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<title>GREAT Score: Global Robustness Evaluation of
Adversarial Perturbation using Generative Models</title>
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<h1 class="title is-1 publication-title">Be Your Own Neighborhood: Detecting Adversarial Examples by the Neighborhood Relations Built on Self-Supervised Learning</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="#" target="_blank">ZAITANG LI</a><sup>1</sup>,</span>
<span class="author-block">
<a href="https://sites.google.com/site/pinyuchenpage/home" target="_blank">Pin-Yu Chen</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://tsungyiho.github.io/" target="_blank">Tsung-Yi Ho</a><sup>1</sup>,
</span>
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<div class="is-size-5 publication-authors">
<span class="author-block"><sup>1</sup>The Chinese University of Hong Kong,</span>
<span class="author-block"><sup>2</sup>IBM Research</span>
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<span class="dnerf">Nerfies</span> turns selfie videos from your phone into
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<h2 class="title is-3">Abstract</h2>
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<p>
Current studies on adversarial robustness mainly focus on aggregating <i>local</i> robustness results from a set of data samples to evaluate and rank different models. However, the local statistics may not well represent the true <i>global</i> robustness of the underlying unknown data distribution. To address this challenge, this paper makes the first attempt to present a new framework, called <strong>GREAT Score</strong>, for global robustness evaluation of adversarial perturbation using generative models. Formally, GREAT Score carries the physical meaning of a global statistic capturing a mean certified attack-proof perturbation level over all samples drawn from a generative model. For finite-sample evaluation, we also derive a probabilistic guarantee on the sample complexity and the difference between the sample mean and the true mean. GREAT Score has several advantages: (1) Robustness evaluations using GREAT Score are efficient and scalable to large models, by sparing the need of running adversarial attacks. In particular, we show high correlation and significantly reduced computation cost of GREAT Score when compared to the attack-based model ranking on RobustBench<sup>1</sup>. (2) The use of generative models facilitates the approximation of the unknown data distribution. In our ablation study with different generative adversarial networks (GANs), we observe consistency between global robustness evaluation and the quality of GANs. (3) GREAT Score can be used for remote auditing of privacy-sensitive black-box models, as demonstrated by our robustness evaluation on several online facial recognition services.
</p>
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<!-- References -->
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<p>
<sup>1</sup> Croce, F., Andriushchenko, M., Sehwag, V., Debenedetti, E., Flammarion, N., Chiang, M., Mittal, P., & Hein, M. (2021). RobustBench: a standardized adversarial robustness benchmark. In <i>Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2)</i>. <a href="https://openreview.net/forum?id=SSKZPJCt7B" target="_blank">https://openreview.net/forum?id=SSKZPJCt7B</a>
</p>
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</div>
<!--/ Abstract. -->
</div>
</section>
<!-- Relations -->
<section class="section">
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<h2 class="title is-3">Neighborhood Relations of AEs and Clean Samples</h2>
<div class="columns is-centered">
<div class="column container-centered">
<img src="./static/images/relations.jpg" alt="Neighborhood Relations of Benign Examples and AEs"/>
<p>
<strong>Figure 1. Neighborhood Relations of AEs and Clean Samples.</strong>
</p>
</div>
</div>
<div class="columns is-centered">
<div class="column has-text-justified">
<p>
The previous method, Latent Neighbourhood Graph (LNG), represents the relationship between the input sample and the reference
sample as a graph, whose nodes are embeddings extracted by DNN and edges are built according to distances between the input node
and reference nodes, and train a graph neural network to detect AEs.
</p>
<p>
In this work, We explore the relationship between inputs and their test-time augmented neighbours. As shown in Figure. 1,
clean samples exhibit a stronger correlation with their neighbors in terms of label consistency and representation
similarity. In contrast, AEs are distinctly separated from their neighbors. According to this observation, we propose <strong>BEYOND</strong>
to detection adversarial examples.
