Not noisy, just wrong: the role of suboptimal inference in behavioral variability

Metrics of two-dimensional smooth pursuit are diverse across participants and stable across days

Smooth pursuit eye movements are used to volitionally track moving objects, keeping their image near the fovea. Pursuit gain, the ratio of eye to stimulus speed, is used to quantify tracking accuracy and is usually close to 1 for healthy observers. Although previous studies have shown directional asymmetries such as horizontal gain exceeding vertical gain, the temporal stability of these biases and the correlation between oculomotor metrics for tracking in different directions and speeds have not been investigated. Here, in testing sessions 4 to 10 days apart, 45 human observers tracked targets moving along two-dimensional trajectories. Horizontal, vertical, and radial pursuit gain had high test-retest reliability (mean intraclass correlation 0.84). The frequency of all saccades and anticipatory saccades during pursuit also had high test-retest reliability (intraclass correlation coefficients = 0.66 and 0.73, respectively). In addition, gain metrics showed strong intermetric correlation, and saccade metrics separately showed strong intercorrelation; however, gain and saccade metrics showed only weak intercorrelation. These correlations are likely to originate from a mixture of sensory, motor, and integrative mechanisms. The test-retest reliability of multiple distinct pursuit metrics represents a "pursuit identity" for individuals, but we argue against this ultimately contributing to an oculomotor biomarker.

Discretized representations in V1 predict suboptimal orientation discrimination

Neuronal population activity in sensory cortices is the substrate for perceptual decisions. Yet, we still do not understand how neuronal information content in sensory cortices relates to behavioral reports. To reconcile neurometric and psychometric performance, we recorded the activity of V1 neurons in mice performing a Go/NoGo orientation discrimination task. We found that, around the discrimination threshold, V1 does not represent the orientation of the stimuli as canonically expected. Instead, it forms categorical representations characterized by a relocation of activity at task-relevant domains of the orientation representational space. The relative neuronal activity at those discrete domains accurately predicted the probabilities of the animals' decisions. Our results thus suggest that the categorical integration of discretized feature representations from sensory cortices explains perceptual decisions.

The geometry of correlated variability leads to highly suboptimal discriminative sensory coding

The brain represents the world through the activity of neural populations; however, whether the computational goal of sensory coding is to support discrimination of sensory stimuli or to generate an internal model of the sensory world is unclear. Correlated variability across a neural population (noise correlations) is commonly observed experimentally, and many studies demonstrate that correlated variability improves discriminative sensory coding compared to a null model with no correlations. However, such results do not address whether correlated variability is optimal for discriminative sensory coding. If the computational goal of sensory coding is discriminative, than correlated variability should be optimized to support that goal. We assessed optimality of noise correlations for discriminative sensory coding in diverse datasets by developing two novel null models, each with a biological interpretation. Across datasets, we found that correlated variability in neural populations leads to highly suboptimal discriminative sensory coding according to both null models. Furthermore, biological constraints prevent many subsets of the neural populations from achieving optimality, and subselecting based on biological criteria leaves red discriminative coding performance suboptimal. Finally, we show that optimal subpopulations are exponentially small as the population size grows. Together, these results demonstrate that the geometry of correlated variability leads to highly suboptimal discriminative sensory coding.NEW & NOTEWORTHY The brain represents the world through the activity of neural populations that exhibit correlated variability. We assessed optimality of correlated variability for discriminative sensory coding in diverse datasets by developing two novel null models. Across datasets, correlated variability in neural populations leads to highly suboptimal discriminative sensory coding according to both null models. Biological constraints prevent the neural populations from achieving optimality. Together, these results demonstrate that the geometry of correlated variability leads to highly suboptimal discriminative sensory coding.

The representational instability in the generalization of fear learning

Perception and perceptual memory play crucial roles in fear generalization, yet their dynamic interaction remains understudied. This research (N = 80) explored their relationship through a classical differential conditioning experiment. Results revealed that while fear context perception fluctuates over time with a drift effect, perceptual memory remains stable, creating a disjunction between the two systems. Surprisingly, this disjunction does not significantly impact fear generalization behavior. Although most participants demonstrated generalization aligned with perceptual rather than physical stimulus distances, incorporating perceptual memory data into perceptual distance calculations did not enhance model performance. This suggests a potential shift in the mapping of the perceptual memory component of fear context, occurring alongside perceptual dynamics. Overall, this work provides evidence for understanding fear generalization behavior through different stimulus representational processes. Such mechanistic investigations can enhance our understanding of how individuals behave when facing threats and potentially aid in developing mechanism-specific diagnoses and treatments.

Using recurrent neural network to estimate irreducible stochasticity in human choice behavior

Theoretical computational models are widely used to describe latent cognitive processes. However, these models do not equally explain data across participants, with some individuals showing a bigger predictive gap than others. In the current study, we examined the use of theory-independent models, specifically recurrent neural networks (RNNs), to classify the source of a predictive gap in the observed data of a single individual. This approach aims to identify whether the low predictability of behavioral data is mainly due to noisy decision-making or misspecification of the theoretical model. First, we used computer simulation in the context of reinforcement learning to demonstrate that RNNs can be used to identify model misspecification in simulated agents with varying degrees of behavioral noise. Specifically, both prediction performance and the number of RNN training epochs (i.e., the point of early stopping) can be used to estimate the amount of stochasticity in the data. Second, we applied our approach to an empirical dataset where the actions of low IQ participants, compared with high IQ participants, showed lower predictability by a well-known theoretical model (i.e., Daw's hybrid model for the two-step task). Both the predictive gap and the point of early stopping of the RNN suggested that model misspecification is similar across individuals. This led us to a provisional conclusion that low IQ subjects are mostly noisier compared to their high IQ peers, rather than being more misspecified by the theoretical model. We discuss the implications and limitations of this approach, considering the growing literature in both theoretical and data-driven computational modeling in decision-making science.

The neural network RTNet exhibits the signatures of human perceptual decision-making

Convolutional neural networks show promise as models of biological vision. However, their decision behaviour, including the facts that they are deterministic and use equal numbers of computations for easy and difficult stimuli, differs markedly from human decision-making, thus limiting their applicability as models of human perceptual behaviour. Here we develop a new neural network, RTNet, that generates stochastic decisions and human-like response time (RT) distributions. We further performed comprehensive tests that showed RTNet reproduces all foundational features of human accuracy, RT and confidence and does so better than all current alternatives. To test RTNet's ability to predict human behaviour on novel images, we collected accuracy, RT and confidence data from 60 human participants performing a digit discrimination task. We found that the accuracy, RT and confidence produced by RTNet for individual novel images correlated with the same quantities produced by human participants. Critically, human participants who were more similar to the average human performance were also found to be closer to RTNet's predictions, suggesting that RTNet successfully captured average human behaviour. Overall, RTNet is a promising model of human RTs that exhibits the critical signatures of perceptual decision-making.

