Bayesian natural selection and the evolution of perceptual systems

A Variational Synthesis of Evolutionary and Developmental Dynamics

This paper introduces a variational formulation of natural selection, paying special attention to the nature of 'things' and the way that different 'kinds' of 'things' are individuated from-and influence-each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain-and are constrained by-fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (Bayesian model) selection. The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations of distinct natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses-and identify points of contact with related mathematical formulations of evolution.

Calibrating Vision: Concepts and Questions

The idea that visual coding and perception are shaped by experience and adjust to changes in the environment or the observer is universally recognized as a cornerstone of visual processing, yet the functions and processes mediating these calibrations remain in many ways poorly understood. In this article we review a number of facets and issues surrounding the general notion of calibration, with a focus on plasticity within the encoding and representational stages of visual processing. These include how many types of calibrations there are - and how we decide; how plasticity for encoding is intertwined with other principles of sensory coding; how it is instantiated at the level of the dynamic networks mediating vision; how it varies with development or between individuals; and the factors that may limit the form or degree of the adjustments. Our goal is to give a small glimpse of an enormous and fundamental dimension of vision, and to point to some of the unresolved questions in our understanding of how and why ongoing calibrations are a pervasive and essential element of vision.

Visual segmentation of complex naturalistic structures in an infant eye-tracking search task

An infant’s everyday visual environment is composed of a complex array of entities, some of which are well integrated into their surroundings. Although infants are already sensitive to some categories in their first year of life, it is not clear which visual information supports their detection of meaningful elements within naturalistic scenes. Here we investigated the impact of image characteristics on 8-month-olds’ search performance using a gaze contingent eye-tracking search task. Infants had to detect a target patch on a background image. The stimuli consisted of images taken from three categories: vegetation, non-living natural elements (e.g., stones), and manmade artifacts, for which we also assessed target background differences in lower- and higher-level visual properties. Our results showed that larger target-background differences in the statistical properties scaling invariance and entropy, and also stimulus backgrounds including low pictorial depth, predicted better detection performance. Furthermore, category membership only affected search performance if supported by luminance contrast. Data from an adult comparison group also indicated that infants’ search performance relied more on lower-order visual properties than adults. Taken together, these results suggest that infants use a combination of property- and category-related information to parse complex visual stimuli.

Bayes and Darwin: How replicator populations implement Bayesian computations

Bayesian learning theory and evolutionary theory both formalize adaptive competition dynamics in possibly high-dimensional, varying, and noisy environments. What do they have in common and how do they differ? In this paper, we discuss structural and dynamical analogies and their limits, both at a computational and an algorithmic-mechanical level. We point out mathematical equivalences between their basic dynamical equations, generalizing the isomorphism between Bayesian update and replicator dynamics. We discuss how these mechanisms provide analogous answers to the challenge of adapting to stochastically changing environments at multiple timescales. We elucidate an algorithmic equivalence between a sampling approximation, particle filters, and the Wright-Fisher model of population genetics. These equivalences suggest that the frequency distribution of types in replicator populations optimally encodes regularities of a stochastic environment to predict future environments, without invoking the known mechanisms of multilevel selection and evolvability. A unified view of the theories of learning and evolution comes in sight.

Exploring the Evolution of Perception: An Agent-Based Approach

Perception is central to the survival of an individual for many reasons, especially as it affects the ability to gather resources. Consequently, costs associated with perception are partially shaped by resource availability. Understanding the interplay of environmental factors (such as the density and distribution of resources) with species-specific factors (such as growth rate, mutation, and metabolic costs) allows the exploration of possible trajectories by which perception may evolve. Here, we used an agent-based foraging model with a context-dependent movement strategy in which each agent switches between undirected and directed movement based on its perception of resources. This switching behavior is central to our goal of exploring how environmental and species-specific factors determine the evolution and maintenance of perception in an ecological system. We observed a non-linear response in the evolved perceptual ranges as a function of parameters in our model. Overall, we identified two groups of parameters, one of which promotes evolution of perception and another group that restricts it. We found that resource density, basal energy cost, perceptual cost and mutation rate were the best predictors of the resultant perceptual range distribution, but detailed exploration indicated that individual parameters affect different parts of the distribution in different ways.

No evidence for abnormal priors in early vision in schizophrenia

The predictive coding account of psychosis postulates the abnormal formation of prior beliefs in schizophrenia, resulting in psychotic symptoms. One domain in which priors play a crucial role is visual perception. For instance, our perception of brightness, line length, and motion direction are not merely based on a veridical extraction of sensory input but are also determined by expectation (or prior) of the stimulus. Formation of such priors is thought to be governed by the statistical regularities within natural scenes. Recently, the use of such priors has been attributed to a specific set of well-documented visual illusions, supporting the idea that perception is biased toward what is statistically more probable within the environment. The Predictive Coding account of psychosis proposes that patients form abnormal representations of statistical regularities in natural scenes, leading to altered perceptual experiences. Here we use classical vision experiments involving a specific set of visual illusions to directly test this hypothesis. We find that perceptual judgments for both patients and control participants are biased in accordance with reported probability distributions of natural scenes. Thus, despite there being a suggested link between visual abnormalities and psychotic symptoms in schizophrenia, our results provide no support for the notion that altered formation of priors is a general feature of the disorder. These data call for a refinement in the predictions of quantitative models of psychosis.