</p>
</div>
</div>
</div>
</section>
<!-- Relations -->
<!-- Overview -->
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<h2 class="title is-3">Method Overview of BEYOND</h2>
<div class="columns is-centered">
<div class="column container-centered">
<img src="./static/images/overview.png" alt="Method Overview of BEYOND"/>
<p><strong>Figure 2. Overview of BEYOND.</strong> First, we augment the input image to obtain a bunch of its neighbors. Then, we
perform the label consistency detection mechanism on the classifier’s prediction of the input image and that of neighbors predicted by
SSL’s classification head. Meanwhile, the representation similarity mechanism employs cosine distance to measure the similarity among
the input image and its neighbors. Finally, The input image with poor label consistency or representation similarity is flagged as AE.</p>
</div>
</div>
</div>
</section>
<!-- Overview -->
<!-- Results -->
<section class="section">
<div class="container is-max-desktop">
<h2 class="title is-3">Detection Performance</h2>
<div class="columns is-centered">
<div class="column container-centered">
<table class="tg" border="1" style="width:100%;">
<caption><strong>Table 1.</strong>The Area Under the ROC Curve (AUC) of Different Adversarial Detection Approaches on CIFAR-10. LNG
is not open-sourced and the data comes from its report. To align with baselines, classifier: ResNet110, FGSM: &epsilon; = 0.05, PGD:
&epsilon; = 0.02. Note that BEYOND needs no AE for training, leading to the same value on both seen and unseen settings. The <strong>bold</strong> values
are the best performance, and the <u><i>underlined italicized</i></u> values are the second-best performanc</caption>
<thead>
<tr>
<th class="tg-amwm" rowspan="2">AUC(%)</th>
<th class="tg-baqh" colspan="4"><span style="font-weight:bold;font-style:italic">Unse</span><span style="font-weight:bold">e</span><span style="font-weight:bold;font-style:italic">n</span><span style="font-weight:bold">: </span>Attacks used in training are preclude from tests</th>
<th class="tg-baqh" colspan="5"><span style="font-weight:bold;font-style:italic">Seen</span><span style="font-weight:bold">:</span> Attacks used in training are included in tests</th>
</tr>
<tr>
<th class="tg-baqh">FGSM</th>
<th class="tg-baqh">PGD</th>
<th class="tg-baqh">AutoAttack</th>
<th class="tg-baqh">Square</th>
<th class="tg-baqh">FGSM</th>
<th class="tg-baqh">PGD</th>
<th class="tg-baqh">CW</th>
<th class="tg-baqh">AutoAttack</th>
<th class="tg-baqh">Square</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-baqh">DkNN</td>
<td class="tg-baqh">61.55</td>
<td class="tg-baqh">51.22</td>
<td class="tg-baqh">52.12</td>
<td class="tg-baqh">59.46</td>
<td class="tg-baqh">61.55</td>
<td class="tg-baqh">51.22</td>
<td class="tg-baqh">61.52</td>
<td class="tg-baqh">52.12</td>
<td class="tg-baqh">59.46</td>
</tr>
<tr>
<td class="tg-baqh">kNN</td>
<td class="tg-baqh">61.83</td>
<td class="tg-baqh">54.52</td>
<td class="tg-baqh">52.67</td>
<td class="tg-baqh">73.39</td>
<td class="tg-baqh">61.83</td>
<td class="tg-baqh">54.52</td>
<td class="tg-baqh">62.23</td>
<td class="tg-baqh">52.67</td>
<td class="tg-baqh">73.39</td>
</tr>
<tr>
<td class="tg-baqh">LID</td>
<td class="tg-baqh">71.08</td>
<td class="tg-baqh">61.33</td>
<td class="tg-baqh">55.56</td>
<td class="tg-baqh">66.18</td>
<td class="tg-baqh">73.61</td>
<td class="tg-baqh">67.98</td>
<td class="tg-baqh">55.68</td>
<td class="tg-baqh">56.33</td>
<td class="tg-baqh">85.94</td>
</tr>
<tr>
<td class="tg-baqh">Hu</td>
<td class="tg-baqh">84.51</td>
<td class="tg-baqh">58.59</td>
<td class="tg-baqh">53.55</td>
<td class="tg-2imo">95.82</td>
<td class="tg-baqh">84.51</td>
<td class="tg-baqh">58.59</td>
<td class="tg-2imo">91.02</td>
<td class="tg-baqh">53.55</td>
<td class="tg-baqh">95.82</td>
</tr>
<tr>
<td class="tg-baqh">Mao</td>
<td class="tg-baqh">95.33</td>
<td class="tg-2imo">82.61</td>
<td class="tg-2imo">81.95</td>
<td class="tg-baqh">85.76</td>
<td class="tg-baqh">95.33</td>
<td class="tg-baqh">82.61</td>
<td class="tg-baqh">83.10</td>
<td class="tg-baqh">81.95</td>
<td class="tg-baqh">85.76</td>
</tr>
<tr>
<td class="tg-baqh">LNG</td>
<td class="tg-2imo">98.51 </td>
<td class="tg-baqh">63.14 </td>
<td class="tg-baqh">58.47 </td>
<td class="tg-baqh">94.71 </td>
<td class="tg-amwm">99.88 </td>
<td class="tg-2imo">91.39 </td>
<td class="tg-baqh">89.74 </td>
<td class="tg-2imo">84.03 </td>
<td class="tg-2imo">98.82 </td>
</tr>
<tr>
<td class="tg-baqh">BEYOND</td>
<td class="tg-amwm">98.89</td>
<td class="tg-amwm">99.28</td>
<td class="tg-amwm">99.16</td>
<td class="tg-amwm">99.27</td>
<td class="tg-2imo">98.89</td>
<td class="tg-amwm">99.28</td>
<td class="tg-amwm">99.20</td>
<td class="tg-amwm">99.16</td>
<td class="tg-amwm">99.27</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</section>
<!-- Results -->
<!-- Adaptive Attack -->
<section class="section">
<div class="container is-max-desktop">
<h2 class="title is-3">Adaptive Attack</h2>
<div class="columns is-centered">
<div class="column container formula">
<p>
Attackers can design adaptive attacks to try to bypass BEYOND when the attacker knows all the parameters of the model
and the detection strategy. For an SSL model with a feature extractor <i>f</i>, a projector <i>h</i>, and a classification head <i>g</i>,
the classification branch can be formulated as <strong>C</strong>= <i>f</i> &deg; <i>g</i> and the representation branch as <strong>R</strong> = <i>f</i> &deg; <i>h</i>.
