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Please cite this article in press as: Halberstadt AL. Recent advances in the neuropsychopharmacology of serotonergic hallucinogens. Behav Brain Res (2014), http://dx. doi. org/10. 1016/j. bbr. 2014. 07. 016ARTICLE IN PRESSG Model BBR 9035 1-22 16 A. L. Halberstadt / Behavioural Brain Research xxx (2014) xxx-xxx [97] Smith RL, Barrett RJ, Sanders-Bush E. Discriminative stimulus properties of 1-(2,5-dimethoxy-4-iodophenyl)-2-aminopropane [(+/-)DOI] in C57BL/6J mice. Psychopharmacology (Berl) 2003;166:61-8. [98] Benneyworth MA, Smith RL, Barrett RJ, Sanders-Bush E. Complex discrimi-native stimulus properties of (+)lysergic acid diethylamide (LSD) in C57Bl/6J mice. Psychopharmacology (Berl) 2005;179:854-62. [99] Winter JC, Rice KC, Amorosi DJ, Rabin RA. Psilocybin-induced stimulus control in the rat. Pharmacol Biochem Behav 2007;87:472-80. [100] Fantegrossi WE, Reissig CJ, Katz EB, Yarosh HL, Rice KC, Winter JC. 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Functional interactions between prefrontal and visual association cortex contribute1527 15281529153015311532153315341535153615371538153915401541154215431544154515461547154815491550155115521553155415551556155715581559156015611562156315641565156615671568156915701571157215731574157515761577157815791580158115821583158415851586158715881589159015911592159315941595159615971598159916001601160216031604160516061607160816091610161116121613 1614161516161617161816191620162116221623162416251626162716281629163016311632163316341635163616371638163916401641164216431644164516461647164816491650165116521653165416551656165716581659166016611662166316641665166616671668166916701671167216731674167516761677167816791680168116821683168416851686168716881689169016911692169316941695169616971698	Recent advances in the neuropsychopharmacology of -- Halberstadt Adam L_ -- Behavioural Brain Research 277 pages 99-120 2015 jan -- Elsevier -- 10_1016_j_bbr_2014_07_016 -- 95e2af2df9463e8c4ed63dee046
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Psy-chopharmacology (Berl) 1989;98:321-9. 1699 1700170117021703170417051706170717081709171017111712171317141715171617171718171917201721172217231724172517261727172817291730173117321733173417351736173717381739174017411742174317441745174617471748174917501751175217531754175517561757175817591760176117621763176417651766176717681769177017711772177317741775177617771778177917801781178217831784 178517861787178817891790179117921793179417951796179717981799180018011802180318041805180618071808180918101811181218131814181518161817181818191820182118221823182418251826182718281829183018311832183318341835183618371838183918401841184218431844184518461847184818491850185118521853185418551856185718581859186018611862186318641865186618671868	Recent advances in the neuropsychopharmacology of -- Halberstadt Adam L_ -- Behavioural Brain Research 277 pages 99-120 2015 jan -- Elsevier -- 10_1016_j_bbr_2014_07_016 -- 95e2af2df9463e8c4ed63dee046
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Modelling perception as a hierarchical competition differentiates imagined, veridical, and hallucinated percepts Alexander A. Sulfaro1,†,, Amanda K. Robinson1,2, Thomas A. Carlson1 1School of Psychology, Griffith Taylor Building, The University of Sydney, Camperdown, NSW 2006, Australia; 2Queensland Brain Institute, QBI Building 79, The University of Queensland, St Lucia, QLD 4067, Australia †Alexander A. Sulfaro, http://orcid. org/0000-0001-5525-3935 Corresponding author. School of Psychology, Griffith Taylor Building, The University of Sydney, Camperdown, NSW 2006, Australia. E-mail: alexander. sulfaro@sydney. edu. au Abstract Mental imagery is a process by which thoughts become experienced with sensory characteristics. Yet, it is not clear why mental images appear diminished compared to veridical images, nor how mental images are phenomenologically distinct from hallucinations, another type of non-veridical sensory experience. Current evidence suggests that imagination and veridical perception share neural resources. If so, we argue that considering how neural representations of externally generated stimuli (i. e. sensory input) and internally generated stimuli (i. e. thoughts) might interfere with one another can sufficiently differentiate between veridical, imaginary, and hallucinatory perception. We here use a simple computational model of a serially connected, hierarchical network with bidirectional information flow to emulate the primate visual system. We show that modelling even first approximations of neural competition can more coher-ently explain imagery phenomenology than non-competitive models. Our simulations predict that, without competing sensory input, imagined stimuli should ubiquitously dominate hierarchical representations. However, with competition, imagination should dominate high-level representations but largely fail to outcompete sensory inputs at lower processing levels. To interpret our findings, we assume that low-level stimulus information (e. g. in early visual cortices) contributes most to the sensory aspects of perceptual experience, while high-level stimulus information (e. g. towards temporal regions) contributes most to its abstract aspects. Our findings therefore suggest that ongoing bottom-up inputs during waking life may prevent imagination from overriding veridical sensory experience. In contrast, internally generated stimuli may be hallucinated when sensory input is dampened or eradicated. Our approach can explain individual differences in imagery, along with aspects of daydreaming, hallucinations, and non-visual mental imagery. Keywords: mental imagery; hallucinations; aphantasia; hyperphantasia; daydreaming; perception © The Author(s) 2023. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons. org/licenses/by/4. 0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Introduction Mental images are internally generated thoughts which can be seen, heard, or in some way perceived with sensory qualities. Yet, how does the brain generate sensory experiences without a real sensory stimulus in the environment to perceive? One answer might be that mental imagery involves similar processes to those used during veridical perception, yet with an opposite direction of information flow. Instead of pooling together sensory informa-tion to extract abstract knowledge from a real stimulus, mental imagery may involve retrohierarchically reconstructing the sen-sory features of an imagined stimulus from abstract knowledge we already possess. In line with this idea, mental imagery seems to use the same neural machinery as that used during veridical perception ( Kosslyn et al. 1993; Ishai 2010 ; Cichy et al. 2012; Dijk-stra et al. 2017, 2018, 2019a; Xie et al. 2020 ), yet with neural activity during the early stages of veridical visual perception resembling neural activity during the later stages of visual mental imagery and vice versa ( Dentico et al. 2014 ; Linde-Domingo et al. 2019 ; Breedlove et al. 2020; Dijkstra et al. 2020). However, mental imagery is unlikely to be an exact reverse of feedforward processes in veridical perception given that indi-viduals reliably report that their mental images are experienced with some form of reduced sensory quality (termed 'vividness') compared to real images (Galton 1880; Marks 1973). Some researchers have proposed that this difference follows from dif-ferences between feedforward and feedback processes, the latter of which are believed to be responsible for propagating men-tal images. For instance, information about mental image con-tent tends to be most detectable in superficial and deep cortical layers, but not granular mid-layers, in contrast to information about environmental stimulus content, which can be detected across all cortical layers (Lawrence et al. 2018; Bergmann et al. 2019). Other accounts suggest that imagery could be propa-gated using weak feedback connections in the visual system, in Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
2 Sulfaro et al. contrast to feedforward connections that stereotypically drive, rather than modulate, action potentials (Koenig-Robert and Pearson 2021 ). However, feedback to early visual regions can drive action potentials depending on local neurochemistry ( Aru et al. 2020 ). Furthermore, neither of these differences between feedforward and feedback processes can explain the unique expe-rience of mental imagery without a framework specifying what it means for a mental image to be a quasi-sensory experience to begin with. A more readily interpretable explanation is that mental images appear impoverished simply because the features of the images they depict are distorted relative to those of real images. That is, mental images might merely have less-precise image statistics (e. g. spatial frequency, location, and size) compared to real images, but are otherwise just as visible. Breedlove et al. (2020) provide an account that allows for this possibility, finding that represen-tations of mental images in early visual cortices are deficient in detailed sensory information compared to real images. As hierar-chical feedforward processes combine multiple pieces of sensory information (e. g. edges) to form fewer pieces of more abstract information (e. g. a shape), reconstructing sensory information using retrohierarchical feedback requires extrapolating from a rel-atively information-deficient source material. This process should distort imagined stimuli in predictable ways such that neural pop-ulations that represent mental images in early visual cortices have lower spatial frequency preferences, more foveal receptive fields, and larger receptive fields than when responding to real images (Breedlove et al. 2020). Ultimately, many factors may distinguish between veridical and mental percepts given that the former are externally gen-erated while the latter are internally generated. However, any complete explanation of the unique appearance of mental images must also account for how the quasi-sensory experience of mental imagery might be differentiated from other internally generated, yet unambiguously sensory experiences, such as which occur in hallucinations, many dreams, and eidetic imagery. Regardless of the image statistics of the internally generated content being depicted, these latter phenomena tend to involve a sensory expe-rience of internally generated content that is entirely equivalent to the subjective experience of externally generated content (Chiu 1989 ; Ffytche et al. 1998) except that the content experienced is non-veridical and is not typically experienced as part of normal waking life. For the purposes of this article, we refer to the inter-nally generated, unambiguously sensory experience common to each of hallucinations, dreams, and eidetic imagery as hallucina-tory imagery, or a hallucination generally, regardless of whether such imagery is voluntary or involuntary, regardless of whether it is believed to be real or unreal, and regardless of where exactly within the visual field it is perceived to be located. Crucially, while mental imagery is quasi-sensory, seemingly seen yet unseen, hal-lucinatory imagery is definitively visible. This should require that non-veridical, internally generated sensory content or features replace veridical sensory content or features, overwriting them in a given region of the visual field. For instance, hallucinations may involve seeing a cat on this page instead of text, or seeing the text on this page as moving instead of still, or seeing any-thing at all during a dream instead of merely the back of our eyelids. Here, we propose that imagined, veridical, and hallucinated percepts can be clearly distinguished by considering perception as a competitive, hierarchical process. While mental image gen-eration can be modelled without competition from veridical per-ception (e. g. Breedlove et al. 2020), mental imagery almost never occurs in isolation. Instead, mental images are invariably gener-ated while we are awake and receiving sensory input from the external world. If mental imagery and veridical perception share neural resources, then both processes should interact such that neural representations of imagined and real stimuli interfere or compete with one another. Interactions between real and imagined stimuli have been previously demonstrated, lending support to the idea that percep-tion may be a competitive process, although the exact outcome and nature of this interaction seems to vary. For instance, men-tal images can constructively interfere with real image content, depending on stimulus congruency (Dijkstra et al. 2022), and can induce priming or adaptation to veridical stimuli, depending on the individual ( Keogh and Pearson 2017 ; Dijkstra et al. 2019b, 2021). Increasing environmental luminance can also impede the priming effects of mental imagery ( Keogh and Pearson 2017 ), while real modality-specific distractors reduce the recall of modality-specific information (Wais et al. 2010 ; Vredeveldt et al. 2011 ), potentially reflecting competitive interference. We sought to predict whether perceptual interference could account for the quasi-sensory, rather than hallucinatory, experi-ence of mental imagery. Yet, any valid explanation of the quasi-sensory experience of mental imagery must first clearly specify what it means to have a quasi-sensory experience at all. Such an experience may be possible under a framework where per-ceptual experience itself is considered as a multifaceted phe-nomenon, composed of both sensory and abstract experiences at any given time. In vision, this entails having an experience of low-level features of an image, such as its hues and edge ori-entations, while also having an experience of high-level features of what the image actually depicts, such as recognizing that an image is depicting a duck. Usually, low-and high-level features of an image seem intertwined such that it is unintuitive to con-sider them as separate components of perceptual experience. Yet, these aspects become clearly separable when we consider bistable percepts (e. g. the rabbit-duck illusion), where the same low-level information can give rise to different abstract experi-ences. These abstract experiences feel perceptually distinct from one another even though the spatial pattern of light in our visual field, and our purely low-level visual experience of it, remains unchanged. To anchor these experiences to physical processes, we assume that the sensory and abstract aspects of experience are dependent on neural systems encoding each respective type of information in the brain, such as those along the visual ventral stream. However, as neural representations of externally and internally generated stimuli are not explicitly sensory or abstract, but distributed on a spectrum, so too may perceptual experience itself be composed of a spectrum of sensory and abstract aspects. Given that internally generated perceptual experiences also seem to use similar neural resources to their externally generated counterparts, including in a feature-specific manner (Ffytche et al. 1998), then mental and hallucinatory imagery processes may also be experienced with a spectrum of abstract and sensory features. Under this framework, the quasi-sensory experience of mental imagery can be clearly conceptualized as the experience arising from the activation of high-level to mid-level, but not low-level, feature representations of internally generated content, regardless of the content itself. Hallucinatory imagery, in contrast, may invoke low-level sen-sory representations, with or without more abstract components, while veridical percepts should at least invoke low-level featural representations given their bottom-up entryway into the visual system. Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