Fast decisions reflect biases; slow decisions do not

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased and hence make better choices. We obtain asymptotic expressions in the large population limit quantifying how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in nontrivial ways to determine the reliability of decisions in a group.

How does V1 population activity inform perceptual certainty?

Neural population activity in sensory cortex informs our perceptual interpretation of the environment. Oftentimes, this population activity will support multiple alternative interpretations. The larger the spread of probability over different alternatives, the more uncertain the selected perceptual interpretation. We test the hypothesis that the reliability of perceptual interpretations can be revealed through simple transformations of sensory population activity. We recorded V1 population activity in fixating macaques while presenting oriented stimuli under different levels of nuisance variability and signal strength. We developed a decoding procedure to infer from V1 activity the most likely stimulus orientation as well as the certainty of this estimate. Our analysis shows that response magnitude, response dispersion, and variability in response gain all offer useful proxies for orientation certainty. Of these three metrics, the last one has the strongest association with the decoder's uncertainty estimates. These results clarify that the nature of neural population activity in sensory cortex provides downstream circuits with multiple options to assess the reliability of perceptual interpretations.

Conditional independence as a statistical assessment of evidence integration processes

Intuitively, combining multiple sources of evidence should lead to more accurate decisions than considering single sources of evidence individually. In practice, however, the proper computation may be difficult, or may require additional data that are inaccessible. Here, based on the concept of conditional independence, we consider expressions that can serve either as recipes for integrating evidence based on limited data, or as statistical benchmarks for characterizing evidence integration processes. Consider three events, A, B, and C. We find that, if A and B are conditionally independent with respect to C, then the probability that C occurs given that both A and B are known, P(C|A, B), can be easily calculated without the need to measure the full three-way dependency between A, B, and C. This simplified approach can be used in two general ways: to generate predictions by combining multiple (conditionally independent) sources of evidence, or to test whether separate sources of evidence are functionally independent of each other. These applications are demonstrated with four computer-simulated examples, which include detecting a disease based on repeated diagnostic testing, inferring biological age based on multiple biomarkers of aging, discriminating two spatial locations based on multiple cue stimuli (multisensory integration), and examining how behavioral performance in a visual search task depends on selection histories. Besides providing a sound prescription for predicting outcomes, this methodology may be useful for analyzing experimental data of many types.

Chaotic neural dynamics facilitate probabilistic computations through sampling

Cortical neurons exhibit highly variable responses over trials and time. Theoretical works posit that this variability arises potentially from chaotic network dynamics of recurrently connected neurons. Here, we demonstrate that chaotic neural dynamics, formed through synaptic learning, allow networks to perform sensory cue integration in a sampling-based implementation. We show that the emergent chaotic dynamics provide neural substrates for generating samples not only of a static variable but also of a dynamical trajectory, where generic recurrent networks acquire these abilities with a biologically plausible learning rule through trial and error. Furthermore, the networks generalize their experience in the stimulus-evoked samples to the inference without partial or all sensory information, which suggests a computational role of spontaneous activity as a representation of the priors as well as a tractable biological computation for marginal distributions. These findings suggest that chaotic neural dynamics may serve for the brain function as a Bayesian generative model.

The role of framing, agency and uncertainty in a focus-divide dilemma

How to prioritise multiple objectives is a common dilemma of daily life. A simple and effective decision rule is to focus resources when the tasks are difficult, and divide when tasks are easy. Nonetheless, in experimental paradigms of this dilemma, participants make highly variable and suboptimal strategic decisions when asked to allocate resources to two competing goals that vary in difficulty. We developed a new version in which participants had to choose where to park a fire truck between houses of varying distances apart. Unlike in the previous versions of the dilemma, participants approached the optimal strategy in this task. Three key differences between the fire truck version and previous versions of the task were investigated: (1) Framing (whether the objectives are familiar or abstract), by comparing a group who placed cartoon trucks between houses to a group performing the same task with abstract shapes; (2) Agency (how much of the task is under the participants' direct control), by comparing groups who controlled the movement of the truck to those who did not; (3) Uncertainty, by adding variability to the driving speed of the truck to make success or failure on a given trial more difficult to predict. Framing and agency did not influence strategic decisions. When adding variability to outcomes, however, decisions shifted away from optimal. The results suggest choices become more variable when the outcome is less certain, consistent with exploration of response alternatives triggered by an inability to predict success.

Response sub-additivity and variability quenching in visual cortex

Sub-additivity and variability are ubiquitous response motifs in the primary visual cortex (V1). Response sub-additivity enables the construction of useful interpretations of the visual environment, whereas response variability indicates the factors that limit the precision with which the brain can do this. There is increasing evidence that experimental manipulations that elicit response sub-additivity often also quench response variability. Here, we provide an overview of these phenomena and suggest that they may have common origins. We discuss empirical findings and recent model-based insights into the functional operations, computational objectives and circuit mechanisms underlying V1 activity. These different modelling approaches all predict that response sub-additivity and variability quenching often co-occur. The phenomenology of these two response motifs, as well as many of the insights obtained about them in V1, generalize to other cortical areas. Thus, the connection between response sub-additivity and variability quenching may be a canonical motif across the cortex.

Rationality, preferences, and emotions with biological constraints: it all starts from our senses

Is the role of our sensory systems to represent the physical world as accurately as possible? If so, are our preferences and emotions, often deemed irrational, decoupled from these 'ground-truth' sensory experiences? We show why the answer to both questions is 'no'. Brain function is metabolically costly, and the brain loses some fraction of the information that it encodes and transmits. Therefore, if brains maximize objective functions that increase the fitness of their species, they should adapt to the objective-maximizing rules of the environment at the earliest stages of sensory processing. Consequently, observed 'irrationalities', preferences, and emotions stem from the necessity for our early sensory systems to adapt and process information while considering the metabolic costs and internal states of the organism.

