Adaptive pattern classification and universal recoding: II. Feedback,expectation, olfaction,illusions

Part I of this paper describes a model for the parallel development and adult coding of neural feature detectors. It shows how any set of arbitrary spatial patterns can be recoded, or transformed, into any other spatial patterns (universal recoding), if there are sufficiently many cells in the network's cortex. This code is, however, unstable through time if arbitrarily many patterns can perturb a fixed number of cortical cells. This paper shows how to stabilize the code in the general case using feedback between cellular sites. A biochemically defined critical period is not necessary to stabilize the code, nor is it sufficient to ensure useful coding properties.We ask how short term memory can be reset in response to temporal sequences of spatial patterns. This leads to a context-dependent code in which no feature detector need uniquely characterize an input pattern; yet unique classification by the pattern of activity across feature detectors is possible. This property uses learned expectation mechanisms whereby unexpected patterns are temporarily suppressed and/or activate nonspecific arousal. The simplest case describes reciprocal interactions via trainable synaptic pathways (long term memory traces) between two recurrent on-center off-surround networks undergoing mass action (shunting) interactions. This unit can establish an adaptive resonance, or reverberation, between two regions if their coded patterns match, and can suppress the reverberation if their patterns do not match. This concept yields a model of olfactory coding within the olfactory bulb and prepyriform cortex. The resonance idea also includes the establishment of reverberation between conditioned reinforcers and generators of contingent negative variation if presently avialable sensory cues are compatible with the network's drive requirements at that time; and a search and lock mechanism whereby the disparity between two patterns can be minimized and the minimal disparity images locked into position. Stabilizing the code uses attentional mechanisms, in particular nonspecific arousal as a tuning and search device. We suggest that arousal is gated by a chemical transmitter system—for example, norepinephrine—whose relative states of accumulation at antagonistic pairs of on-cells and off-cells through time can shift the spatial pattern of STM activity across a field of feature detectors. For example, a sudden arousal increment in response to an un-expected pattern can reverse, or rebound, these relative activities, thereby suppressing incorrectly classified populations. The rebound mechanism has formal properties analogous to negative afterimages and spatial frequency adaptation.Supported in part by the Advanced Research Projects Agency under ONR Contract No. N00014-76-C-0185     

On the development of feature detectors in the visual cortex with applications to learning and reaction-diffusion systems

Developmental mechanisms for tuning of visual cortex are derived from adult learning mechanisms: an adaptational property of shunting on-center off-surround networks that prevents saturation of parallel processed patterns at high input intensities, a contrast enhancement and short-term memory mechanism, and plastic synaptic strengths that compute a time average of presynaptic signals and postsynaptic activities and multiplicatively gate signals. The mechanisms can generate fields of feature detectors; e.g., line or picture detectors. A developing hierarchy of such fields can be synthesized in which successive critical developmental periods are triggered as a dynamic equilibrium is established between shortterm memory and long-term memory at each stage. Shunting adaptation can account for some data on spatial frequency adaptation. Shunting network properties resemble properties of certain reaction-diffusion systems that have been used to model developmental data in various species; e.g., Hydra, Xenopus retina, slime molds. For example, positional information due to regulation in reaction-diffusion systems is analogous to constancies due to network adaptation, firing of a developmental gradient is analogous to contrast enhancement, and maintenance of a pattern of morphogens is analogous to short-term memory.Supported in part by the Advanced Research Projects Agency (DAHC15-73-C-0320) administered by Computer Corporation America.     

A theory for the development of feature detecting cells in visual cortex

Passive modification of the strength of synaptic junctions that results in the construction of internal mappings with some of the properties of memory is shown to lead to the development of Hubel-Wiesel type feature detectors in visual cortex. With such synaptic modification a cortical cell can become committed to an arbitrary but repeated external pattern, and thus fire every time the pattern is presented even if that cell has no genetic pre-disposition to respond to the particular pattern. The additional assumption of lateral inhibition between cortical cells severely limits the number of cells which respond to one pattern as well as the number of patterns that are picked up by a cell. The introduction of a simple neural mapping from the visual field to the lateral geniculate leads to an interaction between patterns which, combined with our assumptions above, seems to lead to a progression of patterns from column to column of the type observed by Hubel and Wiesel in monkey.     