To attack effectively, the adversary must deceive the target model while guaranteeing the label consistency and representation similarity of the SSL model.
</div>
</div>
<div class="columns is-centered">
<div class="column container-centered">
<div id="adaptive-loss-formula" class="container">
<div id="adaptive-loss-formula-list" class="row align-items-center formula-list">
<a href=".label-loss" class="selected">Label Consistency Loss</a>
<a href=".representation-loss">Representation Similarity Loss</a>
<a href=".total-loss">Total Loss</a>
<div style="clear: both"></div>
</div>
<div class="row align-items-center adaptive-loss-formula-content">
<span class="formula label-loss formula-content">
$$
\displaystyle
Loss_{label} = \frac{1}{k} \sum_{i=1}^{k} \mathcal{L}\left(\mathbb{C}\left(W^i(x+\delta) \right), y_t\right)
$$
</span>
<span class="formula representation-loss formula-content" style="display: none;">
$$
\displaystyle
Loss_{repre} = \frac{1}{k} \sum_{i=1}^{k}\mathcal{S}(\mathbb{R}(W^i(x+\delta)), \mathbb{R}(x+\delta))
$$
</span>
<span class="formula total-loss formula-content" style="display: none;">
$$\displaystyle \mathcal{L}_C(x+\delta, y_t) + Loss_{label} - \alpha \cdot Loss_{repre}$$
</span>
</div>
</div>
</div>
</div>
<div class="columns is-centered">
<div class="column container adaptive-loss-formula-content">
<p class="formula label-loss formula-content">
where k represents the number of generated neighbors, <i>y</i><sub><i>t</i></sub> is the target class, and <strong><i>L</i></strong> is the cross entropy loss function.
</p>
<p class="formula representation-loss formula-content" style="display: none">
where k represents the number of generated neighbors, and <strong><i>S</i></strong> is the cosine similarity.
</p>
<p class="formula total-loss formula-content" style="display: none;">
where <strong><i>L</i></strong><sub>C</sub> indicates classifier's loss function, <i>y</i><sub><i>t</i></sub> is the targeted class, and &alpha; refers to a hyperparameter,
which is a trade-off parameter between label consistency and representation similarity..
</p>
</div>
</div>
<div class="columns is-centered">
<div class="column is-full-width">
<h3 class="title is-4">Performance of BEYOND against Adaptive Attacks</h3>
<div class="content has-text-justified">
<p>
We evaluate the detection performance of BEYOND against adaptive attacks on different datasets and show the ROC curves under different perturbation budgets as follows:
</p>
</div>
<div class="columns is-vcentered interpolation-panel">
<div id="adaptive-dataset" class="column is-3 align-items-center" style="width: 30%;">
<a href="#c10" class="selected">CIFAR-10</a>
<!-- <a href="#c100" class="selected">CIFAR-100</a> -->
<a href="#imgnet" >ImageNet</a>
<div style="clear: both"></div>
</div>
<div id="c10" class="column interpolation-video-column" style="width: 70%;">
<div id="c10-image-wrapper" >
Loading...
</div>
<input name="c10" class="slider is-full-width is-large is-info interpolation-slider"
step="1" min="0" max="6" value="0" type="range">
<label for="interpolation-slider"><strong>Perturbation Budget &Epsilon;</strong> from 2/255 to 128/255</label>
</div>
<!-- <div id="c100" class="column interpolation-video-column" style="width: 70%; display: none;">
<div id="c100-image-wrapper" >
Loading...
</div>
<input name="c100" class="slider is-full-width is-large is-info interpolation-slider"
step="1" min="0" max="6" value="0" type="range">
<label for="interpolation-slider"><strong>Perturbation Budget &Epsilon;</strong> from 2/255 to 128/255</label>
</div> -->
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<div id="imgnet-image-wrapper" >
Loading...
</div>
<input name="imgnet" class="slider is-full-width is-large is-info interpolation-slider"
step="1" min="0" max="6" value="0" type="range">
<label for="interpolation-slider"><strong>Perturbation Budget &epsilon;</strong> from 2/255 to 128/255</label>
</div>
</div>
<br/>
</div>
</div>
</section>
<!-- Adaptive Attack -->
<section class="section" id="BibTeX">
<div class="container is-max-desktop content">
<h2 class="title">BibTeX</h2>
<pre><code>@article{li2024greatscore,
title = {GREAT Score: Global Robustness Evaluation of Adversarial Perturbation using Generative Models},
author = {Zaitang, Li and Pin-Yu, Chen and Tsung-Yi, Ho},
journal = {NeurIPS},
year = {2024},
}</code></pre>
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