Modelling perception as a hierarchical competition 3 Figure 1. A hierarchical network modelling interference between externally and internally generated stimuli Note. (a) A hierarchical network model of visual perception. Layer size indicates the relative dimensionality of the encoded representation. Information is pooled via feedforward processes (red, upward arrows) and extrapolated via feedback processes (blue, downward arrows). Lock icons indicate input layers with clamped representations during simulations where mental imagery is attempted during veridical perception. Clamped representations do not evolve with time. Note that a 'thought' here could be any internally generated representation. (b) Evolution rule for unclamped layers. Each value r in the representational matrix of each layer l evolves at each time point t according to a weighted average of the adjacent layers and the current layer at the previous time step with weights w. The ascending value array was convolved with an averaging kernel before being weighted to facilitate feedforward dimensionality reduction. Under these assumptions, we constructed a simple compu-tational model of a serially connected network with bidirec-tional information flow as a first approximation to simulating the hierarchical interaction of internally and externally gener-ated stimulus representations (Fig. 1). We used this model to evaluate the degree to which internally generated (i. e. imagined) stimulus representations are able to spread throughout a hier-archical system, with and without competition from externally generated stimuli. We demonstrate that competition from exter-nal sensory input could prevent internally generated content from ever recruiting the low-level neural infrastructure best suited to representing highly sensory, highly modal information. In doing so, we show that accounting for perceptual interference, even with preliminary models, can provide an arguably more coher-ent explanation for the unique phenomenology of mental imagery than approaches that consider mental imagery in isolation. We explore the perceptual implications of such predictions on the subjective experience of mental imagery, provide a neurochemi-cally grounded hypothesis for variance in imagery across individ-uals and states, and delineate how perceptual interference may relate to hallucinations and mental imagery in non-visual modal-ities. Ultimately, we demonstrate that reconceptualizing mental imagery as an intrinsically competitive process can resolve major lingering questions in imagery research. Materials and Methods Computational model Our goal was to assess the degree and extent to which internally generated stimuli are able to spread throughout a hierarchical system, with and without competition from externally generated stimuli. To do this, a dynamic, serially connected, five-layer com-putational network was constructed as a simple model of how stimulus information may flow bidirectionally in the hierarchical human visual system (Fig. 1). Each layer l encoded a represen-tation r consisting of a square matrix of values. The number of units available to represent information (i. e. dimensionality) in each layer shrank in size from 256 × 256 matrix elements at the lowest layer ( l=0) to 208 × 208 elements at the higher layer (l =4) by linearly decreasing the square root of the number of elements in each layer. This mimics feedforward dimensionality reduction in the visual system such that upper layers encode information that is more abstract than lower layers, analogous to neural struc-tures towards the parietal and temporal lobes ( Binder 2016 ). Each element in the matrix could vary in value along a single dimen-sion, from 0 to 1, encoding the variation of an arbitrary stimulus feature. The lowest layer acted as an input layer for externally generated stimuli and never received feedback, analogous to the retina in visual perception. The network allowed representations to propagate between layers and for bottom-up processes to interact with top-down pro-cesses. Hence, the representation r of each layer l was updated at each time step t according to a weighted average of the ascending representation rl-1 from the layer below, descending representa-tion rl+1 from the layer above, and representation rl of the current layer, each at the previous time step t-1 (Fig. 1b). We note that despite the simplicity of this approach, weighted averaging is approximately equivalent to the biologically plausible additive combination of neural inputs, followed by a decay of activity pro-portional to the strength of activation. However, unlike in real neurons, decay here occurs instantaneously. We allow for this sim-plification given that we simulate the perception of static images only and are therefore most concerned with the steady-state, rather than moment-to-moment, profile of the system. Each layer was updated sequentially, first as part of a feedfor-ward sweep, then as part of a feedback sweep, and then alternating with every subsequent iteration. Weightings wl-1, wl+1, and wl for the ascending, descending, and current representations, respec-tively, were each equal to one except where the effect of weighting ratios was explicitly investigated. However, if a layer acted as a constant source of information in the network (representing either an internally or externally generated stimulus), the values in its representational matrix were locked in place (clamped) by set-ting the weightings of ascending and/or descending inputs to that layer to zero. Given that the retina is always receiving visual input in an awake state, the lowest layer of the network was always Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
4 Sulfaro et al. clamped to some predetermined set of input values. Drawing from modelling by Breedlove et al. (2020), the highest layer in the network was also clamped to a fixed set of input values to simulate an internally generated stimulus (i. e. a thought) during mental imagery. To simulate feedforward information pooling in the visual ven-tral stream, ascending representations were combined using a 13 × 13 square convolutional kernel such that each element of the layer above received the average of inputs from multiple elements from the layer below. Hence, from l=0 to l=4, the receptive field size of each element in each representation increased while layer dimensionality decreased. Because forming a mental image of an object first requires at some point seeing the object or its con-stituent parts, internally generated stimulus representations were formed from externally generated (e. g. retinal) stimulus inputs first processed through a single complete feedforward sweep from the lowest to the highest layer. To assess the degree to which mental imagery was able to compete with veridical sensory input, we allowed the network to evolve under three main sets of initial conditions: veridical perception without imagination, imagination without veridical perception, and imagination during veridical perception. In the first case, to simulate a scenario where externally generated visual input is present without competition, only the bottom layer was clamped to a stimulus representation (veridical perception without imagination). Second, to simulate a scenario where an internally generated stimulus is present without competition, the top layer was clamped to an imagined stimulus representation (imagination without veridical perception). The ascending input from the base layer was downweighted to zero in this scenario to enforce a state of sensory disconnection. Third, in what we con-sider a more realistic mental imagery scenario, both the top and bottom layers were simultaneously clamped to different stimu-lus representations to simulate mental imagery occurring in the presence of competing sensory input (imagination during veridi-cal perception). All intervening or non-input layers were initialized with white noise. In each scenario, we measured the steady-state contribution of top-down representations relative to bottom-up representations at each layer. This was achieved by taking the average value of all elements in each layer for the case where the initial low-level or high-level input representations were set homogenously to zeros or ones, respectively (Fig. 2d-f). Each scenario was also replicated using images as inputs with each element of a representation cor-responding to one pixel in the image such that the collective pixel values of each image equate to a simulated neural activity pat-tern (Fig. 2a-c). A 256 × 256 greyscale image of a camel was used for sensory input, and a 256 × 256 greyscale image of a hat was used for imagined input after conversion to a reduced dimensionality of 208 × 208 via feedforward pooling. Both were sourced from the BOSS image database (Brodeur et al. 2010 ). The similarity between layer activity patterns and the original imagined or veridical stim-ulus patterns can be quantified by calculating the absolute mean pixel difference between the images. We also separately explored how varying the ascending and descending weighting schemes affected competition between simulated imagined and veridical stimulus representations (Fig. 3). For each scenario in Fig. 3, all mid-layer feedforward or feedback weightings were ≤1 with the ratio specified in the figure for the duration of the simulation. Model interpretation Our model can be interpreted as analogous to a simplified model of the human visual processing hierarchy, with a basal layer encoding externally generated retinal input and an apical layer housing more abstract internally generated stimulus represen-tations encoded by neural structures towards the parietal and temporal lobes ( Binder 2016 ). To interpret simulation outcomes phenomenologically, we considered that a single perceptual expe-rience can contain a distribution of information, spanning from highly sensory (modal) in nature to highly abstract (amodal). We assume that each representational layer in the visual hier-archy contributes information to the construction of conscious perceptual experience if it receives both feedforward and feed-back input. We also assume that the type of information provided by each layer aligns with the layer's dimensionality such that high-dimensional representations contribute most to the sensory aspects of the experience, while low-dimensional representations contribute most to the non-sensory aspects of the experience. Hence, low-level representations would be most influential in determining the literal image content of a visual experience (e. g. the exact location, orientation, and contrast of high-spatial fre-quency edges), while high-level representations would contribute most to the abstract understanding of what is being thought about or observed (e. g. knowing whether the edges in a scene form a hat or a camel), with a spectrum of quasi-sensory or quasi-abstract features in between. Crucially, this implies that a perceptual experience gains sensory or abstract properties depending on how well neural regions with the corresponding high-or low-dimensional struc-ture, respectively, are recruited during that experience. Therefore, the further an internally generated stimulus representation is able to spread towards the primary visual cortex, for instance, the more it may be experienced with properties approaching that of an actual visual image (i. e. a true mental image) rather than something pondered without sensory qualia (i. e. a non-sensory thought). This approach can therefore maintain consistency with traditional accounts implicating the primary visual cortex in men-tal imagery ( Kosslyn and Thompson 2003 ; Kosslyn 2005 ; Pearson and Kosslyn 2015; Pearson 2019). Note that, as hallucinatory visual experience is possible with-out corresponding retinal activity, we consider the lowest level in the hierarchy purely as a non-conscious input layer to the rest of the network. We also note that while there is compelling evi-dence that some high-level representations are stored in a largely amodal form (e. g. Popham et al. 2021), they are not necessar-ily completely non-sensory. Late-stage object representations can still contain some degree of sensory information (e. g. Di Carlo and Cox 2007), albeit in a considerably more low-dimensional form relative to primary sensory areas. Our model only requires higher-level representations to be less sensory than low-level representations rather than completely non-sensory. Results Perception without competition T wo scenarios were simulated where competition was not present: veridical perception without imagination and imagination with-out veridical perception. Initiation of veridical perception was simulated by allowing the lowest representational layer to have a non-zero contribution to the layer above. Imagination was sim-ulated by preventing the highest layer from being affected by feedforward inputs below such that it provided a constant source of top-down information to the system. In both cases, only one fixed source of perceptual information was present within the network, either an externally or internally generated stimulus rep-resentation. An example simulation is shown in Fig. 2 using an Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