Spatial stereoresolution for depth corrugations may be set in primary visual cortex

Stereo "3D" depth perception requires the visual system to extract binocular disparities between the two eyes' images. Several current models of this process, based on the known physiology of primary visual cortex (V1), do this by computing a piecewise-frontoparallel local cross-correlation between the left and right eye's images. The size of the "window" within which detectors examine the local cross-correlation corresponds to the receptive field size of V1 neurons. This basic model has successfully captured many aspects of human depth perception. In particular, it accounts for the low human stereoresolution for sinusoidal depth corrugations, suggesting that the limit on stereoresolution may be set in primary visual cortex. An important feature of the model, reflecting a key property of V1 neurons, is that the initial disparity encoding is performed by detectors tuned to locally uniform patches of disparity. Such detectors respond better to square-wave depth corrugations, since these are locally flat, than to sinusoidal corrugations which are slanted almost everywhere. Consequently, for any given window size, current models predict better performance for square-wave disparity corrugations than for sine-wave corrugations at high amplitudes. We have recently shown that this prediction is not borne out: humans perform no better with square-wave than with sine-wave corrugations, even at high amplitudes. The failure of this prediction raised the question of whether stereoresolution may actually be set at later stages of cortical processing, perhaps involving neurons tuned to disparity slant or curvature. Here we extend the local cross-correlation model to include existing physiological and psychophysical evidence indicating that larger disparities are detected by neurons with larger receptive fields (a size/disparity correlation). We show that this simple modification succeeds in reconciling the model with human results, confirming that stereoresolution for disparity gratings may indeed be limited by the size of receptive fields in primary visual cortex.     

The role of additive neurogenesis and synaptic plasticity in a hippocampal memory model with grid-cell like input

Recently, we presented a study of adult neurogenesis in a simplified hippocampal memory model. The network was required to encode and decode memory patterns despite changing input statistics. We showed that additive neurogenesis was a more effective adaptation strategy compared to neuronal turnover and conventional synaptic plasticity as it allowed the network to respond to changes in the input statistics while preserving representations of earlier environments. Here we extend our model to include realistic, spatially driven input firing patterns in the form of grid cells in the entorhinal cortex. We compare network performance across a sequence of spatial environments using three distinct adaptation strategies: conventional synaptic plasticity, where the network is of fixed size but the connectivity is plastic; neuronal turnover, where the network is of fixed size but units in the network may die and be replaced; and additive neurogenesis, where the network starts out with fewer initial units but grows over time. We confirm that additive neurogenesis is a superior adaptation strategy when using realistic, spatially structured input patterns. We then show that a more biologically plausible neurogenesis rule that incorporates cell death and enhanced plasticity of new granule cells has an overall performance significantly better than any one of the three individual strategies operating alone. This adaptation rule can be tailored to maximise performance of the network when operating as either a short- or long-term memory store. We also examine the time course of adult neurogenesis over the lifetime of an animal raised under different hypothetical rearing conditions. These growth profiles have several distinct features that form a theoretical prediction that could be tested experimentally. Finally, we show that place cells can emerge and refine in a realistic manner in our model as a direct result of the sparsification performed by the dentate gyrus layer.     

Optic flow representation in the optic lobes of Diptera: modeling innervation matrices onto collators and their evolutionary implications

A network model of optic flow processing, based on physiological and anatomical features of motion-processing neurons, is used to investigate the role of small-field motion detectors emulating T5 cells in producing optic flow selective properties in wide-field collator neurons. The imposition of different connectivities can mimic variations observed in comparative studies of lobula plate architecture across the Diptera. The results identify two features that are crucial for optic flow selectivity: the broadness of the spatial patterns of synaptic connections from motion detectors to collators, and the relative contributions of excitatory and inhibitory synaptic outputs. If these two aspects of the innervation matrix are balanced appropriately, the network's sensitivity to perturbations in physiological properties of the small-field motion detectors is dramatically reduced, suggesting that sensory systems can evolve robust mechanisms that do not rely upon precise control of network parameters. These results also suggest that alternative lobula plate architectures observed in insects are consistent in allowing optic flow selective properties in wide-field neurons. The implications for the evolution of optic flow selective neurons are discussed.     

