Bistable perception modeled as competing stochastic integrations at two levels

Synaptic ring attractor: A unified framework for attractor dynamics and multiple cues integration

Effective cue integration is essential for an animal's survival. The ring attractor network has emerged as a powerful framework for understanding how animals seamlessly integrate various cues. This network not only elucidates neural dynamics within the brain, especially in spatial encoding systems like the heading direction (HD) system, but also sheds light on cue integration within decision-making processes. Yet, many significant phenomena across different fields lack clear explanations. For instance, in physiology, the integration mechanism of Drosophila's compass neuron when confronted with conflicting self-motion cues and external sensory cues with varying gain control settings is not well elucidated. Similarly, in ethology, the decision-making system shows Bayesian integration (BI) under minimal cue conflicts, but shifts to a winner-take-all (WTA) mode as conflicts surpass a certain threshold. To address these gaps, we introduce a ring attractor network with asymmetrical neural connections and synaptic dynamics in this paper. A thorough series of simulations has been conducted to assess its ability to track external cues and integrate conflicting cues. The results from these simulations demonstrate that the proposed model replicates observed neural dynamics and offers a framework for modeling biologically plausible cue integration behaviors. Furthermore, our findings yield several testable predictions that could inform future neuroethological research, providing insights into the role of ring attractor dynamics in the animal brain.

Binocular rivalry reveals an out-of-equilibrium neural dynamics suited for decision-making

In ambiguous or conflicting sensory situations, perception is often 'multistable' in that it perpetually changes at irregular intervals, shifting abruptly between distinct alternatives. The interval statistics of these alternations exhibits quasi-universal characteristics, suggesting a general mechanism. Using binocular rivalry, we show that many aspects of this perceptual dynamics are reproduced by a hierarchical model operating out of equilibrium. The constitutive elements of this model idealize the metastability of cortical networks. Independent elements accumulate visual evidence at one level, while groups of coupled elements compete for dominance at another level. As soon as one group dominates perception, feedback inhibition suppresses supporting evidence. Previously unreported features in the serial dependencies of perceptual alternations compellingly corroborate this mechanism. Moreover, the proposed out-of-equilibrium dynamics satisfies normative constraints of continuous decision-making. Thus, multistable perception may reflect decision-making in a volatile world: integrating evidence over space and time, choosing categorically between hypotheses, while concurrently evaluating alternatives.

Pupillometry in auditory multistability

In multistability, a constant stimulus induces alternating perceptual interpretations. For many forms of visual multistability, the transition from one interpretation to another ("perceptual switch") is accompanied by a dilation of the pupil. Here we ask whether the same holds for auditory multistability, specifically auditory streaming. Two tones were played in alternation, yielding four distinct interpretations: the tones can be perceived as one integrated percept (single sound source), or as segregated with either tone or both tones in the foreground. We found that the pupil dilates significantly around the time a perceptual switch is reported ("multistable condition"). When participants instead responded to actual stimulus changes that closely mimicked the multistable perceptual experience ("replay condition"), the pupil dilated more around such responses than in multistability. This still held when data were corrected for the pupil response to the stimulus change as such. Hence, active responses to an exogeneous stimulus change trigger a stronger or temporally more confined pupil dilation than responses to an endogenous perceptual switch. In another condition, participants randomly pressed the buttons used for reporting multistability. In Study 1, this "random condition" failed to sufficiently mimic the temporal pattern of multistability. By adapting the instructions, in Study 2 we obtained a response pattern more similar to the multistable condition. In this case, the pupil dilated significantly around the random button presses. Albeit numerically smaller, this pupil response was not significantly different from the multistable condition. While there are several possible explanations-related, e.g., to the decision to respond-this underlines the difficulty to isolate a purely perceptual effect in multistability. Our data extend previous findings from visual to auditory multistability. They highlight methodological challenges in interpreting such data and suggest possible approaches to meet them, including a novel stimulus to simulate the experience of perceptual switches in auditory streaming.

A functional theory of bistable perception based on dynamical circular inference

When we face ambiguous images, the brain cannot commit to a single percept; instead, it switches between mutually exclusive interpretations every few seconds, a phenomenon known as bistable perception. While neuromechanistic models, e.g., adapting neural populations with lateral inhibition, may account for the dynamics of bistability, a larger question remains unresolved: how this phenomenon informs us on generic perceptual processes in less artificial contexts. Here, we propose that bistable perception is due to our prior beliefs being reverberated in the cortical hierarchy and corrupting the sensory evidence, a phenomenon known as “circular inference”. Such circularity could occur in a hierarchical brain where sensory responses trigger activity in higher-level areas but are also modulated by feedback projections from these same areas. We show that in the face of ambiguous sensory stimuli, circular inference can change the dynamics of the perceptual system and turn what should be an integrator of inputs into a bistable attractor switching between two highly trusted interpretations. The model captures various aspects of bistability, including Levelt’s laws and the stabilizing effects of intermittent presentation of the stimulus. Since it is related to the generic perceptual inference and belief updating mechanisms, this approach can be used to predict the tendency of individuals to form aberrant beliefs from their bistable perception behavior. Overall, we suggest that feedforward/feedback information loops in hierarchical neural networks, a phenomenon that could lead to psychotic symptoms when overly strong, could also underlie perception in nonclinical populations.

In cases of high ambiguity, our perceptual system cannot commit to a single percept and switches between different interpretations, giving rise to bistable perception. In this paper we outline a computational model of bistability based on the notion of circular inference, i.e. a form of suboptimal hierarchical inference in which priors and / or sensory inputs are reverberated and over-counted. We suggest that descending loops (i.e. reverberated priors) transform our perceptual system from a simple accumulator of sensory inputs into a bistable attractor, that switches between two highly-trusted interpretations. Using analytical methods we derive the necessary conditions for bistable perception to occur. We show that our dynamical circular inference model is able to capture many features of bistability, such as Levelt’s laws and the stabilizing effects of intermittent presentation of the stimulus. Finally we make novel predictions about the behavior of psychotic patients.