Modelling perception as a hierarchical competition 5 Figure 2. Veridical stimuli outcompete imagined stimuli at low-level sensory representations, but not high-level abstract representations Note. How simulated neural representations of an internally generated (imagined) hat and an externally generated (veridical) camel spread through a perceptual processing hierarchy with and without competition. (a-c) Simulated neural activity patterns, coded as image pixel values, evolving over 0, 2, and 20 alternating feedforward-feedback sweeps. Initial activity patterns are the same in each scenario and mimic thinking about a hat while receiving a retinal image of a camel. Lock icons indicate clamped representations that do not evolve. The crossed arrow indicates disconnected sensory input (wl=0=0). (a) All layers except the base layer are free to evolve, causing activity patterns to be dominated by the initial veridical input. (b) Mid-layers are free to evolve only. Sensory input is present but disconnected. All evolving activity patterns become dominated by the initial imagined input. (c) Mid-layers are free to evolve only, and sensory input is present and connected. Imagined content dominates upper layers, and veridical content dominates lower layers. The dashed, magenta line indicates the 'representational equilibrium point' where the internally and externally generated stimuli equally contribute to a layer. (d-f) One-dimensional simulations of each scenario in (a)-(c), illustrating how the character of each layer evolves over time. The dominance of the original externally generated stimulus representation at l =0 can be obtained by subtracting the internally generated stimulus dominance from 100%. image of a camel as the externally generated veridical stimulus input (i. e. retinal activity pattern) and a compressed image of a hat as the internally generated imagined stimulus input (i. e. high-level neural activity pattern). Without competition from imagination, all freely evolving (unclamped) layers in the network converged asymptotically to a representation dominated by the externally generated stimu-lus representation (Fig. 2a). Conversely, without competition from veridical perception, all unclamped layers converged to a repre-sentation dominated by the internally generated stimulus repre-sentation (Fig. 2b). As all unclamped representations are eventu-ally dominated by the original externally or internally generated source stimulus, both scenarios each result in a state correspond-ing to having a visual experience of the same stimulus that is being simultaneously thought about abstractly. In the case of pure veridical perception, the system evolves to emulate a common perceptual experience: seeing an object while also knowing what it is. Yet, when the internally generated stimulus is uncontested, the sensory characteristics of the imagined stimulus should com-pletely dominate visual experience, resulting in the perception of what was imagined and not what was present in the environment. Hence, pure imagination imitates hallucinating the object that one is thinking about. Although, in both cases, layer l=1 is entirely dominated by one stimulus, each state occurred through a distinct formation route. Note that the top-down, but not bottom-up, formation route resulted in substantial distortions at lower layers, reflecting the findings of Breedlove et al. (2020). Yet, these distortions only affect the content of the imagined stimulus, not the degree to which that stimulus is able to commandeer a hierarchical layer in this model. Perception with competing imagined and veridical stimuli Where two fixed sources of information are simultaneously present within the network, neither the imagined nor veridi-cal stimulus can dominate every unclamped layer in the sys-tem (Fig. 2c). Instead, the network represents both stimuli simul-taneously at the steady state. However, the further a given layer is from an externally or internally generated stimulus input layer, the smaller the contribution of the original veridical or imagined stimulus to the representation held by the given layer. This is Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
6 Sulfaro et al. Figure 3. Decreasing feedforward-to-feedback weighting ratio increases the sensory character of thoughts Note. Hierarchical competition between simulated neural representations of an internally generated (imagined) hat and an externally generated (veridical) camel modelled under different feedforward-to-feedback weighting ratios. Simulated neural activity patterns, coded as image pixel values, are depicted after 20 alternating feedforward-feedback sweeps. Initial activity patterns are the same in each scenario and mimic thinking about a hat while receiving a retinal image of a camel. Lock icons indicate clamped representations that do not evolve. The crossed arrow indicates disconnected sensory input (wl=0=0). Each dashed, magenta line indicates the 'representational equilibrium point' where the internally and externally generated stimuli contribute equally to a layer. (a-c) Globally varying the ratio of bottom-up (wl-1) and top-down (wl+1) weightings affects representational equilibrium and the extent to which thoughts should be experienced visually (e. g. weak, moderate, or high). (d) All unclamped layers converge towards the original internally generated stimulus representation once sensory input is disconnected, even if feedforward and feedback weights are equal. shown in Fig. 2f for the case where feedforward and feedback weightings are equal (wl-1=wl+1=1). Consequently, when imagination occurs in the presence of bottom-up sensory input, the externally generated veridical stim-ulus dominates low-level representations, while the internally generated imagined stimulus dominates high-level representa-tions. Such a system is therefore representing two distinct stimuli, yet at largely separate hierarchical levels. As lower levels are more suited for representing sensory information and higher lev-els for abstract, this state corresponds to a situation where an individual has a visual experience of their veridical environment despite simultaneously having relatively non-sensory thoughts about what they are imagining. Hence, the simulation suggests that external sensory input outcompetes imagination at the low-level regions that most contribute to the sensory aspects of perceptual experience. Modelling variation in imagery quality (e. g. aphantasia and hyperphantasia) as a shift in representational equilibrium This model can also be used to understand states where thoughts are experienced in a highly sensory way (hyperphantasia) or in a non-sensory or weakly sensory way (aphantasia; Fig. 3). When sen-sory input and imagination compete, our simulation showed that spanning along the perceptual hierarchy from bottom to top cor-responded to transitioning from primarily representing a veridical stimulus to primarily representing an imagined stimulus. The exact point where the two stimuli are represented in equal propor-tion is here dubbed the 'representational equilibrium point' for the system. Representations contain more veridical stimulus charac-ter below this point and more imagined stimulus character above it. The location of the representational equilibrium point can summarize how far an imagined representation can penetrate towards lower layers before it is outcompeted by the veridical stimulus, or how far a veridical stimulus representation can penetrate towards upper layers before it is outcompeted by the imagined stimulus. Where ascending and descending informa-tion is weighted equally ( wl-1=wl+1=1; Fig. 3b), the equilibrium point lies in the middle layer at the centre of the hierarchy such that lower layers (e. g. towards the primary visual cortex) are dominated by externally generated sensory input and upper layers (e. g. towards the temporal lobe) are dominated by inter-nally generated thoughts, symmetrically. However, overweight-ing feedforward information ( wl-1/wl+1> 1) elevates the equilib-rium point such that the imagined stimulus is restricted to only the highest, least-modal hierarchical layers, correspond-ing to a state of aphantasia (Fig. 3a). In contrast, overweighting feedback information (wl-1/wl+1< 1) lowers the equilibrium point such that the imagined stimulus dominates the majority of the hierarchy, corresponding to a state of hyperphantasia (Fig. 3c). Feedforward-to-feedback weighting ratio variation could there-fore account for between-person and moment-to-moment dif-ferences in the apparent sensory quality of mental imagery experiences. Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
Modelling perception as a hierarchical competition 7 Discussion Distinguishing imagined, veridical, and hallucinatory percepts In this study, we aimed to explain the apparent differences in vividness between veridical, imagined, and hallucinated percepts. We show that, for a hierarchical system with bidirectional infor-mation flow, the presence of competing sensory input can prevent internally generated stimuli from dominating low-level regions most suited for supporting a modal, highly sensory neural rep-resentation. We interpret this finding as suggesting that, when competing sensory input is present, the sensory content of imag-ination does not supersede the sensory content of veridical per-ception. That is, for instance, even if we imagine a hat, our mental image of the hat does not replace the image of a real camel in our visual field: the camel is still more visible. In con-trast, the attenuation or abolition of competing external sensory input could facilitate internally generated stimuli becoming the dominant contributor to sensory experience, creating hallucina-tory imagery. Our model therefore illustrates that the apparent difference in reported vividness between veridical and imagined percepts could be explained by the degree to which imagined and veridical stimulus representations spread hierarchically and that this difference can arise due to external sensory input competing with our internally generated thoughts. Neurological consequences of perceptual competition Our model results in some counterintuitive implications. Despite the suitability of the early visual cortex for representing retino-topic, visual information, our account suggests that hierarchically low-level neural regions (e. g. primary sensory cortices) may be less involved in representing an imagined stimulus than any other region in the corresponding perceptual hierarchy. However, this implication is consistent with existing findings. Individuals still report being able to create mental images despite near-complete bilateral lesions to primary visual cortex, suggesting that the pri-mary visual cortex is not necessary for visual mental imagery (Chatterjee and Southwood 1995; Zago et al. 2010 ; Bridge et al. 2012 ; de Gelder et al. 2015 ). Even mid-level impairments to the visual system, a potential cause of visual agnosia, can leave visual mental imagery preserved ( Behrmann et al. 1994). Furthermore, a meta-analysis of the neural correlates of visual mental imagery by Spagna et al. (2021) found that the left fusiform gyrus, a high-level region within the visual ventral stream, was reliably involved during mental imagery across studies while early visual cortices were not. These findings are entirely in line with the predictions of our model: while primary sensory cortices can be involved in men-tal imagery, the only essential component of the experience is the internal generation of a non-veridical stimulus representation, which, in our model, occurs at the hierarchical apex, correspond-ing, for instance, to late in the visual ventral stream. This may be why subjective vividness ratings better correlate with how dis-tinctly imagined information is represented in retinotopic, rather than associative, neural regions (Lee et al. 2012 ). Under our model, activation at levels below the clamped internally generated representation can add progressively more sensory components to the experience of imagining, although at what stage a rela-tively amodal, abstract thought formally becomes a truly sensory mental image may be an arbitrary distinction. Our simulations predict that the dominance of internally gen-erated stimuli should increase from posterior to anterior regions of the visual hierarchy. Supporting this prediction, Van Rullen and Reddy (2019) used a mental imagery decoding paradigm to show that more information about imagined face images was present in temporal regions than occipital regions. Lee et al. (2012) likewise showed that less information about imagined object images could be decoded towards more posterior, retinotopic areas of the visual system. Both studies also found that externally and internally generated stimulus representations became more similar towards higher-level regions, aligning with the notion that imagined con-tent is propagated from areas active during late-stage veridical perception. Phenomenological consequences of perceptual competition Our model has implications for the functional and subjective char-acteristics of imagery. For instance, the relegation of imagination to relatively high-level representations suggests that thinking in a non-sensory way may be more commonplace than manifest-ing thoughts in a sensory way (e. g. as an actual visual image). This makes pragmatic sense in everyday life: thinking about what you are seeing is often favourable during veridical visual per-ception, yet it may be quite unfavourable to see what you are thinking about given that such hallucinations may supersede important survival-relevant environmental information. However, this process could involve a functional trade-off