Neural Mechanisms of High-Level Vision

The last three decades have seen major strides in our understanding of neural mechanisms of high-level vision, or visual cognition of the world around us. Vision has also served as a model system for the study of brain function. Several broad insights, as yet incomplete, have recently emerged. First, visual perception is best understood not as an end unto itself, but as a sensory process that subserves the animal's behavioral goal at hand. Visual perception is likely to be simply a side effect that reflects the readout of visual information processing that leads to behavior. Second, the brain is essentially a probabilistic computational system that produces behaviors by collectively evaluating, not necessarily consciously or always optimally, the available information about the outside world received from the senses, the behavioral goals, prior knowledge about the world, and possible risks and benefits of a given behavior. Vision plays a prominent role in the overall functioning of the brain providing the lion's share of information about the outside world. Third, the visual system does not function in isolation, but rather interacts actively and reciprocally with other brain systems, including other sensory faculties. Finally, various regions of the visual system process information not in a strict hierarchical manner, but as parts of various dynamic brain-wide networks, collectively referred to as the "connectome." Thus, a full understanding of vision will ultimately entail understanding, in granular, quantitative detail, various aspects of dynamic brain networks that use visual sensory information to produce behavior under real-world conditions. © 2017 American Physiological Society. Compr Physiol 8:903-953, 2018.

Rationality, perception, and the all-seeing eye

Seeing-perception and vision-is implicitly the fundamental building block of the literature on rationality and cognition. Herbert Simon and Daniel Kahneman's arguments against the omniscience of economic agents-and the concept of bounded rationality-depend critically on a particular view of the nature of perception and vision. We propose that this framework of rationality merely replaces economic omniscience with perceptual omniscience. We show how the cognitive and social sciences feature a pervasive but problematic meta-assumption that is characterized by an "all-seeing eye." We raise concerns about this assumption and discuss different ways in which the all-seeing eye manifests itself in existing research on (bounded) rationality. We first consider the centrality of vision and perception in Simon's pioneering work. We then point to Kahneman's work-particularly his article "Maps of Bounded Rationality"-to illustrate the pervasiveness of an all-seeing view of perception, as manifested in the extensive use of visual examples and illusions. Similar assumptions about perception can be found across a large literature in the cognitive sciences. The central problem is the present emphasis on inverse optics-the objective nature of objects and environments, e.g., size, contrast, and color. This framework ignores the nature of the organism and perceiver. We argue instead that reality is constructed and expressed, and we discuss the species-specificity of perception, as well as perception as a user interface. We draw on vision science as well as the arts to develop an alternative understanding of rationality in the cognitive and social sciences. We conclude with a discussion of the implications of our arguments for the rationality and decision-making literature in cognitive psychology and behavioral economics, along with suggesting some ways forward.

Post-decision biases reveal a self-consistency principle in perceptual inference

Making a categorical judgment can systematically bias our subsequent perception of the world. We show that these biases are well explained by a self-consistent Bayesian observer whose perceptual inference process is causally conditioned on the preceding choice. We quantitatively validated the model and its key assumptions with a targeted set of three psychophysical experiments, focusing on a task sequence where subjects first had to make a categorical orientation judgment before estimating the actual orientation of a visual stimulus. Subjects exhibited a high degree of consistency between categorical judgment and estimate, which is difficult to reconcile with alternative models in the face of late, memory related noise. The observed bias patterns resemble the well-known changes in subjective preferences associated with cognitive dissonance, which suggests that the brain's inference processes may be governed by a universal self-consistency constraint that avoids entertaining 'dissonant' interpretations of the evidence.

Determinants of neural responses to disparity in natural scenes

We studied disparity-evoked responses in natural scenes using high-density electroencephalography (EEG) in an event-related design. Thirty natural scenes that mainly included outdoor settings with trees and buildings were used. Twenty-four subjects viewed a series of trials composed of sequential two-alternative temporal forced-choice presentation of two different versions (two-dimensional [2D] vs. three-dimensional [3D]) of the same scene interleaved by a scrambled image with the same power spectrum. Scenes were viewed orthostereoscopically at 3 m through a pair of shutter glasses. After each trial, participants indicated with a key press which version of the scene was 3D. Performance on the discrimination was >90%. Participants who were more accurate also tended to respond faster; scenes that were reported more accurately as 3D also led to faster reaction times. We compared visual evoked potentials elicited by scrambled, 2D, and 3D scenes using reliable component analysis to reduce dimensionality. The disparity-evoked response to natural scene stimuli, measured from the difference potential between 2D and 3D scenes, comprised a sustained relative negativity in the dominant response component. The magnitude of the disparity-specific response was correlated with the observer's stereoacuity. Scenes with more homogeneous depth maps also tended to elicit large disparity-specific responses. Finally, the magnitude of the disparity-specific response was correlated with the magnitude of the differential response between scrambled and 2D scenes, suggesting that monocular higher-order scene statistics modulate disparity-specific responses.

dipIQ: Blind Image Quality Assessment by Learning-to-Rank Discriminable Image Pairs