Amnesia and neglect: beyond the Delay-Brion system and the Hebb synapse.

Hippocampal damage in people causes impairments of episodic memory, but in rats it causes impairments of spatial learning. Experiments in macaque monkeys show that these two kinds of impairment are functionally similar to each other. After any lesion that interrupts the Delay-Brion system (hippocampus, fornix, mamillary bodies and anterior thalamus) monkeys are impaired in scene-specific memory, where an event takes place against a background that is specific to that event. Scene-specific memory in the monkey corresponds to human episodic memory, which is the memory of a unique event set in a particular scene, as opposed to scene-independent human knowledge, which is abstracted from many different scenes. However, interruption of the Delay-Brion system is not sufficient to explain all of the memory impairments that are seen in amnesic patients. To explain amnesia the specialized function of the hippocampus in scene memory needs to be considered alongside the other, qualitatively different functional specializations of other memory systems of the temporal lobe, including the perirhinal cortex and the amygdala. In all these specialized areas, however, including the hippocampus, there is no fundamental distinction between memory systems and perceptual systems. In explaining memory disorders in amnesia it is also important to consider them alongside the memory disorders of neglect patients. Neglect patients fail to represent in memory the side of the world that is contralateral to the current fixation point, in both short- and long-term memory retrieval. Neglect was produced experimentally by unilateral visual disconnection in the monkey, confirming the idea that visual memory retrieval is retinotopically organized; patients with unilateral medial temporal-lobe removals showed lateralized memory impairments for half-scenes in the visual hemifield contralateral to the removal. Thus, in scene-memory retrieval the Delay-Brion system contributes to the retrieval of visual memories into the retinotopically organized visual cortex. This scene memory interpretation of hippocampal function needs to be contrasted with the cognitive-map hypothesis. The cognitive-map model of hippocampal function shares some common assumptions with the Hebb-synapse model of association formation, and the Hebb-synapse model can be rejected on the basis of recent evidence that monkeys can form direct associations in memory between temporally discontiguous events. Our general conclusion is that the primate brain encompasses widespread and powerful memory mechanisms which will continue to be poorly understood if theory and experimentation continue to concentrate too much, as they have in the past, on the hippocampus and the Hebb synapse.     

Spatio-temporal self-organization of bone mineral metabolism and trabecular structure of primary bone

A nonlinear two-variable reaction-diffusion model of bone mineral metabolism, built from an overall self-oscillatory compartmental model of calcium metabolism in vivo, has been studied for its ability to generate spatial and spatio-temporal self-organizations in a two-dimensional space. Analytical and numerical results confirm the theoretical properties previously described for this kind of model. In particular, it is shown that, for a given set of reactional parameter values and certain values of the ratio of the two diffusion coefficients, there exists a set of unstable wavenumbers leading spontaneously to the development, from the homogeneous steady state, of either different types of stationary spatial patterns (hexagonal, striped and re-entrant hexagonal patterns) or more or less complex spatio-temporal expressions. We discuss the relevance of analogies established between some spatial or spatio-temporal structures predicted by the model and some peculiar features of the primary bone trabecular architecture which appear during embryonic ossification.     

Extremely Dilute Modular Neuronal Networks: Neocortical Memory Retrieval Dynamics

A model of columnar networks of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others, randomly chosen. Any module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are peculiar combinations of features sparsely distributed over the multi-modular network. Any feature stored in any module can be involved in several of the stored patterns; feature-sharing is in fact source of local ambiguities and, consequently, a potential cause of erroneous memory retrieval spreading through the model network in pattern completion tasks.The memory retrieval dynamics of the large modular autoassociator is investigated by combining mathematical analysis and numerical simulations. An oscillatory retrieval process is proposed that is very efficient in overcoming feature-sharing drawbacks; it requires a mechanism that modulates the robustness of local attractors to noise, and neuronal activity sparseness such that quiescent and active modules are about equally noisy to any post-synaptic module.Moreover, it is shown that statistical correlation between 'kinds' of features across the set of memory patterns can be exploited to obtain a more efficient achievement of memory retrieval capabilities.It is also shown that some spots of the network cannot be reached by retrieval activity spread if they are not directly cued by the stimulus. The locations of these activity isles depend on the pattern to retrieve, while their extension only depends (in large networks) on statistics of inter-modular connections and stored patterns. The existence of activity isles determines an upper-bound to retrieval quality that does not depend on the specific retrieval dynamics adopted, nor on whether feature-sharing is permitted. The oscillatory retrieval process nearly saturates this bound.     