as the seman-tic content of sensory input may be processed poorly if high-level regions are already occupied by unrelated thoughts. Mental imagery could push internally generated high-level representa-tions towards mid-level regions, interfering with the ascending processing of externally generated stimuli. This could explain why internal attention can affect the processing of environmental stimuli, such as during daydreaming (Schooler et al. 2011; Small-wood 2011). States of immersive mental imagery (e. g. daydream-ing) might then loosely and transiently share phenomenological similarities with agnosia given that high-level processing of exter-nally generated stimuli may be impeded despite low-level visual feature processing being relatively unaffected. For instance, when reading text while distracted by other thoughts, one may find themselves rereading the same paragraph repeatedly, seeing the words each time, yet failing to process the meaning of the text. Another effect of abstract representations being activated without any significant low-level representation during imagery is that a perceiver might plausibly even 'feel' like they have seen their imagined thought without ever experiencing it in any sub-stantially visual way. That is, units involved in the recognition of an object may be activated despite minimal low-level activation. Hence, people could theoretically report being able to visualize objects, yet fail to be able to reconstruct the details of these imagined stimuli accurately. Additionally, experiencing imagery on a spectrum from highly abstract to highly sensory may explain why the unique quasi-sensory experience of mental imagery may be difficult to describe. Common language generally only allows perceptual experience to be described as explicitly sensory (e. g. seen) or explicitly non-sensory (e. g. unseen), forcing ambiguously defined terms like 'vividness' to fill in the gaps. While the content of mental imagery could be described in terms of objectively quantifiable stimu-lus properties (e. g. contrast, size, and duration), the experience of such content is modified by the degree to which a mental image gains sensory features as well as just abstract features. This modulation, encapsulated by the aforementioned concept of a representational equilibrium point, could be the underlying variable commonly measured (albeit somewhat indistinctly) by Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
8 Sulfaro et al. subjective ratings of imagery 'vividness'. If so, this would justify why vividness ratings are generally only investigated concern-ing imagined, not veridical, experiences: veridical percepts are maximally sensory by default. Hallucinations Our model also delineates conditions for hallucinations. Visually, a hallucination entails seeing a non-veridical sensory percept in a given region of the visual field instead of a percept that reflects external reality. Under our model, for any modality, the most per-ceptually compelling hallucinations would then be those where a non-veridical stimulus dominates most, if not all, low-level rep-resentations. The notion of non-veridical information penetrating sensory systems top-down to cause hallucinations has been pre-viously explored in depth under a predictive coding framework (Powers et al. 2016). In our model, it can occur from overweighting top-down information relative to bottom-up information. How-ever, hallucinations could also occur simply if aberrant low-level activity is fed through an otherwise normal perceptual system (Hahamy et al. 2021). Note that, in both cases, our model only accounts for the perceptual experience of imagery, hallucinated or otherwise, and not whether it was induced voluntarily (as imagery tends to be) or involuntarily (as hallucinations tend to be). In the first suggested route to hallucinations, top-down infor-mation becomes overweighted such that non-veridical thoughts can permeate low-level areas to nearly the same extent as uncontested bottom-up veridical input. In this case, hallucina-tions are modelled as an anomalous case of mental imagery with an extremely low representational equilibrium point, sim-ilar to hyperphantasia. If our model is correct, then individu-als with hallucinatory disorders should tend to have improved mental imagery abilities. Accordingly, Parkinson's hallucinators tend to have stronger mental imagery priming effects than non-hallucinating controls, with the degree of imagery-induced priming predicting hallucination frequency (Shine et al. 2015 ). Parkinson's hallucinators also mind-wander more than non-hallucinators, corresponding to increased connectivity to the early visual cortex from default network regions (Walpola et al. 2020 ). Additionally, although individuals with schizophrenia can have impaired memory, their abilities on visuospatial mental imagery manipulation tasks are enhanced compared to neurotypical con-trols ( Benson and Park 2013 ; Matthews et al. 2014 ). However, note that some individuals are able to complete mental imagery manipulation tasks while reporting no visual mental imagery (Zeman et al. 2010 ). Hallucinations should also occur when sensory input is dis-connected altogether such that internally generated percepts are entirely uncontested. If feedforward information is downweighted completely (wl-1=0) to any layer, then that layer and any layer above it are free to be commandeered by any high-level inter-nally generated stimulus present. Representations at such layers will then inevitably converge towards the internally generated stimulus representation (Figs 2b, e, and 3d). This could con-tribute to hallucinations in disorders of afferent visual processing (e. g. Charles Bonnet syndrome; Reichert et al. 2013 ). Hallucina-tions are reasonably common following cortical blindness (Aldrich et al. 1987), and in one such reported case, hallucinations could be induced directly from attempting voluntary mental imagery (Wunderlich et al. 2000 ). Dampening external sensory input might also contribute to hypnagogic hallucinations, which occur during sleep onset. When falling asleep, the cortex remains active sev-eral minutes after the thalamus begins silencing external sensory information (Magnin et al. 2010), potentially providing a window of time in which internally generated cortical activity has reduced competition from the external environment. Top-down effects are probably not solely responsible for hal-lucinatory perception, however. Hallucinations can be visually detailed and sometimes reportedly even clearer than veridical per-cepts (Teunisse et al. 1996; Ffytche et al. 1998; Manford and Ander-mann 1998). This implies that hallucinations may not be a purely top-down phenomenon given that retrohierarchically extrapolat-ing high-level information into low-level regions should result in a degradation of visual information (Breedlove et al. 2020). Many hallucinations are therefore likely to also involve aberrant low-level cortical activity ( Manford and Andermann 1998 ; Hahamy et al. 2021) perhaps independent of, or in tandem with, amplified feedback signals. Eyes-open versus eyes-closed imagery We note that the model proposed in this paper does not presume any difference between an eyes-closed and eyes-open state apart from the change to the content of the sensory input each act pro-duces. Although closing one's eyes might be ostensibly interpreted as disconnecting external sensory input to the visual system, if this were the case, our model would predict that closing one's eyes would rapidly result in hallucinations. While hallucinations can happen when the eyes are deprived of light, such phenomena gen-erally require either drugs (Fisher 1991) or multiple hours (if not days) of light deprivation to manifest (Merabet et al. 2004). It could be that darkness constitutes a genuine sensory disconnection, yet with neural activity adapting to a lack of competition on slow timescales, or it could be that sensory deprivation alone does not equate to a true sensory disconnection. A formal disconnection or downweighting of sensory input could instead require large-scale neurochemical or neurophysiological changes, such as those which occur when shifting between different states of arousal (see the following section, 'Serotonin and acetylcholine: neuro-logically plausible bottom-up and top-down weighting agents', for details). This may be why eye closure (or darkness) is not sufficient for hallucinations in neurotypical individuals during normal wak-ing states, but does co-occur with hallucinations during altered neurochemical states, such as during sleep onset and offset (i. e. hypnagogic and hypnopompic hallucinations) and during sleep itself (i. e. dreaming). Even in blind individuals who cannot per-ceive environmental light levels, hallucinations are not ubiquitous and tend to occur later in the day when drowsy (Manford and Andermann 1998), suggesting that darkness alone is not a form of sensory disconnection. Closing one's eyes (at least on short time scales) might then be most aptly interpreted as changing sensory input to a dif-fuse, dark, and generally unremarkable stimulus image rather than disconnecting it altogether. Still, visual mental imagery is more likely to be reported when eyes are closed rather than open (Sulfaro et al. 2023). However, while eye closure tends to aid the recall of fine-grained sensory information, potentially by improv-ing mental imagery, recall is not significantly improved compared to merely looking at blank space ( Vredeveldt et al. 2011 ). Yet, we acknowledge that our conceptualization of eye closure may be a simplification given that neural activity patterns between eyes-closed and eyes-open states can differ substantially even when both occur in darkness ( Marx et al. 2003, 2004). Even so, an eyes-closed state could still improve mental imagery simply due to the signal-to-noise ratio advantage gained by pitting an imagined stimulus representation against a homogenous closed-eye scene, with the additional benefit of hiding attentional distractors. Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
Modelling perception as a hierarchical competition 9 Serotonin and acetylcholine: neurologically plausible bottom-up and top-down weighting agents This model implies that neural agents exist which modulate the relative contribution of top-down and bottom-up processes. Given that this model predicts that weighting schemes affect veridical and hallucinatory perception as well as mental imagery, agents that modulate these processes might also be apt candidate weighting agents in our current model. Serotonin may be one such agent that modulates the contribution of bottom-up information during visual percep-tion. Classic hallucinogens act on the serotonergic system via 5-hydroxytryptamine 2A (5HT2A) receptors ( Nichols 2016), and cortical serotonin levels are dependent on plasma levels of tryptophan, serotonin's precursor, which readily crosses the blood-brain barrier (Fernstrom and Wurtman 1971 ). Plasma tryp-tophan increases over the course of the day, peaking in the late evening ( Rao et al. 1994), approximately corresponding to the most common time of hallucination onset for individuals with Charles Bonnet syndrome, peduncular hallucinosis, and Parkin-son's disease, including for those without any ability to perceive light ( Manford and Andermann 1998 ). Furthermore, 5HT2A recep-tor expression in the ventral visual pathway of Parkinson's disease hallucinators is elevated compared to non-hallucinators ( Bal-langer et al. 2010 ; Huot et al. 2010 ), while inverse agonists for this receptor are used to treat Parkinson's disease hallucinations (Yasue et al. 2016). Outside of hallucinatory states, serotonin administered in the primary visual cortex of awake macaques acts as a gain modulator, dampening cell responses to external sen-sory input without affecting stimulus tuning or selectivity profiles (Seillier et al. 2017). In mice, this dampening in V1 was mediated by a 5HT2A receptor agonist (Michaiel et al. 2019). Additionally, acetylcholine may modulate the contribution of top-down information during visual experience. The ratio of acetylcholine to serotonin is a factor in hallucination aetiology (Manford and Andermann 1998), and both serotonin and acetyl-choline target Layer 5 cortical pyramidal neurons, cells which have been proposed as essential for manifesting conscious sen-sory perception (Aru et al. 2019 ). High concentrations of acetyl-choline can transition the activity of Layer 5 cortical pyrami-dal neurons from being driven by feedforward inputs to feed-back inputs, which may mediate the hallucinatory experience of dreaming (Aru et al. 2020 ). The concentration of cortical acetyl-choline peaks during rapid eye movement sleep, where dreaming is most likely, higher than during wakefulness and higher still than during non-rapid eye movement sleep where consciousness is greatly impaired (Lee et al. 2005). Hence, cortical acetylcholine concentrations may modulate feedback connectivity in sensory cortices. Given their actions in the visual system, serotonin and acetyl-choline levels could be plausible factors accounting for contextual and interindividual differences in the perceptual experience of mental imagery. Accordingly, they could also be considered as fac-tors which modulate interlayer weightings within our proposed model. However, ascertaining the role of such neurotransmit-ters in mental imagery research is challenged by a reliance on human models for self-report, indistinct metrics and constructs (e. g. vividness ratings), and the restricted access of psychoactive serotonergic drugs. Ultimately, there are many mechanisms by which our model can facilitate hallucinations and such mecha-nisms may work in tandem. Note that in all cases, our model does not explain how the initial internally generated source stimulus might be produced, only how it may be represented, regard-less of whether it was generated as part of a voluntary thought, involuntary hallucination, or otherwise. Mental imagery as a dynamic process So far, our predictions have been based on simulations where imagery, once generated, continues to be generated indefinitely and without interruption. Under these conditions, internally gen-erated content