Objective assessment of image quality is fundamentally important in many image processing tasks. In this paper, we focus on learning blind image quality assessment (BIQA) models, which predict the quality of a digital image with no access to its original pristine-quality counterpart as reference. One of the biggest challenges in learning BIQA models is the conflict between the gigantic image space (which is in the dimension of the number of image pixels) and the extremely limited reliable ground truth data for training. Such data are typically collected via subjective testing, which is cumbersome, slow, and expensive. Here, we first show that a vast amount of reliable training data in the form of quality-discriminable image pairs (DIPs) can be obtained automatically at low cost by exploiting large-scale databases with diverse image content. We then learn an opinion-unaware BIQA (OU-BIQA, meaning that no subjective opinions are used for training) model using RankNet, a pairwise learning-to-rank (L2R) algorithm, from millions of DIPs, each associated with a perceptual uncertainty level, leading to a DIP inferred quality (dipIQ) index. Extensive experiments on four benchmark IQA databases demonstrate that dipIQ outperforms the state-of-the-art OU-BIQA models. The robustness of dipIQ is also significantly improved as confirmed by the group MAximum Differentiation competition method. Furthermore, we extend the proposed framework by learning models with ListNet (a listwise L2R algorithm) on quality-discriminable image lists (DIL). The resulting DIL inferred quality index achieves an additional performance gain.

What Do Evolutionary Models Teach Us About Sensitive Periods in Psychological Development?

Abstract. Sensitive periods in development are widespread in nature. Many psychologists and biologists regard sensitive periods as byproducts of developmental processes. Although this view may be correct in some cases, it is unlikely to be the whole story. There is large variation in sensitive periods (a) between species in the same trait ( Beecher & Brenowitz, 2005 ), (b) between individuals of the same species ( Frankenhuis, Panchanathan, & Belsky, 2016 ), and (c) between different traits within a single individual ( Zeanah, Gunnar, McCall, Kreppner, & Fox, 2011 ). In this article, we discuss recent insights provided by formal models of the evolution of sensitive periods. These models help to identify the conditions in which sensitive periods are likely to evolve, and make predictions about the factors that affect their development. We conclude by discussing future directions for empirical research.

Why do animals differ in their susceptibility to geometrical illusions?

In humans, geometrical illusions are thought to reflect mechanisms that are usually helpful for seeing the world in a predictable manner. These mechanisms deceive us given the right set of circumstances, correcting visual input where a correction is not necessary. Investigations of non-human animals' susceptibility to geometrical illusions have yielded contradictory results, suggesting that the underlying mechanisms with which animals see the world may differ across species. In this review, we first collate studies showing that different species are susceptible to specific illusions in the same or reverse direction as humans. Based on a careful assessment of these findings, we then propose several ecological and anatomical factors that may affect how a species perceives illusory stimuli. We also consider the usefulness of this information for determining whether sight in different species might be more similar to human sight, being influenced by contextual information, or to how machines process and transmit information as programmed. Future testing in animals could provide new theoretical insights by focusing on establishing dissociations between stimuli that may or may not alter perception in a particular species. This information could improve our understanding of the mechanisms behind illusions, but also provide insight into how sight is subjectively experienced by different animals, and the degree to which vision is innate versus acquired, which is difficult to examine in humans.

Allostatic Self-efficacy: A Metacognitive Theory of Dyshomeostasis-Induced Fatigue and Depression

This paper outlines a hierarchical Bayesian framework for interoception, homeostatic/allostatic control, and meta-cognition that connects fatigue and depression to the experience of chronic dyshomeostasis. Specifically, viewing interoception as the inversion of a generative model of viscerosensory inputs allows for a formal definition of dyshomeostasis (as chronically enhanced surprise about bodily signals, or, equivalently, low evidence for the brain's model of bodily states) and allostasis (as a change in prior beliefs or predictions which define setpoints for homeostatic reflex arcs). Critically, we propose that the performance of interoceptive-allostatic circuitry is monitored by a metacognitive layer that updates beliefs about the brain's capacity to successfully regulate bodily states (allostatic self-efficacy). In this framework, fatigue and depression can be understood as sequential responses to the interoceptive experience of dyshomeostasis and the ensuing metacognitive diagnosis of low allostatic self-efficacy. While fatigue might represent an early response with adaptive value (cf. sickness behavior), the experience of chronic dyshomeostasis may trigger a generalized belief of low self-efficacy and lack of control (cf. learned helplessness), resulting in depression. This perspective implies alternative pathophysiological mechanisms that are reflected by differential abnormalities in the effective connectivity of circuits for interoception and allostasis. We discuss suitably extended models of effective connectivity that could distinguish these connectivity patterns in individual patients and may help inform differential diagnosis of fatigue and depression in the future.

What Are the "True" Statistics of the Environment?

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world-the actual "statistics of the environment." But in fact the idea of a "true" prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that "ground truth" probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be "tuned" to its environment.

