to the generative mechanism of the signals and clean samples from the probability distribution defined over sets X and N .", "In many practical settings, none of these may be feasible.In this paper, we consider the problem of separating constituent signals from superposed observations when we do not have access to the clean samples from any of the distributions (fully unsupervised approach).", "In particular, we are given a set of superposed observations DISPLAYFORM1 where X i ∈ X and Y i ∈ N are i.i.d samples from their respective (unknowns) distributions.", "In this setup, we explore two questions: First, How can one learn the prior knowledge about the individual components from superposition samples?", "; hence, we concern with a learning problem.", "Second, Can we leverage the implicitly learned constituent distributions for tasks such as demixing of a test image?", ". As a result, in the latter question, we deal with a inference task.", "In this paper, we considered a GAN framework for learning the structure of the constituent components in a superposition observation model.", "We empirically showed that it is possible to implicitly learn the underlying distribution of each component and use them in the downstream task such as demixing of a test mixed image.", "We also investigated the conditions under which the proposed demixing framework fails through extensive experimental simulations and provided some theoretical insights." ]

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[ "An unsupervised learning approach for separating two structured signals from their superposition" ]