can continue to spread downwards until it reaches an equilibrium point and can spread no further. Yet, if imagery is interrupted or generated intermittently, it may never be gen-erated for a period long enough for it to spread to its maximum possible extent, even if the balance of top-down and bottom-up processes favours a very low equilibrium point (i. e. highly sensory mental imagery). Analogously, even though the maximum possi-ble speed of a sports car may be faster than that of a van, the sports car will be outpaced if the van driver keeps the pedal floored while the sports car driver only taps the pedal on and off. If mental image content can be generated continuously, or supported by a stream of simulated sensory information at lower levels, then the chances of that content spreading to its maximum possible extent are increased. Visual versus auditory mental imagery Although we have focused on visual mental imagery, men-tal imagery can occur in other sensory modalities, presumably through similar generative feedback. A complete account of men-tal imagery should be able to predict and explain modality-specific differences in imagined experience. Auditory hallucinations are roughly twice as common as visual hallucinations in schizophre-nia and bipolar disorder (Waters et al. 2014), although how experi-ences differ between modalities specifically for mental imagery is not well understood. Comparisons generally rely on mental image vividness ratings (e. g. Betts 1910 ; Sheehan 1967 ; Switras 1978; Gissurarson 1992 ; Schifferstein 2009 ; Andrade et al., 2014; Talamini et al. 2022 ). Yet, as such rating systems are ambigu-ously defined and difficult to meaningfully interpret ( Richardson 1988), findings have been understandably mixed. Here, we make predictions about how the quality of mental imagery may differ between visual and auditory mental imagery, perhaps the two most-studied imagery modalities, based on the differences in the brain's ability to synthesize sensory information in each modality. Unlike with visual stimuli, our bodies are readily capable of producing their own auditory stimuli using speech. Self-initiated movements, including the act of speech, produce signals (e. g. efference copies) that carry temporally precise predictions of the sensory consequences of such movements (Curio et al. 2000 ). Sen-sory predictions related to motor movements have been suggested to aid mental imagery when they are produced in the absence of real movements (Scott 2013 ; Whitford et al. 2017; Gelding et al. 2019; Jack et al. 2019; Pruitt et al. 2019 ). This could occur by supplying imagination with the sensory content needed to gen-erate a mental image or by supporting existing mental imagery with a stream of sensory predictions linked to real or simulated movements. As discussed previously, anchoring mental images to continuous sensory information should improve the quality of mental imagery under our model. While visual mental images could be supported by sensory pre-dictions from real or simulated eye movements, eye movements generally contain information about where imagined content is, was, or will be (e. g. Fourtassi et al. 2017). However, they are far less informative about what the content actually is that is being Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
10 Sulfaro et al. imagined in a given region of the visual field. In comparison, con-sider inner speech, a type of auditory imagery specifically related to the imagination of oral sound content like words. If audi-tory imagery can be expressed as inner speech, such as through converting imagined sounds to onomatopoeia, then real or sim-ulated vocal movements could produce a stream of temporally precise sensory information not just informing on when a par-ticular imagined sound should be heard but also informing on what the imagined sound content should actually be. In essence, using motor systems, the brain could have a greater capacity to simulate sensory features of imagined sounds compared to images, provided that the imagined sounds are somewhat possi-ble to replicate vocally. Yet, even when not readily imitable, sounds could still be imagined as some form of onomatopoeia, sacrificing real-world accuracy in order to boost the sensory quality of the imagery experience. Consequently, we expect that auditory men-tal imagery may often be a more compelling sensory experience than visual mental imagery. Recent work supports these predic-tions, finding that auditory imagery is generally superior to visual mental imagery across a number of self-report metrics, although experiences seem to be quite diverse overall (Sulfaro et al., 2023). Limitations and future directions The primary intention of this article is to highlight that competi-tion from externally generated sensory input could be a major fac-tor that explains the unique phenomenology of mental imagery. Our modelling is mainly intended merely to provide a simple example of how treating perception as a competitive process can explain aspects of imagery, supporting the larger theoret-ical argument that mental imagery should always be consid-ered in tandem with co-occurring veridical perceptual processes. Nonetheless, both our argument and our suggested model rely on some assumptions. Our most crucial restraint is that we require that internally and externally generated perceptual processes utilize the same neural substrates such that interference can occur. Our cur-rent understanding is that these processes do overlap ( Ffytche et al. 1998 ; Dijkstra et al. 2017, 2020 ), down to the laminar cortical ( Lawrence et al. 2018; Bergmann et al. 2019 ), if not cel-lular ( Aru et al. 2020), level. However, differences between each process may mean that overlap might vary across the visual hierarchy (e. g. Lawrence et al. 2018), influencing the degree or nature of interference. Yet, even if these processes do over-lap, imagined representations may not necessarily propagate smoothly along a serial, retrohierarchical cascade. If imagery utilizes direct feedback connections from associative cortices to primary sensory cortices, rather than via a series of interme-diate cortical units, interference may have radically different outcomes. We also rely on assumptions about how neural activity trans-lates into subjective experience. Namely, we assume that lower and higher levels of processing, respectively, contribute to sen-sory and abstract features of perceptual experience. Yet, encoding along the visual hierarchy may only correlate with the degree to which semantic content of a perceptual experience is sim-ple or complex, rather than the degree to which such content is experienced in a sensory and modality-specific, rather than non-sensory, way at all. Of course, ascertaining the neural substrates of subjective experience is an immense area of investigation. Although we make broad predictions about the decaying influ-ence of internally generated stimuli towards primary sensory regions, the exact balance of this influence, and its dynam-ics, would likely vary substantially with more neurologically plausible methods of simulating interference beyond the simple weighted-averaging rule used to approximate interference in our model. Also, note that our model does not comment on any of the non-linear transformations necessary to encode a representa-tion within a layer but only makes assumptions about how such representations, once formed, may be transmitted and combined. Modelling a more neurologically plausible system would be a log-ical next step for investigating mental imagery as a competitive process. Furthermore, it is entirely plausible that other mecha-nisms aside from competition could account for the segregated distributions of internally and externally generated content in the visual system. We merely show that simple models of competi-tion can account for these distributions and many other imagery phenomena. Our simulations also use retinal inputs (and generally imag-ined stimulus inputs) that are static and constant, so our sim-ulations cannot account for the effects of neural adaptation on perceptual interference. In reality, retinally stabilized images tend to induce a reversible blindness, greying out the visual field. How-ever, such blindness is suspected to be a very early, low-level effect, at or near the retina (Martinez-Conde et al. 2004). Within our model, this state should then be roughly equivalent to feed-ing in a homogenous field as a real stimulus input, such that the same logic regarding the imagery improvements (or lack thereof) associated with eye closure and the perception of a dark room would also apply to the perceptual greying out that occurs with retinally stabilized images. However, neural adaptation could have many more consequential effects on mental imagery which future studies could explore. Our model also assumes that feedforward and feedback pro-cesses are computationally equivalent. However, Koenig-Robert and Pearson (2021) argue that while feedforward signals initiated from visual input may drive action potentials in the visual cor-tex, feedback signals terminating in early visual areas tend to be more modulatory, guiding but not overriding activity induced by sensory input. They suggest that this asymmetry could account for the apparent difference in vividness between veridical and mental imagery. However, weak feedback could also be a logical consequence of competition within our model. Our simulations predict that the influence of internally generated stimulus infor-mation should gradually diminish towards lower levels in the presence of bottom-up competition. At some point, this declining influence could fall below a threshold such that it can no longer drive action potentials. Yet, our model still uniquely predicts that feedback should remain influential when external competition is not present. Evidence supports this prediction, as feedback can drive action potentials in the visual cortex of neurotypical individuals during dreaming (Aru et al. 2020 ), including in neu-rons that are arguably crucial for manifesting conscious sensory perception (Aru et al. 2019). Hence, it is plausible that weak feedback follows from perceptual competition. Our model may then supplement the account of Koenig-Robert and Pearson (2021) which could otherwise be interpreted as precluding the possi-bility of purely top-down hallucinations. Asymmetries in feed-forward and feedback processing can still be operationalized in our model by manipulating bottom-up and top-down weightings, but our model distinctly predicts that imagined percepts should be experienced in a less sensory manner than veridical percepts, even if feedforward and feedback processes are computationally equivalent, due to the interference caused by competing sensory input. Overall, vindicating or falsifying competition as the origin of the quasi-sensory experience of mental imagery will ultimately Downloaded from https://academic. oup. com/nc/article/2023/1/niad018/7248966 by guest on 25 August 2024	Modelling perception as a hierarchical competition0Adifferentiates imagined veridical and hallucinated0Apercepts.pdf
Modelling perception as a hierarchical competition 11 require a detailed understanding of how neural representations of internally and externally generated perceptual content interact. Future studies may seek to explore the predicted impact of hierar-chical competition on neural activity using alternative models of feedforward-feedback interference, although our model still capa-bly emulates findings on how imagined and veridical information is distributed in real human brains (e. g. Lee et al. 2012 ; Van Rullen and Reddy 2019; Spagna et al. 2021). Conclusion Overall, this work provides a formal framework for explaining the unique quasi-sensory experience of mental imagery. We pro-pose that internally generated thoughts are experienced along an axis from highly abstract to highly sensory in nature, aligning with the degree of dimensionality that a given thought is rep-resented in. Under this assumption, we show that competition from bottom-up sensory input may prevent imagined stimuli from being perceived in any substantially sensory way. Accounting for competition in a hierarchical system can therefore provide suffi-cient conditions for distinguishing imagined, veridical, and hallu-cinatory perception, as well as variation within these phenomena. As modelling imagery competitively may resolve major lingering questions in imagery research, we recommend that future studies investigate the exact manner by which internally and externally generated stimuli may be combined in the brain. Ultimately, we conclude that mental imagery is most logically understood as an intrinsically competitive process and should be largely considered as such in ongoing research. Funding A. A. S was supported by an Australian Government Research Training Program Scholarship. A. K. R. was supported by an Aus-tralian Research Council Discovery Early Career Researcher Award (DE200101159). 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Biological Cybernetics (2021) 115:643-653 https://doi. org/10. 1007/s00422-021-00912-7 60TH ANNIVERSARY RETROSPECTIVE Evolution of the Wilson-Cowan equations Hugh R. Wilson1·Jack D. Cowan2 Published online: 19 November 2021 © The Author(s), under exclusive licence to Springer-Verlag Gmb H Germany, part of Springer Nature 2021 Abstract The Wilson-Cowan equations were developed to provide a simpliﬁed yet powerful description of neural network dynamics. As such, they embraced nonlinear dynamics, but in an interpretable form. Most importantly, it was the ﬁrst mathematical formulation to emphasize the signiﬁcance of interactions between excitatory and inhibitory neural populations, thereby incor-porating both cooperation and competition. Subsequent research by many has documented the Wilson-Cowan signiﬁcancein such diverse ﬁelds as visual hallucinations, memory, binocular rivalry, and epilepsy. The fact that these equations are still being used to elucidate a wide range of phenomena attests to their validity as a dynamical approximation to more detailed descriptions of complex neural computations. 