The Interface Theory of Perception

Perception is a product of evolution. Our perceptual systems, like our limbs and livers, have been shaped by natural selection. The effects of selection on perception can be studied using evolutionary games and genetic algorithms. To this end, we define and classify perceptual strategies and allow them to compete in evolutionary games in a variety of worlds with a variety of fitness functions. We find that veridical perceptions--strategies tuned to the true structure of the world--are routinely dominated by nonveridical strategies tuned to fitness. Veridical perceptions escape extinction only if fitness varies monotonically with truth. Thus, a perceptual strategy favored by selection is best thought of not as a window on truth but as akin to a windows interface of a PC. Just as the color and shape of an icon for a text file do not entail that the text file itself has a color or shape, so also our perceptions of space-time and objects do not entail (by the Invention of Space-Time Theorem) that objective reality has the structure of space-time and objects. An interface serves to guide useful actions, not to resemble truth. Indeed, an interface hides the truth; for someone editing a paper or photo, seeing transistors and firmware is an irrelevant hindrance. For the perceptions of H. sapiens, space-time is the desktop and physical objects are the icons. Our perceptions of space-time and objects have been shaped by natural selection to hide the truth and guide adaptive behaviors. Perception is an adaptive interface.

Perception and Reality: Why a Wholly Empirical Paradigm is Needed to Understand Vision

A central puzzle in vision science is how perceptions that are routinely at odds with physical measurements of real world properties can arise from neural responses that nonetheless lead to effective behaviors. Here we argue that the solution depends on: (1) rejecting the assumption that the goal of vision is to recover, however imperfectly, properties of the world; and (2) replacing it with a paradigm in which perceptions reflect biological utility based on past experience rather than objective features of the environment. Present evidence is consistent with the conclusion that conceiving vision in wholly empirical terms provides a plausible way to understand what we see and why.

Objects of consciousness

Current models of visual perception typically assume that human vision estimates true properties of physical objects, properties that exist even if unperceived. However, recent studies of perceptual evolution, using evolutionary games and genetic algorithms, reveal that natural selection often drives true perceptions to extinction when they compete with perceptions tuned to fitness rather than truth: Perception guides adaptive behavior; it does not estimate a preexisting physical truth. Moreover, shifting from evolutionary biology to quantum physics, there is reason to disbelieve in preexisting physical truths: Certain interpretations of quantum theory deny that dynamical properties of physical objects have definite values when unobserved. In some of these interpretations the observer is fundamental, and wave functions are compendia of subjective probabilities, not preexisting elements of physical reality. These two considerations, from evolutionary biology and quantum physics, suggest that current models of object perception require fundamental reformulation. Here we begin such a reformulation, starting with a formal model of consciousness that we call a "conscious agent." We develop the dynamics of interacting conscious agents, and study how the perception of objects and space-time can emerge from such dynamics. We show that one particular object, the quantum free particle, has a wave function that is identical in form to the harmonic functions that characterize the asymptotic dynamics of conscious agents; particles are vibrations not of strings but of interacting conscious agents. This allows us to reinterpret physical properties such as position, momentum, and energy as properties of interacting conscious agents, rather than as preexisting physical truths. We sketch how this approach might extend to the perception of relativistic quantum objects, and to classical objects of macroscopic scale.

Long-term temporal tracking of speech rate affects spoken-word recognition

Humans unconsciously track a wide array of distributional characteristics in their sensory environment. Recent research in spoken-language processing has demonstrated that the speech rate surrounding a target region within an utterance influences which words, and how many words, listeners hear later in that utterance. On the basis of hypotheses that listeners track timing information in speech over long timescales, we investigated the possibility that the perception of words is sensitive to speech rate over such a timescale (e.g., an extended conversation). Results demonstrated that listeners tracked variation in the overall pace of speech over an extended duration (analogous to that of a conversation that listeners might have outside the lab) and that this global speech rate influenced which words listeners reported hearing. The effects of speech rate became stronger over time. Our findings are consistent with the hypothesis that neural entrainment by speech occurs on multiple timescales, some lasting more than an hour.

A spiking neural network model of self-organized pattern recognition in the early mammalian olfactory system

Olfactory sensory information passes through several processing stages before an odor percept emerges. The question how the olfactory system learns to create odor representations linking those different levels and how it learns to connect and discriminate between them is largely unresolved. We present a large-scale network model with single and multi-compartmental Hodgkin-Huxley type model neurons representing olfactory receptor neurons (ORNs) in the epithelium, periglomerular cells, mitral/tufted cells and granule cells in the olfactory bulb (OB), and three types of cortical cells in the piriform cortex (PC). Odor patterns are calculated based on affinities between ORNs and odor stimuli derived from physico-chemical descriptors of behaviorally relevant real-world odorants. The properties of ORNs were tuned to show saturated response curves with increasing concentration as seen in experiments. On the level of the OB we explored the possibility of using a fuzzy concentration interval code, which was implemented through dendro-dendritic inhibition leading to winner-take-all like dynamics between mitral/tufted cells belonging to the same glomerulus. The connectivity from mitral/tufted cells to PC neurons was self-organized from a mutual information measure and by using a competitive Hebbian-Bayesian learning algorithm based on the response patterns of mitral/tufted cells to different odors yielding a distributed feed-forward projection to the PC. The PC was implemented as a modular attractor network with a recurrent connectivity that was likewise organized through Hebbian-Bayesian learning. We demonstrate the functionality of the model in a one-sniff-learning and recognition task on a set of 50 odorants. Furthermore, we study its robustness against noise on the receptor level and its ability to perform concentration invariant odor recognition. Moreover, we investigate the pattern completion capabilities of the system and rivalry dynamics for odor mixtures.