Identification of competing neural mechanisms underlying positive and negative perceptual hysteresis in the human visual system

Hysteresis is a well-known phenomenon in physics that relates changes in a system with its prior history. It is also part of human visual experience (perceptual hysteresis), and two different neural mechanisms might explain it: persistence (a cause of positive hysteresis), which forces to keep a current percept for longer, and adaptation (a cause of negative hysteresis), which in turn favors the switch to a competing percept early on. In this study, we explore the neural correlates underlying these mechanisms and the hypothesis of their competitive balance, by combining behavioral assessment with fMRI. We used machine learning on the behavioral data to distinguish between positive and negative hysteresis, and discovered a neural correlate of persistence at a core region of the ventral attention network, the anterior insula. Our results add to the understanding of perceptual multistability and reveal a possible mechanistic explanation for the regulation of different forms of perceptual hysteresis.

Buildup and bistability in auditory streaming as an evidence accumulation process with saturation

A repeating triplet-sequence ABA- of non-overlapping brief tones, A and B, is a valued paradigm for studying auditory stream formation and the cocktail party problem. The stimulus is "heard" either as a galloping pattern (integration) or as two interleaved streams (segregation); the initial percept is typically integration then followed by spontaneous alternations between segregation and integration, each being dominant for a few seconds. The probability of segregation grows over seconds, from near-zero to a steady value, defining the buildup function, BUF. Its stationary level increases with the difference in tone frequencies, DF, and the BUF rises faster. Percept durations have DF-dependent means and are gamma-like distributed. Behavioral and computational studies usually characterize triplet streaming either during alternations or during buildup. Here, our experimental design and modeling encompass both. We propose a pseudo-neuromechanistic model that incorporates spiking activity in primary auditory cortex, A1, as input and resolves perception along two network-layers downstream of A1. Our model is straightforward and intuitive. It describes the noisy accumulation of evidence against the current percept which generates switches when reaching a threshold. Accumulation can saturate either above or below threshold; if below, the switching dynamics resemble noise-induced transitions from an attractor state. Our model accounts quantitatively for three key features of data: the BUFs, mean durations, and normalized dominance duration distributions, at various DF values. It describes perceptual alternations without competition per se, and underscores that treating triplets in the sequence independently and averaging across trials, as implemented in earlier widely cited studies, is inadequate.

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

Perceptual bistability-the spontaneous, irregular fluctuation of perception between two interpretations of a stimulus-occurs when observing a large variety of ambiguous stimulus configurations. This phenomenon has the potential to serve as a tool for, among other things, understanding how function varies across individuals due to the large individual differences that manifest during perceptual bistability. Yet it remains difficult to interpret the functional processes at work, without knowing where bistability arises during perception. In this study we explore the hypothesis that bistability originates from multiple sources distributed across the perceptual hierarchy. We develop a hierarchical model of auditory processing comprised of three distinct levels: a Peripheral, tonotopic analysis, a Central analysis computing features found more centrally in the auditory system, and an Object analysis, where sounds are segmented into different streams. We model bistable perception within this system by applying adaptation, inhibition and noise into one or all of the three levels of the hierarchy. We evaluate a large ensemble of variations of this hierarchical model, where each model has a different configuration of adaptation, inhibition and noise. This approach avoids the assumption that a single configuration must be invoked to explain the data. Each model is evaluated based on its ability to replicate two hallmarks of bistability during auditory streaming: the selectivity of bistability to specific stimulus configurations, and the characteristic log-normal pattern of perceptual switches. Consistent with a distributed origin, a broad range of model parameters across this hierarchy lead to a plausible form of perceptual bistability.

Long-Range Temporal Correlations in Alpha Oscillations Stabilize Perception of Ambiguous Visual Stimuli

Ongoing brain dynamics have been proposed as a type of “neuronal noise” that can trigger perceptual switches when viewing an ambiguous, bistable stimulus. However, no prior study has directly quantified how such neuronal noise relates to the rate of percept reversals. Specifically, it has remained unknown whether individual differences in complexity of resting-state oscillations—as reflected in long-range temporal correlations (LRTC)—are associated with perceptual stability. We hypothesized that participants with stronger resting-state LRTC in the alpha band experience more stable percepts, and thereby fewer perceptual switches. Furthermore, we expected that participants who report less discontinuous thoughts during rest, experience less switches. To test this, we recorded electroencephalography (EEG) in 65 healthy volunteers during 5 min Eyes-Closed Rest (ECR), after which they filled in the Amsterdam Resting-State Questionnaire (ARSQ). This was followed by three conditions where participants attended an ambiguous structure-from-motion stimulus—Neutral (passively observe the stimulus), Hold (the percept for as long as possible), and Switch (as often as possible). LRTC of resting-state alpha oscillations predicted the number of switches only in the Hold condition, with stronger LRTC associated with less switches. Contrary to our expectations, there was no association between resting-state Discontinuity of Mind and percept stability. Participants were capable of controlling switching according to task goals, and this was accompanied by increased alpha power during Hold and decreased power during Switch. Fewer switches were associated with stronger task-related alpha LRTC in all conditions. Together, our data suggest that bistable visual perception is to some extent under voluntary control and influenced by LRTC of alpha oscillations.

Differentiating aversive conditioning in bistable perception: Avoidance of a percept vs. salience of a stimulus

Alternating conscious visual perception of bistable stimuli is influenced by several factors. In order to understand the effect of negative valence, we tested the effect of two types of aversive conditioning on dominance durations in binocular rivalry. Participants received either aversive classical conditioning of the stimuli shown alone between rivalry blocks, or aversive percept conditioning of one of the two possible perceptual choices during rivalry. Both groups showed successful aversive conditioning according to skin conductance responses and affective valence ratings. However, while classical conditioning led to an immediate but short-lived increase in dominance durations of the conditioned stimulus, percept conditioning yielded no significant immediate effect but tended to decrease durations of the conditioned percept during extinction. These results show dissociable effects of value learning on perceptual inference in situations of perceptual conflict, depending on whether learning relates to the decision between conflicting perceptual choices or the sensory stimuli per se.

A different view on the Necker cube-Differences in multistable perception dynamics between Asperger and non-Asperger observers

BACKGROUND

During observation of the Necker cube perception becomes unstable and alternates repeatedly between a from-above-perspective ("fap") and a from-below-perspective ("fbp") interpretation. Both interpretations are physically equally plausible, however, observers usually show an a priori top-down bias in favor of the fap interpretation. Patients with Autism spectrum disorder are known to show an altered pattern of perception with a focus on sensory details. In the present study we tested whether this altered perceptual processing affects their reversal dynamics and reduces the perceptual bias during Necker cube observation.