Efficient Decoding of Large-Scale Neural Population Responses With Gaussian-Process Multiclass Regression

Neural decoding methods provide a powerful tool for quantifying the information content of neural population codes and the limits imposed by correlations in neural activity. However, standard decoding methods are prone to overfitting and scale poorly to high-dimensional settings. Here, we introduce a novel decoding method to overcome these limitations. Our approach, the gaussian process multiclass decoder (GPMD), is well suited to decoding a continuous low-dimensional variable from high-dimensional population activity and provides a platform for assessing the importance of correlations in neural population codes. The GPMD is a multinomial logistic regression model with a gaussian process prior over the decoding weights. The prior includes hyperparameters that govern the smoothness of each neuron's decoding weights, allowing automatic pruning of uninformative neurons during inference. We provide a variational inference method for fitting the GPMD to data, which scales to hundreds or thousands of neurons and performs well even in data sets with more neurons than trials. We apply the GPMD to recordings from primary visual cortex in three species: monkey, ferret, and mouse. Our decoder achieves state-of-the-art accuracy on all three data sets and substantially outperforms independent Bayesian decoding, showing that knowledge of the correlation structure is essential for optimal decoding in all three species.

The perception of auditory motion in sighted and early blind individuals

Motion perception is a fundamental sensory task that plays a critical evolutionary role. In vision, motion processing is classically described using a motion energy model with spatiotemporally nonseparable filters suited for capturing the smooth continuous changes in spatial position over time afforded by moving objects. However, it is still not clear whether the filters underlying auditory motion discrimination are also continuous motion detectors or infer motion from comparing discrete sound locations over time (spatiotemporally separable). We used a psychophysical reverse correlation paradigm, where participants discriminated the direction of a motion signal in the presence of spatiotemporal noise, to determine whether the filters underlying auditory motion discrimination were spatiotemporally separable or nonseparable. We then examined whether these auditory motion filters were altered as a result of early blindness. We found that both sighted and early blind individuals have separable filters. However, early blind individuals show increased sensitivity to auditory motion, with reduced susceptibility to noise and filters that were more accurate in detecting motion onsets/offsets. Model simulations suggest that this reliance on separable filters is optimal given the limited spatial resolution of auditory input.

From neural noise to co-adaptability: Rethinking the multifaceted architecture of motor variability

In the last decade, the source and the functional meaning of motor variability have attracted considerable attention in behavioral and brain sciences. This construct classically combined different levels of description, variable internal robustness or coherence, and multifaceted operational meanings. We provide here a comprehensive review of the literature with the primary aim of building a precise lexicon that goes beyond the generic and monolithic use of motor variability. In the pars destruens of the work, we model three domains of motor variability related to peculiar computational elements that influence fluctuations in motor outputs. Each domain is in turn characterized by multiple sub-domains. We begin with the domains of noise and differentiation. However, the main contribution of our model concerns the domain of adaptability, which refers to variation within the same exact motor representation. In particular, we use the terms learning and (social)fitting to specify the portions of motor variability that depend on our propensity to learn and on our largely constitutive propensity to be influenced by external factors. A particular focus is on motor variability in the context of the sub-domain named co-adaptability. Further groundbreaking challenges arise in the modeling of motor variability. Therefore, in a separate pars construens, we attempt to characterize these challenges, addressing both theoretical and experimental aspects as well as potential clinical implications for neurorehabilitation. All in all, our work suggests that motor variability is neither simply detrimental nor beneficial, and that studying its fluctuations can provide meaningful insights for future research.

Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons

Two facts about cortex are widely accepted: neuronal responses show large spiking variability with near Poisson statistics and cortical circuits feature abundant recurrent connections between neurons. How these spiking and circuit properties combine to support sensory representation and information processing is not well understood. We build a theoretical framework showing that these two ubiquitous features of cortex combine to produce optimal sampling-based Bayesian inference. Recurrent connections store an internal model of the external world, and Poissonian variability of spike responses drives flexible sampling from the posterior stimulus distributions obtained by combining feedforward and recurrent neuronal inputs. We illustrate how this framework for sampling-based inference can be used by cortex to represent latent multivariate stimuli organized either hierarchically or in parallel. A neural signature of such network sampling are internally generated differential correlations whose amplitude is determined by the prior stored in the circuit, which provides an experimentally testable prediction for our framework.

Studying the neural representations of uncertainty

The study of the brain's representations of uncertainty is a central topic in neuroscience. Unlike most quantities of which the neural representation is studied, uncertainty is a property of an observer's beliefs about the world, which poses specific methodological challenges. We analyze how the literature on the neural representations of uncertainty addresses those challenges and distinguish between 'code-driven' and 'correlational' approaches. Code-driven approaches make assumptions about the neural code for representing world states and the associated uncertainty. By contrast, correlational approaches search for relationships between uncertainty and neural activity without constraints on the neural representation of the world state that this uncertainty accompanies. To compare these two approaches, we apply several criteria for neural representations: sensitivity, specificity, invariance and functionality. Our analysis reveals that the two approaches lead to different but complementary findings, shaping new research questions and guiding future experiments.

Conditional independence as a statistical assessment of evidence integration processes

Intuitively, combining multiple sources of evidence should lead to more accurate decisions than considering single sources of evidence individually. In practice, however, the proper computation may be difficult, or may require additional data that are inaccessible. Here, based on the concept of conditional independence, we consider expressions that can serve either as recipes for integrating evidence based on limited data, or as statistical benchmarks for characterizing evidence integration processes. Consider three events, A , B , and C . We find that, if A and B are conditionally independent with respect to C , then the probability that C occurs given that both A and B are known, P C | A , B , can be easily calculated without the need to measure the full three-way dependency between A , B , and C . This simplified approach can be used in two general ways: to generate predictions by combining multiple (conditionally independent) sources of evidence, or to test whether separate sources of evidence are functionally independent of each other. These applications are demonstrated with four computer-simulated examples, which include detecting a disease based on repeated diagnostic testing, inferring biological age based on multiple biomarkers of aging, discriminating two spatial locations based on multiple cue stimuli (multisensory integration), and examining how behavioral performance in a visual search task depends on selection histories. Besides providing a sound prescription for predicting outcomes, this methodology may be useful for analyzing experimental data of many types.

Sensorimotor Uncertainty of Immersive Virtual Reality Environments for People in Pain: Scoping Review

INTRODUCTION

Decision making and action execution both rely on sensory information, and their primary objective is to minimise uncertainty. Virtual reality (VR) introduces uncertainty due to the imprecision of perceptual information. The concept of "sensorimotor uncertainty" is a pivotal element in the interplay between perception and action within the VR environment. The role of immersive VR in the four stages of motor behaviour decision making in people with pain has been previously discussed. These four processing levels are the basis to understand the uncertainty that a patient experiences when using VR: sensory information, current state, transition rules, and the outcome obtained.

METHODS

This review examines the different types of uncertainty that a patient may experience when they are immersed in a virtual reality environment in a context of pain. Randomised clinical trials, a secondary analysis of randomised clinical trials, and pilot randomised clinical trials related to the scope of Sensorimotor Uncertainty in Immersive Virtual Reality were included after searching.