Model observers in medical imaging research

Model observers play an important role in the optimization and assessment of imaging devices. In this review paper, we first discuss the basic concepts of model observers, which include the mathematical foundations and psychophysical considerations in designing both optimal observers for optimizing imaging systems and anthropomorphic observers for modeling human observers. Second, we survey a few state-of-the-art computational techniques for estimating model observers and the principles of implementing these techniques. Finally, we review a few applications of model observers in medical imaging research.

Tuning your priors to the world

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of "tuning the prior"-widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of "ecological" tuning has often been held up as an ideal of inference, in fact defining an "ideal observer." But widespread as this viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment-which there almost always is-an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors.

Computational evolutionary perception

Marr proposed that human vision constructs "a true description of what is there". He argued that to understand human vision one must discover the features of the world it recovers and the constraints it uses in the process. Bayesian decision theory (BDT) is used in modem vision research as a probabilistic framework for understanding human vision along the lines laid out by Marr. Marr's contribution to vision research is substantial and justly influential. We propose, however, that evolution by natural selection does not, in general, favor perceptions that are true descriptions of the objective world. Instead, research with evolutionary games shows that perceptual systems tuned solely to fitness routinely outcompete those tuned to truth. Fitness functions depend not just on the true state of the world, but also on the organism, its state, and the type of action. Thus, fitness and truth are distinct. Natural selection depends only on expected fitness. It shapes perceptual systems to guide fitter behavior, not to estimate truth. To study perception in an evolutionary context, we introduce the framework of Computational Evolutionary Perception (CEP). We show that CEP subsumes BDT, and reinterprets BDT as evaluating expected fitness rather than estimating truth.

Marr: an appreciation

The following is based largely on sections of our two recent books: Frisby and Stone (2010, Seeing MIT Press), and Stone (2012, Vision and Brain MIT Press). Those books are aimed at student/ novice audiences, and so we have eliminated material of a wholly introductory nature for this special issue of Perception. However, various debates we have had at vision conferences recently suggest to us that going over basic material on Marr could be useful to many current vision researchers who have had little contact with his work, so we have left in some content of that kind.

Bayesian learning and the psychology of rule induction

In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to spell out the underlying assumptions, and to confront them with the empirical results Frank and Tenenbaum (2011) propose to simulate, as well as with novel experiments. While rule-learning is arguably well suited to rational Bayesian approaches, I show that their models are neither psychologically plausible nor ideal observer models. Further, I show that their central assumption is unfounded: humans do not always preferentially learn more specific rules, but, at least in some situations, those rules that happen to be more salient. Even when granting the unsupported assumptions, I show that all of the experiments modeled by Frank and Tenenbaum (2011) either contradict their models, or have a large number of more plausible interpretations. I provide an alternative account of the experimental data based on simple psychological mechanisms, and show that this account both describes the data better, and is easier to falsify. I conclude that, despite the recent surge in Bayesian models of cognitive phenomena, psychological phenomena are best understood by developing and testing psychological theories rather than models that can be fit to virtually any data.

Map formation in the olfactory bulb by axon guidance of olfactory neurons

The organization of representations in the brain has been observed to locally reflect subspaces of inputs that are relevant to behavioral or perceptual feature combinations, such as in areas receptive to lower and higher-order features in the visual system. The early olfactory system developed highly plastic mechanisms and convergent evidence indicates that projections from primary neurons converge onto the glomerular level of the olfactory bulb (OB) to form a code composed of continuous spatial zones that are differentially active for particular physico-chemical feature combinations, some of which are known to trigger behavioral responses. In a model study of the early human olfactory system, we derive a glomerular organization based on a set of real-world, biologically relevant stimuli, a distribution of receptors that respond each to a set of odorants of similar ranges of molecular properties, and a mechanism of axon guidance based on activity. Apart from demonstrating activity-dependent glomeruli formation and reproducing the relationship of glomerular recruitment with concentration, it is shown that glomerular responses reflect similarities of human odor category perceptions and that further, a spatial code provides a better correlation than a distributed population code. These results are consistent with evidence of functional compartmentalization in the OB and could suggest a function for the bulb in encoding of perceptual dimensions.

Superordinate shape classification using natural shape statistics

This paper investigates the classification of shapes into broad natural categories such as animal or leaf. We asked whether such coarse classifications can be achieved by a simple statistical classification of the shape skeleton. We surveyed databases of natural shapes, extracting shape skeletons and tabulating their parameters within each class, seeking shape statistics that effectively discriminated the classes. We conducted two experiments in which human subjects were asked to classify novel shapes into the same natural classes. We compared subjects' classifications to those of a naive Bayesian classifier based on the natural shape statistics, and found good agreement. We conclude that human superordinate shape classifications can be well understood as involving a simple statistical classification of the shape skeleton that has been "tuned" to the natural statistics of shape.