Differences in Visual-Spatial Input May Underlie Different Compression Properties of Firing Fields for Grid Cell Modules in Medial Entorhinal Cortex

Firing fields of grid cells in medial entorhinal cortex show compression or expansion after manipulations of the location of environmental barriers. This compression or expansion could be selective for individual grid cell modules with particular properties of spatial scaling. We present a model for differences in the response of modules to barrier location that arise from different mechanisms for the influence of visual features on the computation of location that drives grid cell firing patterns. These differences could arise from differences in the position of visual features within the visual field. When location was computed from the movement of visual features on the ground plane (optic flow) in the ventral visual field, this resulted in grid cell spatial firing that was not sensitive to barrier location in modules modeled with small spacing between grid cell firing fields. In contrast, when location was computed from static visual features on walls of barriers, i.e. in the more dorsal visual field, this resulted in grid cell spatial firing that compressed or expanded based on the barrier locations in modules modeled with large spacing between grid cell firing fields. This indicates that different grid cell modules might have differential properties for computing location based on visual cues, or the spatial radius of sensitivity to visual cues might differ between modules.     

Negative regulation of neurogenesis and spatial memory by NR2B-containing NMDA receptors

Several lines of evidence suggest involvement of NMDA receptors (NMDARs) in the regulation of neurogenesis in adults and the formation of spatial memory. Functional properties of NMDARs are strongly influenced by the type of NR2 subunits incorporated. In adult forebrain regions such as the hippocampus and cortex, only NR2A and NR2B subunits are available to form the receptor complex with NR1 subunit. NR2B is predominant NR2 subunit in any of rat or human neural stem cells (NSCs). Thus, we suppose that NR2B-containing NMDAR should be critical in regulating adult neurogenesis, and thereby playing a role in the formation of spatial memory. In the cultured NSCs derived from the embryonic brain of rats, NR2B subunit-specific NMDAR antagonist Ro25-6981 increased cell proliferation, whereas MK-801, non-selective open-channel blocker of NMDARs, inhibited cell proliferation. Blockade of NR2B-containing NMDAR stimulated neurogenesis in the adult hippocampus and facilitated the formation of spatial memory. The enhanced spatial memory dropped back to base level when the NR2B antagonist-induced neurogenesis was neutralized by 3'-azido-deoxythymidine, a telomerase inhibitor. In addition, blockade of NR2B inhibited neuronal nitric oxide synthase (nNOS) enzymatic activity. In null mutant mice lacking nNOS gene (nNOS−/−), the effects of NR2B antagonist on neurogenesis disappeared. Moreover, nitric oxide donor DETA/NONOate attenuated and nNOS inhibitor 7-nitroindazole enhanced the effect of Ro 25-6981 on NSCs proliferation. Our findings suggest that NR2B-containing NMDAR subtypes negatively regulate neurogenesis in the adult hippocampus by activating nNOS activity and thereby hinder the formation of spatial memory.     

Maps of space in human frontoparietal cortex

Prefrontal cortex (PFC) and posterior parietal cortex (PPC) are neural substrates for spatial cognition. We here review studies in which we tested the hypothesis that human frontoparietal cortex may function as a priority map. According to priority map theory, objects or locations in the visual world are represented by neural activity that is proportional to their attentional priority. Using functional magnetic resonance imaging (fMRI), we first identified topographic maps in PFC and PPC as candidate priority maps of space. We then measured fMRI activity in candidate priority maps during the delay periods of a covert attention task, a spatial working memory task, and a motor planning task to test whether the activity depended on the particular spatial cognition. Our hypothesis was that some, but not all, candidate priority maps in PFC and PPC would be agnostic with regard to what was being prioritized, in that their activity would reflect the location in space across tasks rather than a particular kind of spatial cognition (e.g., covert attention). To test whether patterns of delay period activity were interchangeable during the spatial cognitive tasks, we used multivariate classifiers. We found that decoders trained to predict the locations on one task (e.g., working memory) cross-predicted the locations on the other tasks (e.g., covert attention and motor planning) in superior precentral sulcus (sPCS) and in a region of intraparietal sulcus (IPS2), suggesting that these patterns of maintenance activity may be interchangeable across the tasks. Such properties make sPCS in frontal cortex and IPS2 in parietal cortex viable priority map candidates, and suggest that these areas may be the human homologs of the monkey frontal eye field (FEF) and lateral intraparietal area (LIP).     