RESULTS

Fifty studies were included in this review. They were divided into four categories regarding the type of uncertainty the intervention created and the stage of the decision-making model.

CONCLUSIONS

Immersive virtual reality makes it possible to alter sensorimotor uncertainty, but studies of higher methodological quality are needed on this topic, as well as an exploration into the patient profile for pain management using immersive VR.

Motor invariants in action execution and perception

The nervous system is sensitive to statistical regularities of the external world and forms internal models of these regularities to predict environmental dynamics. Given the inherently social nature of human behavior, being capable of building reliable predictive models of others' actions may be essential for successful interaction. While social prediction might seem to be a daunting task, the study of human motor control has accumulated ample evidence that our movements follow a series of kinematic invariants, which can be used by observers to reduce their uncertainty during social exchanges. Here, we provide an overview of the most salient regularities that shape biological motion, examine the role of these invariants in recognizing others' actions, and speculate that anchoring socially-relevant perceptual decisions to such kinematic invariants provides a key computational advantage for inferring conspecifics' goals and intentions.

Knowledge generalization and the costs of multitasking

Humans are able to rapidly perform novel tasks, but show pervasive performance costs when attempting to do two things at once. Traditionally, empirical and theoretical investigations into the sources of such multitasking interference have largely focused on multitasking in isolation to other cognitive functions, characterizing the conditions that give rise to performance decrements. Here we instead ask whether multitasking costs are linked to the system's capacity for knowledge generalization, as is required to perform novel tasks. We show how interrogation of the neurophysiological circuitry underlying these two facets of cognition yields further insights for both. Specifically, we demonstrate how a system that rapidly generalizes knowledge may induce multitasking costs owing to sharing of task contingencies between contexts in neural representations encoded in frontoparietal and striatal brain regions. We discuss neurophysiological insights suggesting that prolonged learning segregates such representations by refining the brain's model of task-relevant contingencies, thereby reducing information sharing between contexts and improving multitasking performance while reducing flexibility and generalization. These proposed neural mechanisms explain why the brain shows rapid task understanding, multitasking limitations and practice effects. In short, multitasking limits are the price we pay for behavioural flexibility.

Challenging the fixed-criterion model of perceptual decision-making

Perceptual decision-making is often conceptualized as the process of comparing an internal decision variable to a categorical boundary or criterion. How the mind sets such a criterion has been studied from at least two perspectives. One idea is that the criterion is a fixed quantity. In work on subjective phenomenology, the notion of a fixed criterion has been proposed to explain a phenomenon called "subjective inflation"-a form of metacognitive mismatch in which observers overestimate the quality of their sensory representation in the periphery or at unattended locations. A contrasting view emerging from studies of perceptual decision-making is that the criterion adjusts to the level sensory uncertainty and is thus sensitive to variations in attention. Here, we mathematically demonstrate that previous empirical findings supporting subjective inflation are consistent with either a fixed or a flexible decision criterion. We further lay out specific task properties that are necessary to make inferences about the flexibility of the criterion: (i) a clear mapping from decision variable space to stimulus feature space and (ii) an incentive for observers to adjust their decision criterion as uncertainty changes. Recent work satisfying these requirements has demonstrated that decision criteria flexibly adjust according to uncertainty. We conclude that the fixed-criterion model of subjective inflation is poorly tenable.

Feature representation under crowding in macaque V1 and V4 neuronal populations

Visual perception depends strongly on spatial context. A profound example is visual crowding, whereby the presence of nearby stimuli impairs the discriminability of object features. Despite extensive work on perceptual crowding and the spatial integrative properties of visual cortical neurons, the link between these two aspects of visual processing remains unclear. To understand better the neural basis of crowding, we recorded activity simultaneously from neuronal populations in V1 and V4 of fixating macaque monkeys. We assessed the information available from the measured responses about the orientation of a visual target both for targets presented in isolation and amid distractors. Both single neuron and population responses had less information about target orientation when distractors were present. Information loss was moderate in V1 and more substantial in V4. Information loss could be traced to systematic divisive and additive changes in neuronal tuning. Additive and multiplicative changes in tuning were more severe in V4; in addition, tuning exhibited other, non-affine transformations that were greater in V4, further restricting the ability of a fixed sensory readout strategy to extract accurate feature information across displays. Our results provide a direct test of crowding effects at different stages of the visual hierarchy. They reveal how crowded visual environments alter the spiking activity of cortical populations by which sensory stimuli are encoded and connect these changes to established mechanisms of neuronal spatial integration.

Sampling motion trajectories during hippocampal theta sequences

Efficient planning in complex environments requires that uncertainty associated with current inferences and possible consequences of forthcoming actions is represented. Representation of uncertainty has been established in sensory systems during simple perceptual decision making tasks but it remains unclear if complex cognitive computations such as planning and navigation are also supported by probabilistic neural representations. Here, we capitalized on gradually changing uncertainty along planned motion trajectories during hippocampal theta sequences to capture signatures of uncertainty representation in population responses. In contrast with prominent theories, we found no evidence of encoding parameters of probability distributions in the momentary population activity recorded in an open-field navigation task in rats. Instead, uncertainty was encoded sequentially by sampling motion trajectories randomly and efficiently in subsequent theta cycles from the distribution of potential trajectories. Our analysis is the first to demonstrate that the hippocampus is well equipped to contribute to optimal planning by representing uncertainty.

Exploration of sensory-motor tradeoff behavior in Parkinson's disease

While slowness of movement is an obligatory characteristic of Parkinson's disease (PD), there are conditions in which patients move uncharacteristically fast, attributed to deficient motor inhibition. Here we investigate deficient inhibition in an optimal sensory-motor integration framework, using a game in which subjects used a paddle to catch a virtual ball. Display of the ball was extinguished as soon as the catching movement started, segregating the task into a sensing and acting phase. We analyzed the behavior of 9 PD patients (ON medication) and 10 age-matched controls (HC). The switching times (between sensing and acting phase) were compared to the predicted optimal switching time, based on the individual estimates of sensory and motor uncertainties. The comparison showed that deviation from predicted optimal switching times were similar between groups. However, PD patients showed a weaker correlation between variability in switching time and sensory-motor uncertainty, indicating a reduced propensity to generate exploratory behavior for optimizing goal-directed movements. Analysis of the movement kinematics revealed that PD patients, compared to controls, used a lower peak velocity of the paddle and intercepted the ball with greater velocity. Adjusting the trial duration to the time for the paddle to stop moving, we found that PD patients spent a smaller proportion of the trial duration for observing the ball. Altogether, the results do not show the premature movement initiation and truncated sensory processing that we predicted to ensue from deficient inhibition in PD.