1 Introduction Astronomy and physics were the ﬁrst of the natural sciencesto be enriched by an intricate link to mathematics. Biology,although developing exceptionally powerful theories such as Darwinian evolution, lagged far behind historically in incor-porating mathematics as an integral, predictive approachin its own right. However, mathematics was beginning to encroach on biology, and particularly neurobiology, in deep ways. Hodgkin and Huxley ( 1952 ) solved the dynamics of the action potential by introducing nonlinear dynamics in four coupled equations. This was rapidly recognized to be brilliant, and they received the Nobel prize in 1962. Upon ﬁnishing my Ph D in theoretical chemistry at The University of Chicago in 1969, I (Wilson) was extremely for-tunate to be offered a postdoctoral fellowship by Jack Cowan at the university. He informed me that nonlinear dynamics Communicated by Peter J. Thomas. To highlight the scientiﬁc impact of our Journal over the last decades,we asked authors of highly inﬂuential papers to reﬂect on thehistory of their study, the long-term effect it had, and futureperspectives of their research. We trust the reader will enjoy theseﬁrst-person accounts of the history of big ideas in Biological Cybernetics. BHugh R. Wilsonhrwilson@yorku. ca 1Centre for Vision Research, York University, Toronto, Canada 2Department of Mathematics, University of Chicago, Chicago,USAwere beginning to have a major impact on neuroscience, and he encouraged me to start working on this subject. That was the beginning of the work that produced the Wilson-Cowanequations. The intellectual background must begin with the Hodgk-in-Huxley equations (Hodgkin and Huxley 1952 ). These four nonlinear differential equations are acknowledged to explainaction potentials, key to all neural computation. As empha-sized previously (Wilson 1999 ), nonlinear dynamics was the essential ingredient in providing a convincing explanation. The experiments, upon which the Hodgkin-Huxley equa-tions were based, required poisoning various ion channels selectively. Thus, Hodgkin and Huxley had at their disposal ameasured action potential plus different ionic ﬂows followingpoisoning of various channels. The glue that put the pic-ture together convincingly was nonlinear dynamics, which deﬁnitively showed that combination of the independent ionchannel results did indeed generate an exceptionally accurate squid action potential. It should be noted that the differ-ential equation computations were performed on an addingmachine and took eleven days of computation just to predict one spike. Given this background, Beurle ( 1956 ) noted the mathe-matical complexity of the Hodgkin-Huxley equations andsought a more simple approximation. Speciﬁcally, he intro-duced the concept of neural populations, which could nat-urally be described by the fraction of active neurones atany given point and time. As a physicist, he developed equations that described the propagation of neural activity waves across a one-dimensional tissue. Simpliﬁed nonlinear 123	s00422-021-00912-7.pdf
644 Biological Cybernetics (2021) 115:643-653 dynamics were manifest in his formulation, and this led him to an analytical travelling wave solution for neural activityof the form: F(x-vt)/equal1M 2 cosh2(k(x-vt))(1) where vis the velocity of the wave (to the right here) and Fis the proportion of neurones active during passage of the wave. Mandkare constants. Beurle acknowledged that this solution was unstable, as initial excitation to an amplitude slightly greater than that for Eq. ( 1) led to a transient increase in wave amplitude to saturation, whereas initial excitation to a slightly lower amplitude led to attenuation. In fact, the solution to Beurle's equation, termed a soliton, is also a solution to the Korteweg-De Vries equation that describes propagation ofwater waves in shallow channels (Korteweg and De Vries 1895 ). It is a soliton that conserves an inﬁnite number of quantities. Although providing several major insights, Beurle ( 1956 ) made a number of errors. First, he modelled the cortex as an unstable system that must be delicately balanced to remainplausible. Under these circumstances, he produced a system that was conservative, rather than dissipative, as the brain is known to be. Finally, and perhaps, the root cause of theseproblems was the omission of inhibition as a co-equal factorin brain function. 2 Wilson-Cowan equations We designed the Wilson-Cowan equations to directly reﬂectthe nonlinear dynamics inherent in excitatory-inhibitory interactions in cortical tissue. In addition, these equations were intended to be simpler than the Hodgkin-Huxley equa-tions (1952) so that the dynamics of much larger populations of neurones could be explored. Given Beurle's ( 1956 ) insight, we chose to describe the activity of localized populations ofneurones rather than the spiking of single neurones. However, it was clear that unstable soliton solutions could not effec-tively describe neural dynamics, so we developed equationsthat could produce travelling waves only under pathologicalconditions, such as epilepsy. Crucially, we argued that studies of neural activity must focus on the balance between exci-tatory and inhibitory activity in cooperating and competingneural populations. Our ﬁrst results examined local temporal interactions of local neural populations (Wilson and Cowan 1972 ). Using phase plane techniques, it was shown that these equations could produce asymptotically stable excited states suggestive of short-term memory, limit cycle oscillations suggesting periodic motor control, and several more com-plex behaviours. Fig. 1 Sigmoid function used in the original Wilson-Cowan equations (dashed line) compared with a sigmoid (Naka-Rushton function, solidcurve) designed as a more accurate approximation of cortical dynamics Within a year, this local model was extended to include interactions among excitatory ( E) and inhibitory ( I) neural populations across space (Wilson and Cowan 1973 ), and this was published in Kybernetic, the parent of Biological Cybernetics. The original equations for the E(x,t) and I(x,t) populations are: τE∂E ∂t/equal1-E+(1-r E)SE(βEE(x)⊗E-βIE(x)⊗I+P(x,t)) τI∂I ∂t/equal1-I+(1-r I)SI(βEI(x)⊗E-βII(x)⊗I+Q(x,t)) (2) where τEandτIare the respective time constants on the order of 10-15 ms, r is the refractory period, Sis a sigmoid function increasing monotonically from its minimum at-∞ to its maximum value at + ∞, and Pand Qdescribe exter-nal inputs to the respective populations. A logistic function was originally used for S, but as the exact mathematical form of sigmoid does not change the qualitative dynamics, otherforms have more recently been used based on the experimen-tal literature. For example, responses of cortical neurones have been described by a Naka-Rushton equation (Naka and Rushton 1966 ) with an exponent of approximately 2. 4 (Sclar et al. 1990 ). A Naka-Rushton function with an exponent of 2 has also been used to facilitate mathematical solutions for equilibrium states (Wilson 1999 ). It is described by Eq. ( 3) and is plotted in Fig. 1. S(x)/equal1 M·x2 σ2+x2,x≥0 S(x)/equal10, x≤0(3) In this equation, Mis the maximum ﬁring rate, while σ deﬁnes the semi-saturation level, as when x/equal1σ,S/equal1M/2. Values of M/equal1100,σ/equal125 are shown in the ﬁgure. 123	s00422-021-00912-7.pdf
Biological Cybernetics (2021) 115:643-653 645 The network inputs to each population are deﬁned by spa-tial convolutions, denoted by ⊗in Eq. ( 2). In the original formulation the kernels were all functions of distance, and data available then suggested that they should be decaying exponentials of distance (Sholl 1956 ). Thus, the ﬁrst convo-lution in Eq. ( 2) took the form: βEE(x)⊗E(x)/equal1∞∫-∞e-⏐⏐x-x′⏐⏐/ ωEEE( x′) dx′(4) which describes recurrent Eto Econnections. The remaining three convolutions similarly describe all possible connectionsamong the Eand Ipopulations. For different neural popula-tions, different space constants can produce different ranges of interaction, thus permitting recurrent, long-range inhibi-tion. More recent data have suggested the use of Gaussian kernels rather than decaying exponentials of distance, but this does not change the dynamics qualitatively. Finally, it rapidly became apparent that the refractory period rmainly reduced the maximum ﬁring rate but did not affect the dynamics substantially. Thus, most subsequentstudies have set r/equal10, thereby eliminating the term before the sigmoid input function. We should also emphasize here that values of parameters have largely been omitted below to emphasize major conceptual developments in the evolu-tion of these equations. Details are available in the original references. In this form the Wilson-Cowan equations exhibit a substantial range of dynamical modes, depending on the parameters chosen, that suggested explanations of a variety of cortical phenomena. The model could produce spatiallystable inhomogeneous steady states that stored informationdynamically and suggested a basis for short term memory. This is illustrated in Fig. 2, where the asymptotic E(red) and I(blue) activity is shown following brief activation at the two loci marked with arrows. Recurrent E-Econnec-tions cooperatively maintain neural activity, while longer range I-Econnections maintain the localization. Another parameter regime produced spatially localized limit cycle oscillations with likely relevance to motor control. In addi-tion, yet another set of parameters resulted in the generationof travelling waves, which were suggestive of epilepsy. Details of both the local computations, in which the con-volution in Eq. 4is replaced with simple multiplication by a weight constant, plus the one-dimensional spatial equationsincorporating convolution, can be found in the original arti-cles (Wilson and Cowan 1972,1973 ). MATLAB scripts for many simulations along with parameter values are availableelsewhere (Wilson 1999 ). Although all of the applications of Wilson-Cowan described below have resulted from simulations, it is impor-tant to note that closed-form analytic solutions have veryrecently been obtained using speciﬁc forms of the sigmoidal nonlinearity and particular parameter values (Cowan et al. 2021 ). For these particular cases, travelling soliton waves of the basic form of Eq. ( 1) have been obtained. This is true even with the extension of Beurle's formulation to includeinhibition. These, of course, are solutions under particu-lar functional conditions and do not encompass the much broader range of Wilson-Cowan dynamics as applied to par-ticular areas of cortex. In the years since the original publication of the Wilson-Cowan equations in Kybernetik, computer power has increased phenomenally. Relative to the Digital Equipment Corporation PDP8 on which the original simulations were done, a desktop i Mac Pro runs more than 10 7times faster (Wilson 2019 )! This has engendered two major developments in neural modelling. First, much larger two-dimensionaland multi-layer network simulations have become possi-ble. Furthermore, these have incorporated more than just the two original Eand Ipopulations, thereby reﬂecting greater accuracy in describing cortical networks. In parallel, vastly more detailed simulations of individual neurones have been developed, some incorporating more than 1000 differen-tial equations (Mainen et al. 1995 ). This reﬂects a trade-off between network complexity and single unit complexity con-strained by available computer power. As the Wilson-Cowanequations emphasize the network approach, we shall focuson salient applications of this approach below. Details of parameter values are seldom given, as they are available in the original references. 3 Visual hallucinations Drug-induced visual hallucinations frequently display one of a small number of geometric spatial patterns: concentric circles, radial spokes or arms spiralling outward from the cen-tre (Siegel 1977 ). The natural question this raised was: what neuronal activity in the visual cortex might generate this per-cept in the absence of appropriate stimulation? The criticalinsight of Ermentrout and Cowan ( 1979 ) was that halluci-nations could be explained by the spatially inhomogeneous steady states of the Wilson-Cowan equations if two addi-tional factors were incorporated. First, the equations must beextended to two dimensions to represent the surface of visual cortex. The second key insight for explaining hallucinations was that the gradient of ganglion cells in the retina, rang-ing from densest in the fovea to very sparse in the periphery, meant that there must be a nonlinear mapping from the retina to the cortex. This mapping was shown to be well approx-imated by a complex logarithm in polar coordinates for the left and right half visual ﬁelds (Schwartz 1977, Schwartz 1980 ). If the retinal location of a stimulus point is described in polar coordinates as radius rand orientation ϕ, then the 123	s00422-021-00912-7.pdf