METHODS

19 participants with Asperger syndrome and 16 healthy controls observed a Necker cube stimulus continuously for 5 minutes and indicated perceptual reversals by key press. We compared reversal rates (number of reversals per minute) and the distributions of dwell times for the two interpretations between observer groups.

RESULTS

Asperger participants showed less perceptual reversal than controls. Six Asperger participants did not perceive any reversal at all, whereas all observers from the control group perceived at least five reversals within the five minutes observation time. Further, control participants showed the typical perceptual bias with significant longer median dwell times for the fap compared to the fbp interpretation. No such perceptual bias was found in the Asperger group.

DISCUSSION

The perceptual system weights the incomplete and ambiguous sensory input with memorized concepts in order to construct stable and reliable percepts. In the case of the Necker cube stimulus, two perceptual interpretations are equally compatible with the sensory information and internal fluctuations may cause perceptual alternations between them-with a slightly larger probability value for the fap interpretation (perceptual bias). Smaller reversal rates in Asperger observers may result from the dominance of bottom-up sensory input over endogenous top-down factors. The latter may also explain the absence of a fap bias.

Classifying the Perceptual Interpretations of a Bistable Image Using EEG and Artificial Neural Networks

In order to classify different human brain states related to visual perception of ambiguous images, we use an artificial neural network (ANN) to analyze multichannel EEG. The classifier built on the basis of a multilayer perceptron achieves up to 95% accuracy in classifying EEG patterns corresponding to two different interpretations of the Necker cube. The important feature of our classifier is that trained on one subject it can be used for the classification of EEG traces of other subjects. This result suggests the existence of common features in the EEG structure associated with distinct interpretations of bistable objects. We firmly believe that the significance of our results is not limited to visual perception of the Necker cube images; the proposed experimental approach and developed computational technique based on ANN can also be applied to study and classify different brain states using neurophysiological data recordings. This may give new directions for future research in the field of cognitive and pathological brain activity, and for the development of brain-computer interfaces.

A hierarchical stochastic model for bistable perception

Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM) for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM), which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group differences to potential underlying mechanisms.

Patients suffering from schizophrenia show specific cognitive deficits. One way to study these cognitive phenomena works with the presentation of ambiguous stimuli. During viewing of an ambiguous stimulus, perception alters spontaneously between different percepts. Percept changes occur as single events during continuous presentation, whereas during intermittent presentation, percept changes occur at regular intervals either as single events or bursts. Here we investigate perceptual responses to continuous and intermittent stimulation in healthy control subjects and patients with schizophrenia. Interestingly, the response patterns can be highly variable but show systematic group differences. We propose a model that connects these perceptual responses to underlying neuronal processes. The model mainly describes the activity difference between competing neuronal populations on different neuronal levels. In a hierarchical manner, the differential activity generates switching between the conflicting percepts as well as between states of higher and lower perceptual stability. By fitting the model directly to empirical responses, a high variety of patterns can be reproduced, and group differences between healthy controls and patients with schizophrenia can be captured. This helps to link the observed group differences to potential neuronal mechanisms, suggesting that patients with schizophrenia tend to spend more time in neuronal states of lower perceptual stability.

Collective Activity of Many Bistable Assemblies Reproduces Characteristic Dynamics of Multistable Perception

The timing of perceptual decisions depends on both deterministic and stochastic factors, as the gradual accumulation of sensory evidence (deterministic) is contaminated by sensory and/or internal noise (stochastic). When human observers view multistable visual displays, successive episodes of stochastic accumulation culminate in repeated reversals of visual appearance. Treating reversal timing as a "first-passage time" problem, we ask how the observed timing densities constrain the underlying stochastic accumulation. Importantly, mean reversal times (i.e., deterministic factors) differ enormously between displays/observers/stimulation levels, whereas the variance and skewness of reversal times (i.e., stochastic factors) keep characteristic proportions of the mean. What sort of stochastic process could reproduce this highly consistent "scaling property?" Here we show that the collective activity of a finite population of bistable units (i.e., a generalized Ehrenfest process) quantitatively reproduces all aspects of the scaling property of multistable phenomena, in contrast to other processes under consideration (Poisson, Wiener, or Ornstein-Uhlenbeck process). The postulated units express the spontaneous dynamics of attractor assemblies transitioning between distinct activity states. Plausible candidates are cortical columns, or clusters of columns, as they are preferentially connected and spontaneously explore a restricted repertoire of activity states. Our findings suggests that perceptual representations are granular, probabilistic, and operate far from equilibrium, thereby offering a suitable substrate for statistical inference.

SIGNIFICANCE STATEMENT

Spontaneous reversals of high-level perception, so-called multistable perception, conform to highly consistent and characteristic statistics, constraining plausible neural representations. We show that the observed perceptual dynamics would be reproduced quantitatively by a finite population of distinct neural assemblies, each with locally bistable activity, operating far from the collective equilibrium (generalized Ehrenfest process). Such a representation would be consistent with the intrinsic stochastic dynamics of neocortical activity, which is dominated by preferentially connected assemblies, such as cortical columns or clusters of columns. We predict that local neuron assemblies will express bistable dynamics, with spontaneous active-inactive transitions, whenever they contribute to high-level perception.

Auditory Streaming as an Online Classification Process with Evidence Accumulation

When human subjects hear a sequence of two alternating pure tones, they often perceive it in one of two ways: as one integrated sequence (a single "stream" consisting of the two tones), or as two segregated sequences, one sequence of low tones perceived separately from another sequence of high tones (two "streams"). Perception of this stimulus is thus bistable. Moreover, subjects report on-going switching between the two percepts: unless the frequency separation is large, initial perception tends to be of integration, followed by toggling between integration and segregation phases. The process of stream formation is loosely named “auditory streaming”. Auditory streaming is believed to be a manifestation of human ability to analyze an auditory scene, i.e. to attribute portions of the incoming sound sequence to distinct sound generating entities. Previous studies suggested that the durations of the successive integration and segregation phases are statistically independent. This independence plays an important role in current models of bistability. Contrary to this, we show here, by analyzing a large set of data, that subsequent phase durations are positively correlated. To account together for bistability and positive correlation between subsequent durations, we suggest that streaming is a consequence of an evidence accumulation process. Evidence for segregation is accumulated during the integration phase and vice versa; a switch to the opposite percept occurs stochastically based on this evidence. During a long phase, a large amount of evidence for the opposite percept is accumulated, resulting in a long subsequent phase. In contrast, a short phase is followed by another short phase. We implement these concepts using a probabilistic model that shows both bistability and correlations similar to those observed experimentally.