Putting perception into action with inverse optimal control for continuous psychophysics

Psychophysical methods are a cornerstone of psychology, cognitive science, and neuroscience where they have been used to quantify behavior and its neural correlates for a vast range of mental phenomena. Their power derives from the combination of controlled experiments and rigorous analysis through signal detection theory. Unfortunately, they require many tedious trials and preferably highly trained participants. A recently developed approach, continuous psychophysics, promises to transform the field by abandoning the rigid trial structure involving binary responses and replacing it with continuous behavioral adjustments to dynamic stimuli. However, what has precluded wide adoption of this approach is that current analysis methods do not account for the additional variability introduced by the motor component of the task and therefore recover perceptual thresholds that are larger compared to equivalent traditional psychophysical experiments. Here, we introduce a computational analysis framework for continuous psychophysics based on Bayesian inverse optimal control. We show via simulations and previously published data that this not only recovers the perceptual thresholds but additionally estimates subjects' action variability, internal behavioral costs, and subjective beliefs about the experimental stimulus dynamics. Taken together, we provide further evidence for the importance of including acting uncertainties, subjective beliefs, and, crucially, the intrinsic costs of behavior, even in experiments seemingly only investigating perception.

Distance estimation from monocular cues in an ethological visuomotor task

In natural contexts, sensory processing and motor output are closely coupled, which is reflected in the fact that many brain areas contain both sensory and movement signals. However, standard reductionist paradigms decouple sensory decisions from their natural motor consequences, and head-fixation prevents the natural sensory consequences of self-motion. In particular, movement through the environment provides a number of depth cues beyond stereo vision that are poorly understood. To study the integration of visual processing and motor output in a naturalistic task, we investigated distance estimation in freely moving mice. We found that mice use vision to accurately jump across a variable gap, thus directly coupling a visual computation to its corresponding ethological motor output. Monocular eyelid suture did not affect gap jumping success, thus mice can use cues that do not depend on binocular disparity and stereo vision. Under monocular conditions, mice altered their head positioning and performed more vertical head movements, consistent with a shift from using stereopsis to other monocular cues, such as motion or position parallax. Finally, optogenetic suppression of primary visual cortex impaired task performance under both binocular and monocular conditions when optical fiber placement was localized to binocular or monocular zone V1, respectively. Together, these results show that mice can use monocular cues, relying on visual cortex, to accurately judge distance. Furthermore, this behavioral paradigm provides a foundation for studying how neural circuits convert sensory information into ethological motor output.

Suboptimal human inference can invert the bias-variance trade-off for decisions with asymmetric evidence

Solutions to challenging inference problems are often subject to a fundamental trade-off between: 1) bias (being systematically wrong) that is minimized with complex inference strategies, and 2) variance (being oversensitive to uncertain observations) that is minimized with simple inference strategies. However, this trade-off is based on the assumption that the strategies being considered are optimal for their given complexity and thus has unclear relevance to forms of inference based on suboptimal strategies. We examined inference problems applied to rare, asymmetrically available evidence, which a large population of human subjects solved using a diverse set of strategies that varied in form and complexity. In general, subjects using more complex strategies tended to have lower bias and variance, but with a dependence on the form of strategy that reflected an inversion of the classic bias-variance trade-off: subjects who used more complex, but imperfect, Bayesian-like strategies tended to have lower variance but higher bias because of incorrect tuning to latent task features, whereas subjects who used simpler heuristic strategies tended to have higher variance because they operated more directly on the observed samples but lower, near-normative bias. Our results help define new principles that govern individual differences in behavior that depends on rare-event inference and, more generally, about the information-processing trade-offs that can be sensitive to not just the complexity, but also the optimality, of the inference process.

People use diverse strategies to make inferences about the world around them, often based on limited evidence. Such inference strategies may be simple but prone to systematic errors or more complex and accurate, but such trends need not always be the rule. We modeled and measured how human participants made rare-event decisions in a preregistered, online study. The participants tended to use suboptimal decision strategies that reflected an inversion of the classic bias-variance trade-off: some used complex, nearly normative strategies with mistuned evidence weights that corresponded to relatively high choice biases but lower choice variance, whereas others used simpler heuristic strategies that corresponded to lower biases but higher variance. These relationships illustrate structure in suboptimality that can be used to identify systematic sources of human errors.

The structures and functions of correlations in neural population codes

The collective activity of a population of neurons, beyond the properties of individual cells, is crucial for many brain functions. A fundamental question is how activity correlations between neurons affect how neural populations process information. Over the past 30 years, major progress has been made on how the levels and structures of correlations shape the encoding of information in population codes. Correlations influence population coding through the organization of pairwise-activity correlations with respect to the similarity of tuning of individual neurons, by their stimulus modulation and by the presence of higher-order correlations. Recent work has shown that correlations also profoundly shape other important functions performed by neural populations, including generating codes across multiple timescales and facilitating information transmission to, and readout by, downstream brain areas to guide behaviour. Here, we review this recent work and discuss how the structures of correlations can have opposite effects on the different functions of neural populations, thus creating trade-offs and constraints for the structure-function relationships of population codes. Further, we present ideas on how to combine large-scale simultaneous recordings of neural populations, computational models, analyses of behaviour, optogenetics and anatomy to unravel how the structures of correlations might be optimized to serve multiple functions.

Tracking the contribution of inductive bias to individualised internal models

Internal models capture the regularities of the environment and are central to understanding how humans adapt to environmental statistics. In general, the correct internal model is unknown to observers, instead they rely on an approximate model that is continually adapted throughout learning. However, experimenters assume an ideal observer model, which captures stimulus structure but ignores the diverging hypotheses that humans form during learning. We combine non-parametric Bayesian methods and probabilistic programming to infer rich and dynamic individualised internal models from response times. We demonstrate that the approach is capable of characterizing the discrepancy between the internal model maintained by individuals and the ideal observer model and to track the evolution of the contribution of the ideal observer model to the internal model throughout training. In particular, in an implicit visuomotor sequence learning task the identified discrepancy revealed an inductive bias that was consistent across individuals but varied in strength and persistence.