Receptive fields in the rat piriform cortex.

Current models of odor discrimination in mammals involve molecular feature detection by a large family of diverse olfactory receptors, refinement of molecular feature extraction through precise projections of olfactory receptor neurons to the olfactory bulb to form an odor-specific spatial map of molecular features across glomerular layer, and synthesis of these features into odor objects within the piriform cortex. This review describes our recent work on odor and spatial receptive fields within the anterior piriform cortex and compares these fields with receptive fields of their primary afferent, olfactory bulb mitral/tufted cells. The results suggest that receptive fields in the piriform cortex are ensemble in nature, highly dynamic, and may contribute to odor discrimination and odor memory.     

Visual illusions in neural networks: Line neutralization,tilt after effect,and angle expansion

Certain visual illusions occur in neural networks that are capable of storing partially contrasted enhanced spatial patterns in short term memory (STM), and whose feature detectors are interconnected by nontrivial generalization gradients. These include neutralization, or adaptation, of nearly vertical or horizontal lines, tilt after-effect of successively viewed lines, and perceived angle expansion. Neutralization can be achieved by networks whose vertical and horizontal representations have higher saturation levels, broader tuning curves, or stronger input pathways. Tilt after-effect and angle expansion can be achieved by shunting lateral inhibition that causes an outward peak shift in the orientationally-coded STM pattern. The amount of outward peak shift is also dependent on the size of the potassium equilibrium point. Differences between the directions of tilt aftereffect (successive contrast) and angle expansion (simultaneous contrast) are ascribed to a normalization of total activity in the STM buffer whereby present stimuli and representations in STM of past stimuli interact to form a consistent action-oriented consensus.     

Pattern formation,contrast control,and oscillations in the short term memory of shunting on-center off-surround networks

The transformation of spatial patterns and their storage in short term memory by shunting neural networks are studied herein. Various mechanisms are described for real-time regulation of the amount of contrast with which a pattern will be stored. Parametric studies are described for the amount of contrast in the network responses to patterns presented at variable background or overall activity levels. Mechanisms for removing spurious peak splits and other disinhibitory responses are described. Furman's (1965) results on processing of patterns by shunting networks are generalized and reanalysed. Periodic responses (stable and unstable) corresponding to the time scale of slow cortical waves can be generated if a tonic input is set between two threshold activity levels. Their frequency as a function of tonic input size is unimodal. Order-preserving limit cycles are never found in STM; hence sustained slow oscillations as a mechanism for storing a pattern in STM are ruled out in favor of steady states (i.e., fast oscillations) with spatially graded activity levels. Such slow oscillations can, nonetheless, continuously retune the network's responsiveness to the patterns that perturb it.     

Memory trace in prefrontal cortex: theory for the cognitive switch

The dorsolateral prefrontal cortex in human and non-human primates functions as the highest-order executor for the perception-action cycle. According to this view, when perceptual stimuli from the environment are novel or complex, the dorsolateral prefrontal cortex serves to set consciously a goal-directed scheme which broadly determines an action repertory to meet the particular demand from the environment. In this respect, the dorsolateral prefrontal cortex is a short-term activation device with the properties of a cognitive switch', because it couples a particular set of perceptual stimuli to a particular set of actions. Here, I suggest that, in order for the organism to react systematically to the environment, neural traces for the switch function must be stored in the brain. Thus, the highest-order, perception-action interface function of the dorsolateral prefrontal cortex per se depends on permanently stored neural traces in the dorsolateral prefrontal cortex and related structures. Such a memory system may be located functionally between two of the well-documented memory systems in the brain: the declarative memory system and the procedural memory system. Finally, based on available neurophysiological data, the possible mechanisms underlying the formation of cognitive switch traces are proposed.     