The 'laws' of binocular rivalry: 50 years of Levelt's propositions

It has been fifty years since Levelt's monograph On Binocular Rivalry (1965) was published, but its four propositions that describe the relation between stimulus strength and the phenomenology of binocular rivalry remain a benchmark for theorists and experimentalists even today. In this review, we will revisit the original conception of the four propositions and the scientific landscape in which this happened. We will also provide a brief update concerning distributions of dominance durations, another aspect of Levelt's monograph that has maintained a prominent presence in the field. In a critical evaluation of Levelt's propositions against current knowledge of binocular rivalry we will then demonstrate that the original propositions are not completely compatible with what is known today, but that they can, in a straightforward way, be modified to encapsulate the progress that has been made over the past fifty years. The resulting modified, propositions are shown to apply to a broad range of bistable perceptual phenomena, not just binocular rivalry, and they allow important inferences about the underlying neural systems. We argue that these inferences reflect canonical neural properties that play a role in visual perception in general, and we discuss ways in which future research can build on the work reviewed here to attain a better understanding of these properties.

Competition with and without priority control: linking rivalry to attention through winner-take-all networks with memory

Competition is ubiquitous in perception. For example, items in the visual field compete for processing resources, and attention controls their priority (biased competition). The inevitable ambiguity in the interpretation of sensory signals yields another form of competition: distinct perceptual interpretations compete for access to awareness. Rivalry, where two equally likely percepts compete for dominance, explicates the latter form of competition. Building upon the similarity between attention and rivalry, we propose to model rivalry by a generic competitive circuit that is widely used in the attention literature-a winner-take-all (WTA) network. Specifically, we show that a network of two coupled WTA circuits replicates three common hallmarks of rivalry: the distribution of dominance durations, their dependence on input strength ("Levelt's propositions"), and the effects of stimulus removal (blanking). This model introduces a form of memory by forming discrete states and explains experimental data better than competitive models of rivalry without memory. This result supports the crucial role of memory in rivalry specifically and in competitive processes in general. Our approach unifies the seemingly distinct phenomena of rivalry, memory, and attention in a single model with competition as the common underlying principle.

Fluctuations of visual awareness: combining motion-induced blindness with binocular rivalry

Binocular rivalry (BR) and motion-induced blindness (MIB) are two phenomena of visual awareness where perception alternates between multiple states despite constant retinal input. Both phenomena have been extensively studied, but the underlying processing remains unclear. It has been suggested that BR and MIB involve the same neural mechanism, but how the two phenomena compete for visual awareness in the same stimulus has not been systematically investigated. Here we introduce BR in a dichoptic stimulus display that can also elicit MIB and examine fluctuations of visual awareness over the course of each trial. Exploiting this paradigm we manipulated stimulus characteristics that are known to influence MIB and BR. In two experiments we found that effects on multistable percepts were incompatible with the idea of a common oscillator. The results suggest instead that local and global stimulus attributes can affect the dynamics of each percept differently. We conclude that the two phenomena of visual awareness share basic temporal characteristics but are most likely influenced by processing at different stages within the visual system.

Stochastic accumulation by cortical columns may explain the scalar property of multistable perception

The timing of certain mental events is thought to reflect random walks performed by underlying neural dynamics. One class of such events--stochastic reversals of multistable perceptions--exhibits a unique scalar property: even though timing densities vary widely, higher moments stay in particular proportions to the mean. We show that stochastic accumulation of activity in a finite number of idealized cortical columns--realizing a generalized Ehrenfest urn model--may explain these observations. Modeling stochastic reversals as the first-passage time of a threshold number of active columns, we obtain higher moments of the first-passage time density. We derive analytical expressions for noninteracting columns and generalize the results to interacting columns in simulations. The scalar property of multistable perception is reproduced by a dynamic regime with a fixed, low threshold, in which the activation of a few additional columns suffices for a reversal.

Perceptual adaptation to structure-from-motion depends on the size of adaptor and probe objects, but not on the similarity of their shapes

Perceptual adaptation destabilizes the phenomenal appearance of multistable visual displays. Prolonged dominance of a perceptual state fatigues the associated neural population, lowering the likelihood of renewed perception of the same appearance (Nawrot & Blake in Perception & Psychophysics, 49, 230-44, 1991). Here, we used a selective adaptation paradigm to investigate perceptual adaptation for the illusory rotation of ambiguous structure-from-motion (SFM) displays. Specifically, we generated SFM objects with different three-dimensional shapes and presented them in random order, separating successive objects by brief blank periods, which included a mask. To assess the specificity of perceptual adaptation to the shape of SFM objects, we established the probability that a perceived direction of rotation persisted between successive objects of similar or dissimilar shape. We found that the strength of negative aftereffects depended on the volume, but not the shape, of adaptor and probe objects. More voluminous objects were both more effective as adaptor objects and more sensitive as probe objects. Surprisingly, we found these volume effects to be completely independent, since any relationship between two shapes (such as overlap between volumes, similarity of shape, or similarity of velocity profiles) failed to modulate the negative aftereffect. This pattern of results was the opposite of that observed for sensory memory of SFM objects, which reflects similarity between objects, but not volume of individual objects (Pastukhov et al. in Attention, Perception & Psychophysics, 75, 1215-1229, 2013). The disparate specificities of perceptual adaptation and sensory memory for identical SFM objects suggest that the two aftereffects engage distinct neural representations, consistent with recent brain imaging results (Schwiedrzik et al. in Cerebral Cortex, 2012).

Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis

Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.