Towards a cross-level understanding of Bayesian inference in the brain

Perception emerges from unconscious probabilistic inference, which guides behaviour in our ubiquitously uncertain environment. Bayesian decision theory is a prominent computational model that describes how people make rational decisions using noisy and ambiguous sensory observations. However, critical questions have been raised about the validity of the Bayesian framework in explaining the mental process of inference. Firstly, some natural behaviours deviate from Bayesian optimum. Secondly, the neural mechanisms that support Bayesian computations in the brain are yet to be understood. Taking Marr's cross level approach, we review the recent progress made in addressing these challenges. We first review studies that combined behavioural paradigms and modelling approaches to explain both optimal and suboptimal behaviours. Next, we evaluate the theoretical advances and the current evidence for ecologically feasible algorithms and neural implementations in the brain, which may enable probabilistic inference. We argue that this cross-level approach is necessary for the worthwhile pursuit to uncover mechanistic accounts of human behaviour.

Task-induced neural covariability as a signature of approximate Bayesian learning and inference

Perception is often characterized computationally as an inference process in which uncertain or ambiguous sensory inputs are combined with prior expectations. Although behavioral studies have shown that observers can change their prior expectations in the context of a task, robust neural signatures of task-specific priors have been elusive. Here, we analytically derive such signatures under the general assumption that the responses of sensory neurons encode posterior beliefs that combine sensory inputs with task-specific expectations. Specifically, we derive predictions for the task-dependence of correlated neural variability and decision-related signals in sensory neurons. The qualitative aspects of our results are parameter-free and specific to the statistics of each task. The predictions for correlated variability also differ from predictions of classic feedforward models of sensory processing and are therefore a strong test of theories of hierarchical Bayesian inference in the brain. Importantly, we find that Bayesian learning predicts an increase in so-called “differential correlations” as the observer’s internal model learns the stimulus distribution, and the observer’s behavioral performance improves. This stands in contrast to classic feedforward encoding/decoding models of sensory processing, since such correlations are fundamentally information-limiting. We find support for our predictions in data from existing neurophysiological studies across a variety of tasks and brain areas. Finally, we show in simulation how measurements of sensory neural responses can reveal information about a subject’s internal beliefs about the task. Taken together, our results reinterpret task-dependent sources of neural covariability as signatures of Bayesian inference and provide new insights into their cause and their function.

Perceptual decision-making has classically been studied in the context of feedforward encoding/ decoding models. Here, we derive predictions for the responses of sensory neurons under the assumption that the brain performs hierarchical Bayesian inference, including feedback signals that communicate task-specific prior expectations. Interestingly, those predictions stand in contrast to some of the conclusions drawn in the classic framework. In particular, we find that Bayesian learning predicts the increase of a type of correlated variability called “differential correlations” over the course of learning. Differential correlations limit information, and hence are seen as harmful in feedforward models. Since our results are also specific to the statistics of a given task, and since they hold under a wide class of theories about how Bayesian probabilities may be represented by neural responses, they constitute a strong test of the Bayesian Brain hypothesis. Our results can explain the task-dependence of correlated variability in prior studies and suggest a reason why these kinds of correlations are surprisingly common in empirical data. Interpreted in a probabilistic framework, correlated variability provides a window into an observer’s task-related beliefs.

Rational inattention in mice

Behavior exhibited by humans and other organisms is generally inconsistent and biased and, thus, is often labeled irrational. However, the origins of this seemingly suboptimal behavior remain elusive. We developed a behavioral task and normative framework to reveal how organisms should allocate their limited processing resources such that sensory precision and its related metabolic investment are balanced to guarantee maximal utility. We found that mice act as rational inattentive agents by adaptively allocating their sensory resources in a way that maximizes reward consumption in previously unexperienced stimulus-reward association environments. Unexpectedly, perception of commonly occurring stimuli was relatively imprecise; however, this apparent statistical fallacy implies "awareness" and efficient adaptation to their neurocognitive limitations. Arousal systems carry reward distribution information of sensory signals, and distributional reinforcement learning mechanisms regulate sensory precision via top-down normalization. These findings reveal how organisms efficiently perceive and adapt to previously unexperienced environmental contexts within the constraints imposed by neurobiology.

Salience of multisensory feedback regulates behavioral variability

Many animal behaviors are robust to dramatic variations in morphophysiological features, both across and within individuals. The control strategies that animals use to achieve such robust behavioral performances are not known. Recent evidence suggests that animals rely on sensory feedback rather than precise tuning of neural controllers for robust control. Here we examine the structure of sensory feedback, including multisensory feedback, for robust control of animal behavior. We re-examined two recent datasets of refuge tracking responses ofEigenmannia virescens, a species of weakly electric fish.Eigenmanniarely on both the visual and electrosensory cues to track the position of a moving refuge. The datasets include experiments that varied the strength of visual and electrosensory signals. Our analyses show that increasing the salience (perceptibility) of visual or electrosensory signals resulted in more robust and precise behavioral responses. Further, we find that robust performance was enhanced by multisensory integration of simultaneous visual and electrosensory cues. These findings suggest that engineers may achieve better system performance by improving the salience of multisensory feedback rather than solely focusing on precisely tuned controllers.

How learning unfolds in the brain: toward an optimization view

How do changes in the brain lead to learning? To answer this question, consider an artificial neural network (ANN), where learning proceeds by optimizing a given objective or cost function. This "optimization framework" may provide new insights into how the brain learns, as many idiosyncratic features of neural activity can be recapitulated by an ANN trained to perform the same task. Nevertheless, there are key features of how neural population activity changes throughout learning that cannot be readily explained in terms of optimization and are not typically features of ANNs. Here we detail three of these features: (1) the inflexibility of neural variability throughout learning, (2) the use of multiple learning processes even during simple tasks, and (3) the presence of large task-nonspecific activity changes. We propose that understanding the role of these features in the brain will be key to describing biological learning using an optimization framework.

Revealing nonlinear neural decoding by analyzing choices

Sensory data about most natural task-relevant variables are entangled with task-irrelevant nuisance variables. The neurons that encode these relevant signals typically constitute a nonlinear population code. Here we present a theoretical framework for quantifying how the brain uses or decodes its nonlinear information. Our theory obeys fundamental mathematical limitations on information content inherited from the sensory periphery, describing redundant codes when there are many more cortical neurons than primary sensory neurons. The theory predicts that if the brain uses its nonlinear population codes optimally, then more informative patterns should be more correlated with choices. More specifically, the theory predicts a simple, easily computed quantitative relationship between fluctuating neural activity and behavioral choices that reveals the decoding efficiency. This relationship holds for optimal feedforward networks of modest complexity, when experiments are performed under natural nuisance variation. We analyze recordings from primary visual cortex of monkeys discriminating the distribution from which oriented stimuli were drawn, and find these data are consistent with the hypothesis of near-optimal nonlinear decoding.