A bayesian foundation for individual learning under uncertainty

Computational learning models are critical for understanding mechanisms of adaptive behavior. However, the two major current frameworks, reinforcement learning (RL) and Bayesian learning, both have certain limitations. For example, many Bayesian models are agnostic of inter-individual variability and involve complicated integrals, making online learning difficult. Here, we introduce a generic hierarchical Bayesian framework for individual learning under multiple forms of uncertainty (e.g., environmental volatility and perceptual uncertainty). The model assumes Gaussian random walks of states at all but the first level, with the step size determined by the next highest level. The coupling between levels is controlled by parameters that shape the influence of uncertainty on learning in a subject-specific fashion. Using variational Bayes under a mean-field approximation and a novel approximation to the posterior energy function, we derive trial-by-trial update equations which (i) are analytical and extremely efficient, enabling real-time learning, (ii) have a natural interpretation in terms of RL, and (iii) contain parameters representing processes which play a key role in current theories of learning, e.g., precision-weighting of prediction error. These parameters allow for the expression of individual differences in learning and may relate to specific neuromodulatory mechanisms in the brain. Our model is very general: it can deal with both discrete and continuous states and equally accounts for deterministic and probabilistic relations between environmental events and perceptual states (i.e., situations with and without perceptual uncertainty). These properties are illustrated by simulations and analyses of empirical time series. Overall, our framework provides a novel foundation for understanding normal and pathological learning that contextualizes RL within a generic Bayesian scheme and thus connects it to principles of optimality from probability theory.

Absence of cue-recruitment for extrinsic signals: sounds, spots, and swirling dots fail to influence perceived 3D rotation direction after training

The visual system can learn to use information in new ways to construct appearance. Thus, signals such as the location or translation direction of an ambiguously rotating wire frame cube, which are normally uninformative, can be learned as cues to determine the rotation direction [1]. This perceptual learning occurs when the formerly uninformative signal is statistically associated with long-trusted visual cues (such as binocular disparity) that disambiguate appearance during training. In previous demonstrations, the newly learned cue was intrinsic to the perceived object, in that the signal was conveyed by the same image elements as the object itself. Here we used extrinsic new signals and observed no learning. We correlated three new signals with long-trusted cues in the rotating cube paradigm: one crossmodal (an auditory signal) and two within modality (visual). Cue recruitment did not occur in any of these conditions, either in single sessions or in ten sessions across as many days. These results suggest that the intrinsic/extrinsic distinction is important for the perceptual system in determining whether it can learn and use new information from the environment to construct appearance. Extrinsic cues do have perceptual effects (e.g. the “bounce-pass” illusion [2] and McGurk effect [3]), so we speculate that extrinsic signals must be recruited for perception, but only if certain conditions are met. These conditions might specify the age of the observer, the strength of the long-trusted cues, or the amount of exposure to the correlation.

Statistically optimal perception and learning: from behavior to neural representations

Human perception has recently been characterized as statistical inference based on noisy and ambiguous sensory inputs. Moreover, suitable neural representations of uncertainty have been identified that could underlie such probabilistic computations. In this review, we argue that learning an internal model of the sensory environment is another key aspect of the same statistical inference procedure and thus perception and learning need to be treated jointly. We review evidence for statistically optimal learning in humans and animals, and re-evaluate possible neural representations of uncertainty based on their potential to support statistically optimal learning. We propose that spontaneous activity can have a functional role in such representations leading to a new, sampling-based, framework of how the cortex represents information and uncertainty.

Comparative Vision Science: Seeing Eye to Eye?

In the study of comparative cognition and perception, disparities in the diverse approaches that researchers take in studying behavior sometimes obscure the interpretation of a particular empirical finding. We describe an approach to the study of comparative cognition and perception which focuses on explaining the ways in which different biological systems solve the computational challenges that are posed by their natural environments. Within this investigative framework, the task of detecting correspondence between a three-dimensional object and its two-dimensional photographic representation falls outside the mainstream of most research in animal visual cognition and is of limited value for divulging the principles or mechanisms that underlie the visual abilities of animals. More productive pursuits seek to elucidate the principles and mechanisms of object recognition and categorization, and to illuminate how they contribute to the animal's survival in the visual world.

Effects of prior information and reward on oculomotor and perceptual choices

Expectations about the environment influence motor behavior. In simple tasks, for example, prior knowledge about which stimulus event will likely occur or which response will likely be rewarded induces a tendency to take the favored action (i.e., a motor or response bias), especially when sensory information is sparse or ambiguous. Models of choice behavior account for this bias by weighting decision alternatives unequally, either at an early sensory-input stage or at a downstream motor-output stage. These two alternatives can be distinguished empirically; the former predicts an altered percept that correlates with motor bias, the latter predicts no perceptual effect. By varying the prior probability of target or reward location, we induced biased oculomotor responses in a brightness selection task with human subjects. We found that the induced motor bias was correlated with an amplification of both the sensory signals and internal noise underlying brightness perception, without a systematic change in perceived overall brightness. We also found that the magnitude of the sensory amplification was correlated with the amount of noise in the brightness percept, consistent with a multiplicative weighting factor located downstream from the limiting internal sensory noise. Our data demonstrate that prior knowledge (about target location or reward) shapes visual signals for perception and action in parallel but does not improve the quality (i.e., signal-to-noise ratio) of sensory processing.