Sensory memory of structure-from-motion is shape-specific

Perceptual priming can stabilize the phenomenal appearance of multistable visual displays (Leopold, Wilke, Maier, & Logothetis, Nature Neuroscience, 5, 605-609, 2002). Prior exposure to such displays induces a sensory memory of their appearance, which persists over long intervals and intervening stimulation, and which facilitates renewed perception of the same appearance. Here, we investigated perceptual priming for the apparent rotation in depth of ambiguous structure-from-motion (SFM) displays. Specifically, we generated SFM objects with different three-dimensional shapes and presented them in random order and with intervening blank periods. To assess perceptual priming, we established the probability that a perceived direction of rotation would persist between successive objects. In general, persistence was greatest between identical objects, intermediate between similar objects, and negligible between dissimilar objects. These results demonstrate unequivocally that sensory memory for apparent rotation is specific to three-dimensional shape, contrary to previous reports (e.g., Maier, Wilke, Logothetis, & Leopold, Current Biology, 13, 1076-1085, 2003). Because persistence did not depend on presentation order for any pair of objects, it provides a commutative measure for the similarity of object shapes. However, it is not clear exactly which features or aspects of object shape determine similarity. At least, we did not find simple, low-level features (such as volume overlap, heterogeneity, or rotational symmetry) that could have accounted for all observations. Accordingly, it seems that sensory memory of SFM (which underlies priming of ambiguous rotation) engages higher-level representations of object surface and shape.

Sensory memory of illusory depth in structure-from-motion

When multistable displays (stimuli consistent with two or more equally plausible perceptual interpretations) are presented intermittently, their perceptions are stabilized by sensory memory. Independent memory traces are generated not only for different types of multistable displays (Maier, Wilke, Logothetis, & Leopold, Current Biology 13:1076-1085, 2003), but also for different ambiguous features of binocular rivalry (Pearson & Clifford, Journal of Vision 4:196-202, 2004). In the present study, we examined whether a similar independence of sensory memories is observed in structure-from-motion (SFM), a multistable display with two ambiguous properties. In SFM, a 2-D planar motion creates a vivid impression of a rotating 3-D volume. Both the illusory rotation and illusory depth (i.e., how close parts of an object appear to the observer) of an SFM object are ambiguous. We dissociated the sensory memories of these two ambiguous properties by using an intermittent presentation in combination with a forced-ambiguous-switch paradigm (Pastukhov, Vonau, & Braun, PLoS ONE 7:e37734, 2012). We demonstrated that the illusory depth of SFM generates a sensory memory trace that is independent from that of illusory rotation. Despite this independence, the specificities levels of the sensory memories were identical for illusory depth and illusory rotation. The history effect was weakened by a change in the volumetric property of a shape (whether it was a hollow band or a filled drum volume), but not by changes in color or size. We discuss how these new results constrain models of sensory memory and SFM processing.

Motion-induced blindness and Troxler fading: common and different mechanisms

Extended stabilization of gaze leads to disappearance of dim visual targets presented peripherally. This phenomenon, known as Troxler fading, is thought to result from neuronal adaptation. Intense targets also disappear intermittently when surrounded by a moving pattern (the “mask”), a phenomenon known as motion-induced blindness (MIB). The similar phenomenology and dynamics of these disappearances may suggest that also MIB is, likewise, solely due to adaptation, which may be amplified by the presence of the mask. Here we directly compared the dependence of both phenomena on target contrast. Observers reported the disappearance and reappearance of a target of varying intensity (contrast levels: 8%–80%). MIB was induced by adding a mask that moved at one of various different speeds. The results revealed a lawful effect of contrast in both MIB and Troxler fading, but with opposite trends. Increasing target contrast increased (doubled) the rate of disappearance events for MIB, but decreased the disappearance rate to half in Troxler fading. The target mean invisible period decreased equally strongly with target contrast in MIB and in Troxler fading. The results suggest that both MIB and Troxler are equally affected by contrast adaptation, but that the rate of MIB is governed by an additional mechanism, possibly involving antagonistic processes between neuronal populations processing target and mask. Our results link MIB to other bi-stable visual phenomena that involve neuronal competition (such as binocular rivalry), which exhibit an analogous dependency on the strength of the competing stimulus components.

Brain mechanisms for simple perception and bistable perception

When faced with ambiguous sensory inputs, subjective perception alternates between the different interpretations in a stochastic manner. Such multistable perception phenomena have intrigued scientists and laymen alike for over a century. Despite rigorous investigations, the underlying mechanisms of multistable perception remain elusive. Recent studies using multivariate pattern analysis revealed that activity patterns in posterior visual areas correlate with fluctuating percepts. However, increasing evidence suggests that vision--and perception at large--is an active inferential process involving hierarchical brain systems. We applied searchlight multivariate pattern analysis to functional magnetic resonance imaging signals across the human brain to decode perceptual content during bistable perception and simple unambiguous perception. Although perceptually reflective activity patterns during simple perception localized predominantly to posterior visual regions, bistable perception involved additionally many higher-order frontoparietal and temporal regions. Moreover, compared with simple perception, both top-down and bottom-up influences were dramatically enhanced during bistable perception. We further studied the intermittent presentation of ambiguous images--a condition that is known to elicit perceptual memory. Compared with continuous presentation, intermittent presentation recruited even more higher-order regions and was accompanied by further strengthened top-down influences but relatively weakened bottom-up influences. Taken together, these results strongly support an active top-down inferential process in perception.

Synthesizing cognition in neuromorphic electronic systems

The quest to implement intelligent processing in electronic neuromorphic systems lacks methods for achieving reliable behavioral dynamics on substrates of inherently imprecise and noisy neurons. Here we report a solution to this problem that involves first mapping an unreliable hardware layer of spiking silicon neurons into an abstract computational layer composed of generic reliable subnetworks of model neurons and then composing the target behavioral dynamics as a "soft state machine" running on these reliable subnets. In the first step, the neural networks of the abstract layer are realized on the hardware substrate by mapping the neuron circuit bias voltages to the model parameters. This mapping is obtained by an automatic method in which the electronic circuit biases are calibrated against the model parameters by a series of population activity measurements. The abstract computational layer is formed by configuring neural networks as generic soft winner-take-all subnetworks that provide reliable processing by virtue of their active gain, signal restoration, and multistability. The necessary states and transitions of the desired high-level behavior are then easily embedded in the computational layer by introducing only sparse connections between some neurons of the various subnets. We demonstrate this synthesis method for a neuromorphic sensory agent that performs real-time context-dependent classification of motion patterns observed by a silicon retina.