How long will long-term potentiation last?

The paramount feature of long-term potentiation (LTP) as a memory mechanism is its characteristic persistence over time. Although the basic phenomenology of LTP persistence was established 30 years ago, new insights have emerged recently about the extent of LTP persistence and its regulation by activity and experience. Thus, it is now evident that LTP, at least in the dentate gyrus, can either be decremental, lasting from hours to weeks, or stable, lasting months or longer. Although mechanisms engaged during the induction of LTP regulate its subsequent persistence, the maintenance of LTP is also governed by activity patterns post-induction, whether induced experimentally or generated by experience. These new findings establish dentate gyrus LTP as a useful model system for studying the mechanisms governing the induction, maintenance and interference with long-term memory, including very long-term memory lasting months or longer. The challenge is to study LTP persistence in other brain areas, and to relate, if possible, the properties and regulation of LTP maintenance to these same properties of the information that is actually stored in those regions.     

Visual associative memory and the orientation-contingent color after-effect

The traditional explanation of the McCollough effect (ME) by selective adaptation of single detectors selective to color and orientation suffers from a number of inconsistencies: 1) the ME lasts much longer (from several days up to 3 months) than the ordinary adaptation, the decay of the effect being completely arrested by night sleep or occluding the eye for a long time; 2) the strength of the ME practically does not depend on the intensity of adapting light; and 3) a set of related pattern-contingent after-effects discovered later required for such an explanation new detectors, specific for other patterns. These properties can be explained, however, in the framework of associative memory and novelty filters. A computational model has been developed, which consists of 1) an input layer of two (left and right eyes) square matrices with two analog receptors (red and green) in each pixel, 2) an isomorphic associative neural layer, each analog neuron being synaptically connected with all receptors of both eyes, and 3) an output layer (novelty filter). The modification of synaptic efficacies conforms to the Hebb learning rule. The function of the model was examined by simulation. After a few presentations of colored gratings, the model displays the ME that is slowly destroyed by subsequent presentations of random pictures. With a sufficiently large receptor matrix, the effect lasts a thousand times longer than the period of adaptation. Continuous darkness does not change the strength of the effect. Like in real ME, the model does not display interocular transfer. The model can account for different pattern-contingent color after-effects without assuming any predetermined specific detectors. Such detectors are constructed in the course of adaptation to specific stimuli (gratings).     

Sexual selection and the evolution of costly female preferences: spatial effects

Abstract.— Models of Fisher's runaway process show that if there is a cost to female preference, no preference or male trait exaggeration will evolve. Surprisingly, this is true no matter how small the cost, which reveals that these models of Fisher's process are structurally unstable (Bulmer 1989). Here a model of Fisher's runaway process is presented to demonstrate that costly female preference evolves very easily when space is explicitly included in the model. The only requirement is that the optimal male phenotype changes across the species' range. The model shows that the spatial average of the female preference and male trait reach an evolutionary equilibrium that is identical to those of nonspatial models, but that the preference and male trait can deviate greatly from these averages at any point in space. For example, if random mating results in the lowest cost to females, then at equilibrium the spatial average preference will be zero. Nevertheless, there will be some locations at which females prefer males with larger ornaments and others where they prefer males with smaller ornaments. Results also show that the structural instability of nonspatial models of Fisher's process is less of a problem in spatial models. In particular, many of the main qualitative features of cost-free spatial models of Fisher's process remain valid even when there are small costs of female preference. Finally, the model shows that abrupt changes in the optimal male phenotype across space can result in an amplification of this pattern when preference has a small cost, but it can also result in a pattern similar to reproductive character displacement. Which of these occurs depends on the magnitude of the cost of female preference. This suggests that some patterns of reproductive character displacement in nature might be explained simply by sexual selection rather than by hybrid dysgenesis and reinforcement.     

Neural field model of binocular rivalry waves

We present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are inhibitory (cross-inhibition). Slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a “symmetry breaking mechanism” that allows waves to propagate.