Predator perception and the interrelation between different forms of protective coloration

Animals possess a range of defensive markings to reduce the risk of predation, including warning colours, camouflage, eyespots and mimicry. These different strategies are frequently considered independently, and with little regard towards predator vision, even though they may be linked in various ways and can be fully understood only in terms of predator perception. For example, camouflage and warning coloration need not be mutually exclusive, and may frequently exploit similar features of visual perception. This paper outlines how different forms of protective markings can be understood from predator perception and illustrates how this is fundamental in determining the mechanisms underlying, and the interrelation between, different strategies. Suggestions are made for future work, and potential mechanisms discussed in relation to various forms of defensive coloration, including disruptive coloration, eyespots, dazzle markings, motion camouflage, aposematism and mimicry.

The radiology task: Bayesian theory and perception

The use of a Bayesian framework to understand how radiologists search images for pathology is important as it formalizes, mathematically, how visual and cognitive processes control eye movements by modelling the ideal searcher against which human performance can be compared. It is important that the interpretation of medical images is understood so that new developments in the ways images are presented and the use of image processing software are matched to human abilities and limitations.

Naturalistic color discriminations in polymorphic platyrrhine monkeys: Effects of stimulus luminance and duration examined with functional substitution

X-linked photopigment polymorphism produces six different color vision phenotypes in most species of New World monkey. In the subfamily Callitrichinae, the three M/L alleles underlying these different phenotypes are present at unequal frequencies suggesting that selective pressures other than heterozygous-advantage operate on these alleles. Earlier we investigated this hypothesis with functional substitution, a technique using a computer monitor to simulate colors as they would appear to humans with monkey visual pigments (Visual Neuroscience21:217–222, 2004). The stimuli were derived from measurements of ecologically relevant fruit and foliage. We found that discrimination performance depended on the relative spectral positioning of the substituted M and L pigment pair. Here we have undertaken a systematic examination of two simulation parameters—test field luminance and stimulus duration. Discriminability of the fruit colors depended on which phenotype was simulated but only at short stimulus durations and/or low luminances. Under such conditions, phenotypes with the larger pigment peak separations performed better. At longer durations and higher luminances, differences in performance across different substitutions tended to disappear. The stimuli used in this experiment were analyzed with several color discrimination models. There was limited agreement among the predictions made by these models regarding the capabilities of animals with different pigment pairs and none predicted the dependence of discrimination on changes in luminance and stimulus duration.

Speech categorization in context: joint effects of nonspeech and speech precursors

The extent to which context influences speech categorization can inform theories of pre-lexical speech perception. Across three conditions, listeners categorized speech targets preceded by speech context syllables. These syllables were presented as the sole context or paired with nonspeech tone contexts previously shown to affect speech categorization. Listeners' context-dependent categorization across these conditions provides evidence that speech and nonspeech context stimuli jointly influence speech processing. Specifically, when the spectral characteristics of speech and nonspeech context stimuli are mismatched such that they are expected to produce opposing effects on speech categorization the influence of nonspeech contexts may undermine, or even reverse, the expected effect of adjacent speech context. Likewise, when spectrally matched, the cross-class contexts may collaborate to increase effects of context. Similar effects are observed even when natural speech syllables, matched in source to the speech categorization targets, serve as the speech contexts. Results are well-predicted by spectral characteristics of the context stimuli.

Demonstration of cue recruitment: change in visual appearance by means of Pavlovian conditioning

Until half a century ago, associative learning played a fundamental role in theories of perceptual appearance [Berkeley, G. (1709) An Essay Towards a New Theory of Vision (Dublin), 1st Ed.]. But starting in 1955 [Gibson, J. J. & Gibson, E. J. (1955) Psychol. Rev. 62, 32-41], most studies of perceptual learning have not been concerned with association or appearance but rather with improvements in discrimination ability. Here we describe a "cue recruitment" experiment, which is a straightforward adaptation of Pavlov's classical conditioning experiment, that we used to measure changes in visual appearance caused by exposure to novel pairings of signals in visual stimuli. Trainees viewed movies of a rotating wire-frame (Necker) cube. This stimulus is perceptually bistable. On training trials, depth cues (stereo and occlusion) were added to force the perceived direction of rotation. Critically, an additional signal was also added, contingent on rotation direction. Stimuli on test trials contained the new signal but not the depth cues. Over 45 min, two of the three new signals that we tested acquired the ability to bias perceived rotation direction on their own. Results were consistent across the eight trainees in each experiment, and the new cue's effectiveness was long lasting. Whereas most adaptation aftereffects on appearance are opposite in direction to the training stimuli, these effects were positive. An individual new signal can be recruited by the visual system as a cue for the construction of visual appearance. Cue recruitment experiments may prove useful for reexamining of the role of experience in perception.