Short term synaptic depression improves information transfer in perceptual multistability

Competitive neural networks are often used to model the dynamics of perceptual bistability. Switching between percepts can occur through fluctuations and/or a slow adaptive process. Here, we analyze switching statistics in competitive networks with short term synaptic depression and noise. We start by analyzing a ring model that yields spatially structured solutions and complement this with a study of a space-free network whose populations are coupled with mutual inhibition. Dominance times arising from depression driven switching can be approximated using a separation of timescales in the ring and space-free model. For purely noise-driven switching, we derive approximate energy functions to justify how dominance times are exponentially related to input strength. We also show that a combination of depression and noise generates realistic distributions of dominance times. Unimodal functions of dominance times are more easily told apart by sampling, so switches induced by synaptic depression induced provide more information about stimuli than noise-driven switching. Finally, we analyze a competitive network model of perceptual tristability, showing depression generates a history-dependence in dominance switching.

Retinotopic patterns of correlated fluctuations in visual cortex reflect the dynamics of spontaneous perceptual suppression

While viewing certain stimuli, perception changes spontaneously in the face of constant input. For example, during "motion-induced blindness" (MIB), a small salient target spontaneously disappears and reappears when surrounded by a moving mask. Models of such bistable perceptual phenomena posit spontaneous fluctuations in neuronal activity throughout multiple stages of the visual cortical hierarchy. We used fMRI to link correlated activity fluctuations across human visual cortical areas V1 through V4 to the dynamics (rate and duration) of MIB target disappearance. We computed the correlations between the time series of fMRI activity in multiple retinotopic subregions corresponding to MIB target and mask. Linear decomposition of the matrix of temporal correlations revealed spatial patterns of activity fluctuations, regardless of whether or not these were time-locked to behavioral reports of target disappearance. The spatial pattern that dominated the activity fluctuations during MIB was spatially nonspecific, shared by all subregions, but did not reflect the dynamics of perception. By contrast, the fluctuations associated with the rate of MIB disappearance were retinotopically specific for the target subregion in V4, and the fluctuations associated with the duration of MIB disappearance states were target-specific in V1. Target-specific fluctuations in V1 have not previously been identified by averaging activity time-locked to behavioral reports of MIB disappearance. Our results suggest that different levels of the visual cortical hierarchy shape the dynamics of perception via distinct mechanisms, which are evident in distinct spatial patterns of spontaneous cortical activity fluctuations.

A model of binocular rivalry and cross-orientation suppression

Binocular rivalry and cross-orientation suppression are well-studied forms of competition in visual cortex, but models of these two types of competition are in tension with one another. Binocular rivalry occurs during the presentation of dichoptic grating stimuli, where two orthogonal gratings presented separately to the two eyes evoke strong alternations in perceptual dominance. Cross-orientation suppression occurs during the presentation of plaid stimuli, where the responses to a component grating presented to both eyes is weakened by the presence of a superimposed orthogonal grating. Conventional models of rivalry that rely on strong competition between orientation-selective neurons incorrectly predict rivalry between the components of plaids. Lowering the inhibitory weights in such models reduces rivalry for plaids, but also reduces it for dichoptic gratings. Using an exhaustive grid search, we show that this problem cannot be solved simply by adjusting the parameters of the model. Instead, we propose a robust class of models that rely on ocular opponency neurons, previously proposed as a mechanism for efficient stereo coding, to yield rivalry only for dichoptic gratings, not for plaids. This class of models reconciles models of binocular rivalry with the divisive normalization framework that has been used to explain cross-orientation. Our model makes novel predictions that we confirmed with psychophysical tests.

Multi-stable perception balances stability and sensitivity

We report that multi-stable perception operates in a consistent, dynamical regime, balancing the conflicting goals of stability and sensitivity. When a multi-stable visual display is viewed continuously, its phenomenal appearance reverses spontaneously at irregular intervals. We characterized the perceptual dynamics of individual observers in terms of four statistical measures: the distribution of dominance times (mean and variance) and the novel, subtle dependence on prior history (correlation and time-constant). The dynamics of multi-stable perception is known to reflect several stabilizing and destabilizing factors. Phenomenologically, its main aspects are captured by a simplistic computational model with competition, adaptation, and noise. We identified small parameter volumes (~3% of the possible volume) in which the model reproduced both dominance distribution and history-dependence of each observer. For 21 of 24 data sets, the identified volumes clustered tightly (~15% of the possible volume), revealing a consistent "operating regime" of multi-stable perception. The "operating regime" turned out to be marginally stable or, equivalently, near the brink of an oscillatory instability. The chance probability of the observed clustering was <0.02. To understand the functional significance of this empirical "operating regime," we compared it to the theoretical "sweet spot" of the model. We computed this "sweet spot" as the intersection of the parameter volumes in which the model produced stable perceptual outcomes and in which it was sensitive to input modulations. Remarkably, the empirical "operating regime" proved to be largely coextensive with the theoretical "sweet spot." This demonstrated that perceptual dynamics was not merely consistent but also functionally optimized (in that it balances stability with sensitivity). Our results imply that multi-stable perception is not a laboratory curiosity, but reflects a functional optimization of perceptual dynamics for visual inference.

Untangling perceptual memory: hysteresis and adaptation map into separate cortical networks

Perception is an active inferential process in which prior knowledge is combined with sensory input, the result of which determines the contents of awareness. Accordingly, previous experience is known to help the brain "decide" what to perceive. However, a critical aspect that has not been addressed is that previous experience can exert 2 opposing effects on perception: An attractive effect, sensitizing the brain to perceive the same again (hysteresis), or a repulsive effect, making it more likely to perceive something else (adaptation). We used functional magnetic resonance imaging and modeling to elucidate how the brain entertains these 2 opposing processes, and what determines the direction of such experience-dependent perceptual effects. We found that although affecting our perception concurrently, hysteresis and adaptation map into distinct cortical networks: a widespread network of higher-order visual and fronto-parietal areas was involved in perceptual stabilization, while adaptation was confined to early visual areas. This areal and hierarchical segregation may explain how the brain maintains the balance between exploiting redundancies and staying sensitive to new information. We provide a Bayesian model that accounts for the coexistence of hysteresis and adaptation by separating their causes into 2 distinct terms: Hysteresis alters the prior, whereas adaptation changes the sensory evidence (the likelihood function).