646 Biological Cybernetics (2021) 115:643-653 Fig. 2 Dynamical response of the Wilson-Cowan equations to brief stimulation by sufﬁciently strong pulses at the pointsmarked by the vertical arrows. Due to recurrent excitation,network activity moves to twosaturated peaks of E populationactivity (red curves), but theseactivity peaks are preventedfrom spreading by the spatiallybroader inhibition (blue curve). As multiple peaks can be thusstabilized, this was interpretedto provide a basis for short termmemory 0 100 200 300 400 500 600 700 800 900 1000 Distance in V10102030405060708090100110E (red) & I (blue) Responses corresponding point of cortical projection in x,ycoordinates is: x/equal1ln(1+r) y/equal1φ (5) This mapping to one hemisphere is illustrated in Fig. 3, where the bounding blue contour represents the verticalmeridian, and the remaining three roughly horizontal lines, converging at the origin, represent orientations of 45°, 0° (horizontal), and-45° respectively. Had two concentric cir-cles with radii of 3. 6° and 7. 2° been imaged on the retina, the cortical activation would be represented by the two almost parallel red horizontal bands. Conversely, a radial patternstarting a few degrees away from the fovea would have generated almost horizontal bands of activation due to this mapping. The critical insight was that these could be approxi-mated as parallel neural activation patterns in V1 (Ermentroutand Cowan 1979 ). With the complex logarithmic mapping in 2D, plus an analysis of steady states for the Wilson-Cowan equations,Ermentrout and Cowan showed convincingly that visual hallucinations could be explained by asymptotically stable patterns of activated parallel lines of Eneurons in V1. When projected back to the retina, these would have been con-centric circles. Given drug activation of V1, higher levels of the visual system would have received the same stim-ulation from V1 as would have resulted from concentriccircles in the visual ﬁeld. In addition, drug activation of hor-izontal contours of V1 activity would have resulted in the illusory percept of radial spokes, and activation of diago-nal contours would have produced a hallucination of spirals. Complex checkerboards with checks increasing in size with distance from the fovea were also generated. Recall the min-imal properties required: 2D generalization, asymptotically stable ﬁring states of the network, and the empirically deter-mined complex logarithmic mapping in Eq. ( 5). This elegant explanation of visual hallucinations (Ermen-trout and Cowan 1979 ) was very powerful, but it simpliﬁed by ignoring a very important organizing principle of V1: ori-entation columns (Hubel and Wiesel 1977 ). A more recent study by Cowan and colleagues has reexamined this by intro-ducing multiple E populations, each tuned to a different peak orientation (Bressloff et al. 2001 ). In addition to incorporat-ing multiple arrays of orientation-tuned Eneurons, the Eto E connectivity functions were altered to incorporate collinear facilitation. Physiological data from V1 had demonstratedthe presence of long range E-Einterconnections among neurones with similar orientation preferences located at a distance from each other but aligned roughly collinearly (Ts'o and Gilbert 1988 ; Gilbert and Wiesel 1989 ). The addi-tion of multiple orientations plus collinear facilitation to the Wilson-Cowan equations permitted a much wider range of visual hallucinations to be explained (Bressloff et al. 2001 ). So far, nothing has been said about spatiotemporal hal-lucinations. It is known that uniformly ﬂickering light, par-123	s00422-021-00912-7.pdf
Biological Cybernetics (2021) 115:643-653 647 Fig. 3 Complex log retina to cortex mapping as deﬁned by Eq. 5. The bounding blue contour represents the verticalmeridian, while the horizontalmeridian (0°) and the twodiagonals are as indicated. Axisunits are in mm along thecortical surface. A reﬂected maprepresents the other half of thevisual ﬁeld in the opposite V1cortex. The two almost parallelhorizontal bands are theprojections of two halfconcentric circles from theretina onto the cortex 0 1 02 03 04 05 06 0 Horizontal V1 Axis (Radius)-25-20-15-10-50510152025Vertical V1 Axis (Polar Angle) ticularly near 10. 0 Hz, can induce spatiotemporal illusions, including auras in migraine sufferers (Crotogino et al. 2001 ). Ermentrout and colleagues have shown that the Wilson— Cowan equations with appropriate parameters can accuratelypredict this behaviour (Rule et al. 2011 ). A mathemati-cal analysis of the equations plus simulations demonstrated the existence of nonlinear spatiotemporal oscillations. Inresponse to a ﬂickering stimulus that was uniform across space, the initial network oscillation was unstable, but after a transient period, broke into a spatially alternating patternof synchronous oscillations. An example is illustrated in Fig. 4, where a network with appropriate parameters for an active transient mode (Wilson 1999 ) generate such a pattern in response to uniform sinusoidal stimulation. This oscil-lation consists of three spatial loci becoming active, then decaying, and the interdigitated three competing active foci beginning to ﬁre. Boundary conditions were periodic, andthe number of active populations per half cycle is deter-mined by the spatial extent of the network. Ermentrout and colleagues went on to conduct experiments using a uniformannulus within which uniform ﬁeld, counterphase ﬂicker wasemployed (Pearson et al. 2016 ). Subjects perceived a ring of equally spaced illusory grey blobs that alternated between clockwise and counterclockwise rotation. As the annuluseffectively reduced the stimulus to one-dimension (Wilson et al. 2001 ), the 1D Wilson-Cowan equations provided a neural model that effectively explained the illusion. Furtherresearch has also invoked Wilson-Cowan in explaining addi-tional spatiotemporal oscillations (Bertalmio et al. 2020 ). 4 Long-term memory The activity depicted in Fig. 2reﬂects short-range recur-rent excitation localized by longer range inhibition. As such,the activity pattern is dependent on the neural connectivity, which is the same throughout this network. This suggested, however, that network connectivity could be learned fromtraining examples and could therefore be used to encode long term memories. This was explored, ﬁrst in networks with step function neural responses and subsequently withsigmoid nonlinearities by Hopﬁeld ( 1982,1984 ). It has been pointed out that Hopﬁeld ( 1984 ) utilized a special case of the Wilson-Cowan equations in which the learned connec-tion matrix was symmetric (i. e. β ij/equal1βji), but no recurrent connections of a population to itself were permitted, so βii /equal10 (Destexhe and Sejnowski 2009 ). In addition, Hopﬁeld networks permitted neurons to have both excitatory andinhibitory connections, so no explicitly inhibitory popula-tion was incorporated. However, a more realistic model with explicit populations of excitatory and inhibitory neurons caneasily be developed (Wilson 1999 ). In Hopﬁeld networks, learning a pattern comprising N distinct neurons uses a Hebbian rule (Hebb 1949 ) to calcu-late the average cross-correlation between the responses of 123	s00422-021-00912-7.pdf
648 Biological Cybernetics (2021) 115:643-653 Fig. 4 Example of a spatiotemporal illusion resulting from uniform ﬁeld ﬂicker. The plot shows one spatialdimension on the abscissa andtime increasing downward onthe ordinate. E neuron activitylevels are pseudocoloured asvery low (black), intermediate(shades of red), and high(yellow). Although the stimulusis uniform ﬂicker, the neuralactivity pattern bifurcates to aspatiotemporal alternation ofcompeting activity foci Cortical Distance Time each ijpair ( i̸/equal1j) active in the pattern. This cross-correlation (without a time lag that would encode causality) guarantees the symmetry of the connection matrix. Under these con-ditions, Hopﬁeld constructed an energy function and provedthat when stimulated with a sufﬁcient percentage of a pattern,the network would asymptotically approach activity repre-senting the full learned pattern. Neural learning models have progressed far beyond Hop-ﬁeld networks in the intervening years. Of particular impor-tance have been deep learning networks. These networks incorporate multiple hierarchical levels of model neuronsthat learn their connection weights from the previous layers. In particular, errors between the desired output and the cur-rent output are calculated, and the relative error is assignedto the weights in the various layers based on the chain rulefrom calculus (Rumelhart et al. 1986 ). The current generic deep learning networks consist of hierarchical layers in which there is ﬁrst a neighbourhood convolution with input fromthe previous layer, followed by a nonlinear transformation, such as the maximum within a neighbourhood, and then a spatial subsampling to a smaller upstream area (Reisenhuberand Poggio 1999 ; Le Cun et al. 2015 ). Recently, alternative networks using both lateral interactions and feedback from higher areas have been shown to provide greater accuracy andenhanced biologically plausiblity (Spoerer et al. 2017 ). Thesenetworks are consonant with multi-layer Wilson-Cowan net-works, as they incorporate convolution of inputs followed by a sigmoid nonlinearity, and this approach has evolved to gen-erate an enormous range of very powerful applications. 5 Binocular rivalry and travelling waves The Wilson-Cowan equations have been used to explain a range of nonlinear visual phenomena, one of the most dramatic ones being binocular rivalry. Under normal stim-ulation, the eyes have evolved to sample the visual world from two slightly different visual perspectives, which the brain then combines to generate a percept of the third dimen-sion, namely depth. However, when two radically differentimages (e. g. orthogonal gratings) are viewed independently by the two eyes, they cannot be interpreted in depth, and rivalry ensues. The brain then defaults to a stochastic oscil-lation in which ﬁrst one monocular image and then the other is perceived, with the transitions between monocular images occurring approximately once every 2 s. Before describing an explanation for binocular rivalry, it is necessary to review some more recent work on single neurons in the mammalian cortex. Since the Hodgkin-Huxley equa-tions were developed to describe action potential generation 123	s00422-021-00912-7.pdf
Biological Cybernetics (2021) 115:643-653 649 in the squid giant axon, studies of mammalian neocortical neurons have shown that many additional ion currents arepresent. In particular, excitatory neocortical neurons self-adapt as the result of a, Ca ++mediated K+current that slowly hyperpolarizes the cell (Mc Cormick and Williamson 1989 ; Sanchez-Vives et al. 2000 ). This current has an exponen-tial time constant of a second or more, almost two orders of magnitude longer than typical synaptic currents. This ﬁts well with the rate of alternations in binocular rivalry. Cru-cially, it is primarily excitatory rather than inhibitory neurons that possess this slow adapting current. The Wilson-Cowan equations have been extended to include this slow currentby introducing an equation for a hyperpolarizing variable H (Wilson 1999,2007 ; Wilson et al. 2000 ) Thus, the equation for E(x,t)i n E q. ( 2) is replaced by the two equations: τ E∂E ∂t/equal1-E+SE( βEE(x)⊗E-βIE(x)⊗I+P(x,t)-g H) τHd H dt/equal1-H+E (6) withτHapproximately 1. 0 s, almost two orders of magni-tude greater than τE. (Alternatively, Hcan be added to the semi-saturation constant σin Eq. ( 3) with no signiﬁcant qual-itative differences. ) The parameter g was assigned a valuesuch that adaptation ultimately reduced the Eﬁring rate to about 1/3 of its maximum, in agreement with electrophys-iology. Finally, the stochastic component of rivalry can besimulated, if desired, by adding a Gaussian noise term to the Hequation in Eq. ( 6), which produces a dominance time distribution that is well ﬁt by either a log-normal or gammadistribution in accord with data (Fox and Herrmann 1967 ). Given this embellishment of the Wilson-Cowan equations to include adaptation, binocular rivalry can now be explained. Separate equations describe excitatory neurons driven bythe left and right eyes, E Land ERrespectively. Competi-tion between them is driven by inhibition, IL, and IR,f r o m the opposite eyes. Thus, limit cycle competition emerges inwhich one eye ﬁrst suppresses the other eye, but it then grad-ually adapts via its H current so the second eye can escape from the suppression and itself become dominant. This isillustrated in Fig. 5. The slow oscillation on a several sec-ond time scale is a result of the very long time constant τ H in Eq. ( 6). Note that the alternation is far too slow to be explained by ordinary synaptic inhibition. Thus far, binocular rivalry had been treated as though it were a unitary phenomenon in which one monocular image uniformly replaced the other, but this is inaccurate. Rather,the suppressed image will ﬁrst begin to replace the visible image at one point, and it will then transform into a trav-elling wave moving across the image from that point. Tomeasure the travelling wave properties rivalry was restrictedto a circular, effectively one-dimensional annulus or “race track” (Wilson et al. 2001 ). A wave of the suppressed pat-tern could then be triggered at any point around the circle, with the subject indicating when it reached the ﬁnish line. Using this psychophysical technique, it was shown that thewave travelled at a roughly constant speed across the cortex,which was estimated using the cortical mapping in Eq. ( 5)t o be about 2. 24 cm/s (Wilson et al. 2001 ). In an elegant subse-quent f MRI experiment, wave speed was directly measuredon the human cortex and found to be in good agreement with the psychophysical estimate (Lee et al. 2007 ). The observed rivalry wave propagation was shown to be predictable by a model based on the Wilson-Cowan equa-tions with adaptation (Wilson et al. 2001 ). The left and right eye patterns were represented by independent groups of E L and E Rneurons that were mutually inhibitory. As the sup-pressed neurons become dominant at the moving front of the wave, they inhibit previously dominant neurons in front of the wave, thereby generating a release from inhibition. A detailed mathematical analysis of this wave propagation was later developed based on a variant of the Wilson-Cowan equations (Bressloff and Webber 2012 ). Rivalry only occurs when the two monocular images are so different that they prevent fusion and the extraction of depth. If the two images are oriented cosine gratings; for example, aninterocular orientation difference up to about ±6° will result in fusion and the depth percept of a grating tilted forward or backward in depth (Blake and Wilson 2011 ). For an interocu-lar orientation difference greater than that, however, fusion isimpossible and rivalry ensues. Importantly, when the interoc-ular orientation difference is continuously varied it has been shown that the switch from fusion to rivalry involves hystere-sis (Buckthought et al. 2008 ). Fusion, rivalry, and hysteresis have all been captured using Wilson-Cowan equations with H current adaptation as shown in Eq. ( 6) (Wilson 2017 ). To particularize the model for V1, the model comprised 12 dif-ferent excitatory populations (difference of 15° in preferred orientation between them) for each eye plus four separate inhibitory populations at each orientation (two for each eye):one for small orientation contrast normalization and one for long range orientation rivalry respectively. By incorporating additional neural populations and particularizing the connec-tivity among cell populations, hysteresis between fusion and rivalry can be explained by the Wilson-Cowan approach. 6 Epilepsy The Wilson-Cowan equations have also been applied to epilepsy. This was based upon the original observations that spatially localized limit cycles could exist and that travelling waves could occur should the inhibition be too weak (Wil-son and Cowan 1973 ). Shusterman and Troy ( 2008 ) later 123	s00422-021-00912-7.pdf