Local luminance and contrast in natural images

Within natural images there is substantial spatial variation in both local contrast and local luminance. Understanding the statistics of these variations is important for understanding the dynamics of receptive field stimulation that occur under natural viewing conditions and for understanding the requirements for effective luminance and contrast gain control. Local luminance and contrast were measured in a large set of calibrated 12-bit gray-scale natural images, for a number of analysis patch sizes. For each image and patch size we measured the range of contrast, the range of luminance, the correlation in contrast and luminance as a function of the distance between patches, and the correlation between contrast and luminance within patches. The same analyses were also performed on hand segmented regions containing only "sky", "ground", "foliage", or "backlit foliage". Within the typical image, the 95% range (2.5-97.5 percentile) for both local luminance and local contrast is somewhat greater than a factor of 10. The correlation in contrast and the correlation in luminance diminish rapidly with distance, and the typical correlation between luminance and contrast within patches is small (e.g., -0.2 compared to -0.8 for 1/f noise). We show that eye movements are frequently large enough that there will be little correlation in the contrast or luminance on a receptive field from one fixation to the next, and thus rapid contrast and luminance gain control are essential. The low correlation between local luminance and contrast implies that efficient contrast gain control mechanisms can operate largely independently of luminance gain control mechanisms.

Contrast statistics for foveated visual systems: fixation selection by minimizing contrast entropy

The human visual system combines a wide field of view with a high-resolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy to be effective, the visual system needs sophisticated central mechanisms that efficiently exploit the varying spatial resolution of the retina. To gain insight into some of the design requirements of these central mechanisms, we have analyzed the effects of variable spatial resolution on local contrast in 300 calibrated natural images. Specifically, for each retinal eccentricity (which produces a certain effective level of blur), and for each value of local contrast observed at that eccentricity, we measured the probability distribution of the local contrast in the unblurred image. These conditional probability distributions can be regarded as posterior probability distributions for the "true" unblurred contrast, given an observed contrast at a given eccentricity. We find that these conditional probability distributions are adequately described by a few simple formulas. To explore how these statistics might be exploited by central perceptual mechanisms, we consider the task of selecting successive fixation points, where the goal on each fixation is to maximize total contrast information gained about the image (i.e., minimize total contrast uncertainty). We derive an entropy minimization algorithm and find that it performs optimally at reducing total contrast uncertainty and that it also works well at reducing the mean squared error between the original image and the image reconstructed from the multiple fixations. Our results show that measurements of local contrast alone could efficiently drive the scan paths of the eye when the goal is to gain as much information about the spatial structure of a scene as possible.

Encoding Multielement Scenes: Statistical Learning of Visual Feature Hierarchies

The authors investigated how human adults encode and remember parts of multielement scenes composed of recursively embedded visual shape combinations. The authors found that shape combinations that are parts of larger configurations are less well remembered than shape combinations of the same kind that are not embedded. Combined with basic mechanisms of statistical learning, this embeddedness constraint enables the development of complex new features for acquiring internal representations efficiently without being computationally intractable. The resulting representations also encode parts and wholes by chunking the visual input into components according to the statistical coherence of their constituents. These results suggest that a bootstrapping approach of constrained statistical learning offers a unified framework for investigating the formation of different internal representations in pattern and scene perception.

Integration of form and motion within a generative model of visual cortex

One of the challenges faced by the visual system is integrating cues within and across processing streams for inferring scene properties and structure. This is particularly apparent in the inference of object motion, where psychophysical experiments have shown that integration of motion signals, distributed across space, must also be integrated with form cues. This has led several to conclude that there exist mechanisms which enable form cues to 'veto' or completely suppress ambiguous motion signals. We describe a probabilistic approach which uses a generative network model for integrating form and motion cues using the machinery of belief propagation and Bayesian inference. We show, using computer simulations, that motion integration can be mediated via a local, probabilistic representation of contour ownership, which we have previously termed 'direction of figure'. The uncertainty of this inferred form cue is used to modulate the covariance matrix of network nodes representing local motion estimates in the motion stream. We show with results for two sets of stimuli that the model does not completely suppress ambiguous cues, but instead integrates them in a way that is a function of their underlying uncertainty. The result is that the model can account for the continuum of bias seen for motion coherence and perceived object motion in psychophysical experiments.

Hierarchical Bayesian inference in the visual cortex

Traditional views of visual processing suggest that early visual neurons in areas V1 and V2 are static spatiotemporal filters that extract local features from a visual scene. The extracted information is then channeled through a feedforward chain of modules in successively higher visual areas for further analysis. Recent electrophysiological recordings from early visual neurons in awake behaving monkeys reveal that there are many levels of complexity in the information processing of the early visual cortex, as seen in the long-latency responses of its neurons. These new findings suggest that activity in the early visual cortex is tightly coupled and highly interactive with the rest of the visual system. They lead us to propose a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system. In this framework, the recurrent feedforward/feedback loops in the cortex serve to integrate top-down contextual priors and bottom-up observations so as to implement concurrent probabilistic inference along the visual hierarchy. We suggest that the algorithms of particle filtering and Bayesian-belief propagation might model these interactive cortical computations. We review some recent neurophysiological evidences that support the plausibility of these ideas.

Coding of the contrasts in natural images by visual cortex (V1) neurons: a Bayesian approach

Individual V1 neurons respond dynamically over only limited ranges of stimulus contrasts, yet we can discriminate contrasts over a wide range. Different V1 neurons cover different parts of the contrast range, and the information they provide must be pooled somehow. We describe a probabilistic pooling model that shows that populations of neurons with contrast responses like those in cat and monkey V1 would most accurately code contrasts in the range actually found in natural scenes. The pooling equation is similar to Bayes's equation; however, explicit inclusion of prior probabilities in the inference increases coding accuracy only slightly.