Effects of time-dependent stimuli in a competitive neural network model of perceptual rivalry

We analyze a competitive neural network model of perceptual rivalry that receives time-varying inputs. Time-dependence of inputs can be discrete or smooth. Spike frequency adaptation provides negative feedback that generates network oscillations when inputs are constant in time. Oscillations that resemble perceptual rivalry involve only one population being “ON” at a time, which represents the dominance of a single percept at a time. As shown in Laing and Chow (J. Comput. Neurosci. 12(1):39–53, 2002), for sufficiently high contrast, one can derive relationships between dominance times and contrast that agree with Levelt’s propositions (Levelt in On binocular rivalry, 1965). Time-dependent stimuli give rise to novel network oscillations where both, one, or neither populations are “ON” at any given time. When a single population receives an interrupted stimulus, the fundamental mode of behavior we find is phase-locking, where the temporally driven population locks its state to the stimulus. Other behaviors are analyzed as bifurcations from this forced oscillation, using fast/slow analysis that exploits the slow timescale of adaptation. When both populations receive time-varying input, we find mixtures of fusion and sole population dominance, and we partition parameter space into particular oscillation types. Finally, when a single population’s input contrast is smoothly varied in time, 1:n mode-locked states arise through period-adding bifurcations beyond phase-locking. Our results provide several testable predictions for future psychophysical experiments on perceptual rivalry.

Neural dynamics and circuit mechanisms of decision-making

In this review, I briefly summarize current neurobiological studies of decision-making that bear on two general themes. The first focuses on the nature of neural representation and dynamics in a decision circuit. Experimental and computational results suggest that ramping-to-threshold in the temporal domain and trajectory of population activity in the state space represent a duality of perspectives on a decision process. Moreover, a decision circuit can display several different dynamical regimes, such as the ramping mode and the jumping mode with distinct defining properties. The second is concerned with the relationship between biologically-based mechanistic models and normative-type models. A fruitful interplay between experiments and these models at different levels of abstraction have enabled investigators to pose increasingly refined questions and gain new insights into the neural basis of decision-making. In particular, recent work on multi-alternative decisions suggests that deviations from rational models of choice behavior can be explained by established neural mechanisms.

Intermittent stimulus presentation stabilizes neuronal responses in macaque area MT

Repeated stimulation impacts neuronal responses. Here we show how response characteristics of sensory neurons in macaque visual cortex are influenced by the duration of the interruptions during intermittent stimulus presentation. Besides effects on response magnitude consistent with neuronal adaptation, the response variability was also systematically influenced. Spike rate variability in motion-sensitive area MT decreased when interruption durations were systematically increased from 250 to 2,000 ms. Activity fluctuations between subsequent trials and Fano factors over full response sequences were both lower with longer interruptions, while spike timing patterns became more regular. These variability changes partially depended on the response magnitude, but another significant effect that was uncorrelated with adaptation-induced changes in response magnitude was also present. Reduced response variability was furthermore accompanied by changes in spike-field coherence, pointing to the possibility that reduced spiking variability results from interactions in the local cortical network. While neuronal response stabilization may be a general effect of repeated sensory stimulation, we discuss its potential link with the phenomenon of perceptual stabilization of ambiguous stimuli as a result of interrupted presentation.

Binocular rivalry alternations and their relation to visual adaptation

When different stimuli are presented dichoptically, perception alternates between the two in a stochastic manner. After a long-lasting and rigorous debate, there is growing consensus that this phenomenon, known as binocular rivalry (BR), is the result of a dynamic competition occurring at multiple levels of the visual hierarchy. The role of low- and high-level adaptation mechanisms in controlling these perceptual alternations has been a key issue in the rivalry literature. Both types of adaptation are dispersed throughout the visual system and have an equally influential, or even causal, role in determining perception. Such an explanation of BR is also in accordance with the relationship between the latter and attention. However, an overall explanation of this intriguing perceptual phenomenon needs to also include noise as an equally fundamental process involved in the stochastic resonance of perceptual bistability.

Robust Working Memory in an Asynchronously Spiking Neural Network Realized with Neuromorphic VLSI

We demonstrate bistable attractor dynamics in a spiking neural network implemented with neuromorphic VLSI hardware. The on-chip network consists of three interacting populations (two excitatory, one inhibitory) of leaky integrate-and-fire (LIF) neurons. One excitatory population is distinguished by strong synaptic self-excitation, which sustains meta-stable states of “high” and “low”-firing activity. Depending on the overall excitability, transitions to the “high” state may be evoked by external stimulation, or may occur spontaneously due to random activity fluctuations. In the former case, the “high” state retains a “working memory” of a stimulus until well after its release. In the latter case, “high” states remain stable for seconds, three orders of magnitude longer than the largest time-scale implemented in the circuitry. Evoked and spontaneous transitions form a continuum and may exhibit a wide range of latencies, depending on the strength of external stimulation and of recurrent synaptic excitation. In addition, we investigated “corrupted” “high” states comprising neurons of both excitatory populations. Within a “basin of attraction,” the network dynamics “corrects” such states and re-establishes the prototypical “high” state. We conclude that, with effective theoretical guidance, full-fledged attractor dynamics can be realized with comparatively small populations of neuromorphic hardware neurons.