650 Biological Cybernetics (2021) 115:643-653 0 2 4 6 8 10 12 14 16 18 20 Time (sec)00. 050. 10. 150. 20. 250. 30. 350. 40. 450. 5Response Fig. 5 Example of binocular rivalry generated by the Wilson-Cowan model with adaptation. Following a brief transient, a limit cycle resultswith left monocular activity (red) alternating with right monocular activ-ity (blue) about once every two seconds. Model responses are in unitsof relative contrast. The stochastic component has been omitted here to emphasize the limit cycle produced by H current adaptation and recip-rocal inhibition showed that, with appropriate parameters, local oscillations would lead to travelling waves and then to synchronous sus-tained activity. The results were comparable to data recordedfrom cortical surface electrodes during passage of epileptic seizures. The explanations of cortical travelling waves in focal epilepsy have also led to a suggested modiﬁcation of the Wilson-Cowan equations. To describe an epileptiform cortex, an effect was incorporated that does not occurunder healthy physiological conditions. The Hodgkin-Hux-ley equations show that if extracellular K +builds up in the extracellular space too much, there is a bifurcation in whichall spiking vanishes. This was simulated in Wilson-Cowanby replacing the sigmoid function in Eq. ( 3) by a Gaussian so that excessive activity could actually drive the ﬁring rate down to zero. Introduction of this physiologically importantclinical observation produced an accurate simulation of focal epilepsy and its spread (Meijer et al. 2015 ). 7 Decisions Contemporary philosophy of mind has been strongly inﬂu-enced by neuroscience. For example, Dennett ( 1996 ) has proposed that conscious decisions are the result of compe-tition among a range of possibilities. Similarly, Dehaene, aneuroscientist who has studied brain function in domains such a mathematics (Dehaene 1997 ), argued in a recent book on consciousness (Dehaene 2014 ): “Rivalry is, indeed, an apt metaphor for the constant ﬁght for conscious access. ” These opinions suggest that decision making by the brain might be usefully interpreted as a form of generalized rivalry amongcompeting neural representations reﬂecting ideas based on past memories. A candidate network for decisions, presumably mimick-ing areas in the prefrontal lobe, has been proposed related to the Wilson-Cowan network for rivalry (Wilson 2009 ; Wil-son2013 ). It can be argued that decisions among alternative interpretations or courses of action require reﬂection andthe expenditure of neural energy in the cases where there is almost equal evidence in favour of several alternative courses of action. In this instance one typically considers each alter-native in turn, seeking new evidence for or against it, and ultimately deciding on one alternative. The small network in Fig. 6can be used to illustrate this. Imagine that each column of neural populations represents a category, perhaps the ﬁrst as subject, second as verb, and so forth. The neural populations in each row are the particular possibilities foreach category, such as I, you, he/she for subject; came, went,gave for verb, etc. Then a particular idea or possibility would be represented by a learned pattern association including one member of each column. With correlation learning (Hopﬁeld 123	s00422-021-00912-7.pdf
Biological Cybernetics (2021) 115:643-653 651 Categories Fig. 6 Model for learning and recalling a series of simple patterns. Each pattern is represented by one active population from each Category (e. g. ﬁve grey circles). During Hebbian learning all connections among allﬁve units are symmetrically strengthened (only nearest neighbour con-nections are shown by double arrows to simplify diagram). Finally, allof the particular instances are mutually exclusive in any pattern and soare coupled via mutual inhibition. This is shown by the lines terminat-ing in solid circles on the far right. Other vertical population arrays ofparticulars are also mutually inhibitory, although connections are notshown for clarity. Even this small network can store up to about ﬁvepartially overlapping patterns. When a subset of these patterns are acti-vated with nearly equivalent stimulus levels, they will become dominant one after another in a generalized rivalry oscillations. This is suggested to be a model for considering several alternatives for a course of actionin deliberation. See text for other details 1982 ), the ﬁve populations in each pattern (grey for example) would have all their interconnection synapses strengthenedas shown by arrows. Within a column all the possibilities aremutually exclusive in any one thought, hence mutual inhibi-tion shown on the right by interconnections with solid circles. Under these conditions, the network will exhibit generalizedrivalry in which one thought pattern will alternate or com-pete with several others in sequence. Furthermore, if a few patterns receive fairly weak evidence or input relative to oth-ers, they are automatically excluded by the dynamics from competition within the network. For a trivially small network of only 15 neurons, about ﬁve patterns can be learned (withpartial pattern overlap), and from 2 to 5 of them will competewhen receiving roughly comparable input. If this network is extended to a more realistic 500 ×1000 neural populations or more, the link to decisions becomes quite plausible. 8 Discussion The Wilson-Cowan equations have produced useful mod-els and insightful explanations in many cortical areas andbrain functions. The original spatial model (Wilson and Cowan 1973 ) was applied to several phenomena in V1, and this has since been extended to visual hallucinations(Ermentrout and Cowan 1979 ), multiple orientations deﬁn-ing E neuron groups (Bressloff et al. 2001 ), and multiple inhibitory groups in fusion and rivalry (Wilson 2017 ). In higher cortical areas Wilson-Cowan has served as a basisfor connectionist learning and memory ﬁrst introduced in the Hopﬁeld ( 1984 ) network. In addition, Wilson-Cowan has provided interpretation for travelling waves, both in binocu-lar rivalry (Wilson et al. 2001 ; Lee et al. 2007 ) and in epilepsy (Shusterman and Troy 2008, Meijer et al. 2015 ). Finally, a generalization of rivalry has generated a possible explanationfor decisions among several plausible alternative possibilities (Wilson 2009 ; Wilson 2013 ). This range of applications of the Wilson-Cowan model depends on a number of extensions to the original model. Most obviously it is possible to generalize to multiple Eand Ipopulations reﬂective of particular cortical areas and func-tions. Among multiple populations there must be multiple population-to-population connectivity functions, which fur-ther individuate models. Furthermore, it has been shown tobe important for connectivity functions to be learned (Hop-ﬁeld 1984 ) in many cortical areas, and others have taken this much further in the development of multi-layer, deep learn-ing convolutional networks (Le Cun et al. 2015 ). To this panoply of extensions must be added the abil-ity to introduce ion currents that generate self-adaptation, particularly in E populations. Since the ﬁrst development of Wilson-Cowan, it was discovered that many cortical pyra-midal neurons, typically excitatory, incorporate slow Ca ++ mediated K+currents that serve to hyperpolarize active cells and thereby reduce their ﬁring rate (Mc Cormick and Williamson 1989 ; Mc Cormick 1998 ). The key here is that this is a slow current, with a time constant much longer than the excitatory and inhibitory postsynaptic currents onwhich the Wilson-Cowan equations were based. Other suit-ably slow potentials can obviously be introduced as they are discovered. This, however, highlights one clear limitation ofthe Wilson-Cowan formalism: it cannot deal with extremely rapid neural variation, where simulation of individual spikes would be required. To cite but one example, humans canaccurately discriminate the direction from which a soundemanates when the arrival time difference at the two ears is as small as 10 microseconds, or about 1/100 the width of an excitatory action potential. This exquisite sensitivity involvesaxonal delay lines and coincidence detection, and is clearly too fast for the Wilson-Cowan approach. As the Wilson-Cowan approach has been very success-ful at incorporating additional populations, particularizing multiple sets of interconnections, and adding slow adap-tive currents, it is appropriate to ask why this approach hassucceeded in capturing key features of neural networks innumerous areas of the cortex. When we began this work a half century ago, it was frequently claimed that nonlinear dynamics was such a vast area, effectively inﬁnite, that onlylinear approximations plus perhaps a few exact nonlinear solutions of particular equations were possible. Despite the clearly vast range of possible nonlinear systems, our argu-ment then was that the nervous system depended on strong, 123	s00422-021-00912-7.pdf
652 Biological Cybernetics (2021) 115:643-653 but understandable nonlinearities. Four key ideas incorpo-rated in the original formulation epitomize this. First, the simpliﬁcation to neural populations and ﬁring rates as espoused by Beurle ( 1956 ) simpliﬁed the descrip-tion of neural networks relative to a detailed descriptionusing multiple equations to describe each individual spike(Hodgkin and Huxley 1952 ). As suggested previously (Wil-son 1999 ), this is analogous to reporting data in terms of post stimulus time histograms (PSTH) rather than describ-ing individual spike trains. Bins in PSTH are typically about 10-20 ms wide, which is reﬂected in the Wilson-Cowan time constants. Regarding human understanding, it is clear that theoverwhelming wealth of our knowledge lies on the several second time scale, with memory vastly extending this back into the past. Thus, the time scale engendered by popula-tion dynamics in Wilson-Cowan ﬁts naturally with humanunderstanding as well. Implicit in the paragraph above is the notion of an exponential time scale. The Wilson-Cowan equations werederived on the assumption that changes in ﬁring rates of populations followed the time constants of typical neural post-synaptic potentials, EPSPs and IPSPs. Given multiplepopulations, multiple time constants have been incorporated. But by constraining our equations to time constants rep-resenting postsynaptic potentials, which implied ignoringindividual spikes, a major simpliﬁcation was accomplished:only population ﬁring rates mattered. Compared to simulat-ing individual spikes, this reduced computational require-ments by almost two orders of magnitude. This meant that Wilson-Cowan could simulate networks about 100 ×larger than spiking networks, given equivalent computing power. Third, Wilson-Cowan was established on the extremely important physiological observation that excitatory and inhibitory neurons formed distinct, interacting populations (Wilson and Cowan 1972 ). This is now a commonplace, but it was ignored by all earlier attempts at network modelling. One can think of neural excitation as active and cooperative (“yang”), while inhibition functions to shut down excitatory activity by introducing competition (“yin”). This generatesa cooperative-competitive dynamic that forms the basis of neural computation. Both components have been integral to Wilson-Cowan from the beginning. This cooperative-competitive theme has been indepen-dently developed into a canonical model for neocortex (Douglas et al. 1989 ; Douglas and Martin 1991 ). These authors developed a model with two excitatory neuron popu-lations, one comprising neurons in the supragranular cortical layers 2 and 3, and one comprising neurons in infragranular layers 5 and 6. Recurrent excitation both within and betweenthe excitatory populations is incorporated into the model. The ﬁnal group contains inhibitory neurons that are connected to themselves and to both excitatory groups to generate nega-tive feedback. All neural populations are described by spikerate dynamics. Thus, this candidate for a canonical circuit for neocortex may be regarded as an embellishment of Wilson—Cowan dynamics. Related E-Idynamics have also been used by Grossberg to develop theories of a large number of cortical functions (Grossberg 2021 ). Finally, the sigmoid function is a key to the power of the Wilson-Cowan equations. The sigmoid captures the impor-tance of neural thresholds, followed by the roughly linear activity increase with increasing stimulation, and ﬁnally by acompressive nonlinearity and saturation at high input levels. Unlike many nonlinear dynamical systems, his nonlinearity has facilitated state space analysis, as neural activity is con-strained by the threshold to be ≥0, and sigmoid saturation guaranteed that activity must be ≤M, the maximum value. This restriction to a hyper-cube in state space has provedvaluable in many mathematical analyses, so the importanceof the sigmoid to physiologically relevant neural modelling cannot be overstated. The Wilson-Cowan equations have clearly proved their value at explaining a wide variety of neural functions in diverse cortical areas. Keys to this success are cooperative— competitive dynamics, population dynamics on a postsynap-tic potential time scale, and sigmoid nonlinear boundedness by thresholds and saturation. Within this framework, there has been a rich evolution, and we suspect that they will con-tinue to enhance our understanding of brain function. References Bertalmio M, Calatroni L, Franceschi V, Franceschiello B, Gomez-Villa A, Prandi D (2020) Visual illusions via neural dynamics:Wilson-Cowan-type models and the efﬁcient representation prin-ciple. J Neurophys 123:1606-1618 Beurle RL (1956a) Properties of a mass of cells capable of regenerating impulses. 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