Collective action or individual choice: Spontaneity and individuality contribute to decision-making in Drosophila

Our own unique character traits make our behavior consistent and define our individuality. Yet, this consistency does not entail that we behave repetitively like machines. Like humans, animals also combine personality traits with spontaneity to produce adaptive behavior: consistent, but not fully predictable. Here, we study an iconically rigid behavioral trait, insect phototaxis, that nevertheless also contains both components of individuality and spontaneity. In a light/dark T-maze, approximately 70% of a group of Drosophila fruit flies choose the bright arm of the T-Maze, while the remaining 30% walk into the dark. Taking the photopositive and the photonegative subgroups and re-testing them reveals the spontaneous component: a similar 70–30 distribution emerges in each of the two subgroups. Increasing the number of choices to ten choices, reveals the individuality component: flies with an extremely negative series of first choices were more likely to show photonegative behavior in subsequent choices and vice versa. General behavioral traits, independent of light/dark preference, contributed to the development of this individuality. The interaction of individuality and spontaneity together explains why group averages, even for such seemingly stereotypical behaviors, are poor predictors of individual choices.

Uncertainty is maintained and used in working memory

What are the contents of working memory? In both behavioral and neural computational models, a working memory representation is typically described by a single number, namely, a point estimate of a stimulus. Here, we asked if people also maintain the uncertainty associated with a memory and if people use this uncertainty in subsequent decisions. We collected data in a two-condition orientation change detection task; while both conditions measured whether people used memory uncertainty, only one required maintaining it. For each condition, we compared an optimal Bayesian observer model, in which the observer uses an accurate representation of uncertainty in their decision, to one in which the observer does not. We find that this “Use Uncertainty” model fits better for all participants in both conditions. In the first condition, this result suggests that people use uncertainty optimally in a working memory task when that uncertainty information is available at the time of decision, confirming earlier results. Critically, the results of the second condition suggest that this uncertainty information was maintained in working memory. We test model variants and find that our conclusions do not depend on our assumptions about the observer's encoding process, inference process, or decision rule. Our results provide evidence that people have uncertainty that reflects their memory precision on an item-specific level, maintain this information over a working memory delay, and use it implicitly in a way consistent with an optimal observer. These results challenge existing computational models of working memory to update their frameworks to represent uncertainty.

Noise Correlations for Faster and More Robust Learning

Distributed population codes are ubiquitous in the brain and pose a challenge to downstream neurons that must learn an appropriate readout. Here we explore the possibility that this learning problem is simplified through inductive biases implemented by stimulus-independent noise correlations that constrain learning to task-relevant dimensions. We test this idea in a set of neural networks that learn to perform a perceptual discrimination task. Correlations among similarly tuned units were manipulated independently of an overall population signal-to-noise ratio to test how the format of stored information affects learning. Higher noise correlations among similarly tuned units led to faster and more robust learning, favoring homogenous weights assigned to neurons within a functionally similar pool, and could emerge through Hebbian learning. When multiple discriminations were learned simultaneously, noise correlations across relevant feature dimensions sped learning, whereas those across irrelevant feature dimensions slowed it. Our results complement the existing theory on noise correlations by demonstrating that when such correlations are produced without significant degradation of the signal-to-noise ratio, they can improve the speed of readout learning by constraining it to appropriate dimensions.SIGNIFICANCE STATEMENT Positive noise correlations between similarly tuned neurons theoretically reduce the representational capacity of the brain, yet they are commonly observed, emerge dynamically in complex tasks, and persist even in well-trained animals. Here we show that such correlations, when embedded in a neural population with a fixed signal-to-noise ratio, can improve the speed and robustness with which an appropriate readout is learned. In a simple discrimination task such correlations can emerge naturally through Hebbian learning. In more complex tasks that require multiple discriminations, correlations between neurons that similarly encode the task-relevant feature improve learning by constraining it to the appropriate task dimension.

Probabilistic discrimination of relative stimulus features in mice

During perceptual decision-making, the brain encodes the upcoming decision and the stimulus information in a mixed representation. Paradigms suitable for studying decision computations in isolation rely on stimulus comparisons, with choices depending on relative rather than absolute properties of the stimuli. The adoption of tasks requiring relative perceptual judgments in mice would be advantageous in view of the powerful tools available for the dissection of brain circuits. However, whether and how mice can perform a relative visual discrimination task has not yet been fully established. Here, we show that mice can solve a complex orientation discrimination task in which the choices are decoupled from the orientation of individual stimuli. Moreover, we demonstrate a typical discrimination acuity of 9°, challenging the common belief that mice are poor visual discriminators. We reached these conclusions by introducing a probabilistic choice model that explained behavioral strategies in 40 mice and demonstrated that the circularity of the stimulus space is an additional source of choice variability for trials with fixed difficulty. Furthermore, history biases in the model changed with task engagement, demonstrating behavioral sensitivity to the availability of cognitive resources. In conclusion, our results reveal that mice adopt a diverse set of strategies in a task that decouples decision-relevant information from stimulus-specific information, thus demonstrating their usefulness as an animal model for studying neural representations of relative categories in perceptual decision-making research.

Neuronal variability reflects probabilistic inference tuned to natural image statistics

Neuronal activity in sensory cortex fluctuates over time and across repetitions of the same input. This variability is often considered detrimental to neural coding. The theory of neural sampling proposes instead that variability encodes the uncertainty of perceptual inferences. In primary visual cortex (V1), modulation of variability by sensory and non-sensory factors supports this view. However, it is unknown whether V1 variability reflects the statistical structure of visual inputs, as would be required for inferences correctly tuned to the statistics of the natural environment. Here we combine analysis of image statistics and recordings in macaque V1 to show that probabilistic inference tuned to natural image statistics explains the widely observed dependence between spike count variance and mean, and the modulation of V1 activity and variability by spatial context in images. Our results show that the properties of a basic aspect of cortical responses-their variability-can be explained by a probabilistic representation tuned to naturalistic inputs.

Musical Expertise Is Associated with Improved Neural Statistical Learning in the Auditory Domain

 

It is poorly known whether musical training is associated with improvements in general cognitive abilities, such as statistical learning (SL). In standard SL paradigms, musicians have shown better performances than nonmusicians. However, this advantage could be due to differences in auditory discrimination, in memory or truly in the ability to learn sequence statistics. Unfortunately, these different hypotheses make similar predictions in terms of expected results. To dissociate them, we developed a Bayesian model and recorded electroencephalography (EEG). Our results confirm that musicians perform approximately 15% better than nonmusicians at predicting items in auditory sequences that embed either low or high-order statistics. These higher performances are explained in the model by parameters governing the learning of high-order statistics and the selection stage noise. EEG recordings reveal a neural underpinning of the musician's advantage: the P300 amplitude correlates with the surprise elicited by each item, and so, more strongly for musicians. Finally, early EEG components correlate with the surprise elicited by low-order statistics, as opposed to late EEG components that correlate with the surprise elicited by high-order statistics and this effect is stronger for musicians. Overall, our results demonstrate that musical expertise is associated with improved neural SL in the auditory domain.