Unmixing binocular signals

Incompatible images presented to the two eyes lead to perceptual oscillations in which one image at a time is visible. Early models portrayed this binocular rivalry as involving reciprocal inhibition between monocular representations of images, occurring at an early visual stage prior to binocular mixing. However, psychophysical experiments found conditions where rivalry could also occur at a higher, more abstract level of representation. In those cases, the rivalry was between image representations dissociated from eye-of-origin information, rather than between monocular representations from the two eyes. Moreover, neurophysiological recordings found the strongest rivalry correlate in inferotemporal cortex, a high-level, predominantly binocular visual area involved in object recognition, rather than early visual structures. An unresolved issue is how can the separate identities of the two images be maintained after binocular mixing in order for rivalry to be possible at higher levels? Here we demonstrate that after the two images are mixed, they can be unmixed at any subsequent stage using a physiologically plausible non-linear signal-processing algorithm, non-negative matrix factorization, previously proposed for parsing object parts during object recognition. The possibility that unmixed left and right images can be regenerated at late stages within the visual system provides a mechanism for creating various binocular representations and interactions de novo in different cortical areas for different purposes, rather than inheriting then from early areas. This is a clear example how non-linear algorithms can lead to highly non-intuitive behavior in neural information processing.

Cortical attractor network dynamics with diluted connectivity

The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding".

Widespread Brain Areas Engaged during a Classical Auditory Streaming Task Revealed by Intracranial EEG

The auditory system must constantly decompose the complex mixture of sound arriving at the ear into perceptually independent streams constituting accurate representations of individual sources in the acoustic environment. How the brain accomplishes this task is not well understood. The present study combined a classic behavioral paradigm with direct cortical recordings from neurosurgical patients with epilepsy in order to further describe the neural correlates of auditory streaming. Participants listened to sequences of pure tones alternating in frequency and indicated whether they heard one or two "streams." The intracranial EEG was simultaneously recorded from sub-dural electrodes placed over temporal, frontal, and parietal cortex. Like healthy subjects, patients heard one stream when the frequency separation between tones was small and two when it was large. Robust evoked-potential correlates of frequency separation were observed over widespread brain areas. Waveform morphology was highly variable across individual electrode sites both within and across gross brain regions. Surprisingly, few evoked-potential correlates of perceptual organization were observed after controlling for physical stimulus differences. The results indicate that the cortical areas engaged during the streaming task are more complex and widespread than has been demonstrated by previous work, and that, by-and-large, correlates of bistability during streaming are probably located on a spatial scale not assessed - or in a brain area not examined - by the present study.

Role of mutual inhibition in binocular rivalry

Binocular rivalry is a phenomenon that occurs when a different image is presented to each eye. The observer generally perceives just one image at a time, with perceptual switches occurring every few seconds. A natural assumption is that this perceptual mutual exclusivity is achieved via mutual inhibition between populations of neurons that encode for either percept. Theoretical models that incorporate mutual inhibition have been largely successful at capturing experimental features of rivalry, including Levelt's propositions, which characterize perceptual dominance durations as a function of image contrasts. However, basic mutual inhibition models do not fully comply with Levelt's fourth proposition, which states that percepts alternate faster as the stimulus contrasts to both eyes are increased simultaneously. This theory-experiment discrepancy has been taken as evidence against the role of mutual inhibition for binocular rivalry. Here, we show how various biophysically plausible modifications to mutual inhibition models can resolve this problem.

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.

Synchronization and redundancy: implications for robustness of neural learning and decision making

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by nonideal biological building blocks that can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error, which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. We discuss range of situations in which the mechanisms we model arise in brain science and draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.

Global convergence of quorum-sensing networks

In many natural synchronization phenomena, communication between individual elements occurs not directly but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general nonlinear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quantities, typically provided by the nodes' environment. Our model includes the case when the dynamics of the shared variables themselves cannot be neglected or indeed play a central part. Applications to examples from system biology illustrate the approach.

Stochastic transitions between neural states in taste processing and decision-making

Noise, which is ubiquitous in the nervous system, causes trial-to-trial variability in the neural responses to stimuli. This neural variability is in turn a likely source of behavioral variability. Using Hidden Markov modeling, a method of analysis that can make use of such trial-to-trial response variability, we have uncovered sequences of discrete states of neural activity in gustatory cortex during taste processing. Here, we advance our understanding of these patterns in two ways. First, we reproduce the experimental findings in a formal model, describing a network that evinces sharp transitions between discrete states that are deterministically stable given sufficient noise in the network; as in the empirical data, the transitions occur at variable times across trials, but the stimulus-specific sequence is itself reliable. Second, we demonstrate that such noise-induced transitions between discrete states can be computationally advantageous in a reduced, decision-making network. The reduced network produces binary outputs, which represent classification of ingested substances as palatable or nonpalatable, and the corresponding behavioral responses of "spit" or "swallow". We evaluate the performance of the network by measuring how reliably its outputs follow small biases in the strengths of its inputs. We compare two modes of operation: deterministic integration ("ramping") versus stochastic decision-making ("jumping"), the latter of which relies on state-to-state transitions. We find that the stochastic mode of operation can be optimal under typical levels of internal noise and that, within this mode, addition of random noise to each input can improve optimal performance when decisions must be made in limited time.

Attractors and noise: twin drivers of decisions and multistability

Perceptual decisions are made not only during goal-directed behavior such as choice tasks, but also occur spontaneously while multistable stimuli are being viewed. In both contexts, the formation of a perceptual decision is best captured by noisy attractor dynamics. Noise-driven attractor transitions can accommodate a wide range of timescales and a hierarchical arrangement with "nested attractors" harbors even more dynamical possibilities. The attractor framework seems particularly promising for understanding higher-level mental states that combine heterogeneous information from a distributed set of brain areas.

Stochastic variations in sensory awareness are driven by noisy neuronal adaptation: evidence from serial correlations in perceptual bistability

When the sensory system is subjected to ambiguous input, perception alternates between interpretations in a seemingly random fashion. Although neuronal noise obviously plays a role, the neural mechanism for the generation of randomness at the slow time scale of the percept durations (multiple seconds) is unresolved. Here significant nonzero serial correlations are reported in series of visual percept durations (to the author's knowledge for the first time accounting for duration impurities caused by reaction time, drift, and incomplete percepts). Serial correlations for perceptual rivalry using structure-from-motion ambiguity were smaller than for binocular rivalry using orthogonal gratings. A spectrum of computational models is considered, and it is concluded that noise in adaptation of percept-related neurons causes the serial correlations. This work bridges, in a physiologically plausible way, widely appreciated deterministic modeling and randomness in experimental observations of visual rivalry.