SIGNIFICANCE STATEMENT

It is poorly known whether musical training leads to improvements in general cognitive skills. One fundamental cognitive ability, SL, is thought to be enhanced in musicians, but previous studies have reported mixed results. This is because such musician's advantage can embrace very different explanations, such as improvement in auditory discrimination or in memory. To solve this problem, we developed a Bayesian model and recorded EEG to dissociate these explanations. Our results reveal that musical expertise is truly associated with an improved ability to learn sequence statistics, especially high-order statistics. This advantage is reflected in the electroencephalographic recordings, where the P300 amplitude is more sensitive to surprising items in musicians than in nonmusicians.

Correlated structure of neuronal firing in macaque visual cortex limits information for binocular depth discrimination

Variability in cortical neural activity potentially limits sensory discriminations. Theoretical work shows that information required to discriminate two similar stimuli is limited by the correlation structure of cortical variability. We investigated these information-limiting correlations by recording simultaneously from visual cortical areas primary visual cortex (V1) and extrastriate area V4 in macaque monkeys performing a binocular, stereo depth discrimination task. Within both areas, noise correlations on a rapid temporal scale (20–30 ms) were stronger for neuron pairs with similar selectivity for binocular depth, meaning that these correlations potentially limit information for making the discrimination. Between-area correlations (V1 to V4) were different, being weaker for neuron pairs with similar tuning and having a slower temporal scale (100+ ms). Fluctuations in these information-limiting correlations just prior to the detection event were associated with changes in behavioral accuracy. Although these correlations limit the recovery of information about sensory targets, their impact may be curtailed by integrative processing of signals across multiple brain areas.

NEW & NOTEWORTHY Correlated noise reduces the stimulus information in visual cortical neurons during experimental performance of binocular depth discriminations. The temporal scale of these correlations is important. Rapid (20–30 ms) correlations reduce information within and between areas V1 and V4, whereas slow (>100 ms) correlations between areas do not. Separate cortical areas appear to act together to maintain signal fidelity. Rapid correlations reduce the neuronal signal difference between stimuli and adversely affect perceptual discrimination.

High-precision coding in visual cortex

Individual neurons in visual cortex provide the brain with unreliable estimates of visual features. It is not known whether the single-neuron variability is correlated across large neural populations, thus impairing the global encoding of stimuli. We recorded simultaneously from up to 50,000 neurons in mouse primary visual cortex (V1) and in higher order visual areas and measured stimulus discrimination thresholds of 0.35° and 0.37°, respectively, in an orientation decoding task. These neural thresholds were almost 100 times smaller than the behavioral discrimination thresholds reported in mice. This discrepancy could not be explained by stimulus properties or arousal states. Furthermore, behavioral variability during a sensory discrimination task could not be explained by neural variability in V1. Instead, behavior-related neural activity arose dynamically across a network of non-sensory brain areas. These results imply that perceptual discrimination in mice is limited by downstream decoders, not by neural noise in sensory representations.

Why are the batteries in the microwave?: Use of semantic information under uncertainty in a search task

A major problem in human cognition is to understand how newly acquired information and long-standing beliefs about the environment combine to make decisions and plan behaviors. Over-dependence on long-standing beliefs may be a significant source of suboptimal decision-making in unusual circumstances. While the contribution of long-standing beliefs about the environment to search in real-world scenes is well-studied, less is known about how new evidence informs search decisions, and it is unclear whether the two sources of information are used together optimally to guide search. The present study expanded on the literature on semantic guidance in visual search by modeling a Bayesian ideal observer's use of long-standing semantic beliefs and recent experience in an active search task. The ability to adjust expectations to the task environment was simulated using the Bayesian ideal observer, and subjects' performance was compared to ideal observers that depended on prior knowledge and recent experience to varying degrees. Target locations were either congruent with scene semantics, incongruent with what would be expected from scene semantics, or random. Half of the subjects were able to learn to search for the target in incongruent locations over repeated experimental sessions when it was optimal to do so. These results suggest that searchers can learn to prioritize recent experience over knowledge of scenes in a near-optimal fashion when it is beneficial to do so, as long as the evidence from recent experience was learnable.

Investigating the representation of uncertainty in neuronal circuits

Skilled behavior often displays signatures of Bayesian inference. In order for the brain to implement the required computations, neuronal activity must carry accurate information about the uncertainty of sensory inputs. Two major approaches have been proposed to study neuronal representations of uncertainty. The first one, the Bayesian decoding approach, aims primarily at decoding the posterior probability distribution of the stimulus from population activity using Bayes’ rule, and indirectly yields uncertainty estimates as a by-product. The second one, which we call the correlational approach, searches for specific features of neuronal activity (such as tuning-curve width and maximum firing-rate) which correlate with uncertainty. To compare these two approaches, we derived a new normative model of sound source localization by Interaural Time Difference (ITD), that reproduces a wealth of behavioral and neural observations. We found that several features of neuronal activity correlated with uncertainty on average, but none provided an accurate estimate of uncertainty on a trial-by-trial basis, indicating that the correlational approach may not reliably identify which aspects of neuronal responses represent uncertainty. In contrast, the Bayesian decoding approach reveals that the activity pattern of the entire population was required to reconstruct the trial-to-trial posterior distribution with Bayes’ rule. These results suggest that uncertainty is unlikely to be represented in a single feature of neuronal activity, and highlight the importance of using a Bayesian decoding approach when exploring the neural basis of uncertainty.

In order to optimize their behavior, animals must continuously represent the uncertainty associated with their beliefs. Understanding the neural code for this uncertainty is a pressing and critical issue in neuroscience. Following a long tradition, some studies have investigated this code by measuring how average statistics of neural responses (like the tuning curves) correlate with uncertainty as stimulus characteristics are varied. We show that this approach can be very misleading. An alternative consists in decoding the neuronal responses to recover the posterior distribution over the encoded sensory variables and using the variance of this distribution as the measure of uncertainty. We demonstrate that this decoding approach can indeed avoid the pitfalls of the traditional approach, while leading to more accurate estimates of uncertainty.

Scaling of sensory information in large neural populations shows signatures of information-limiting correlations

How is information distributed across large neuronal populations within a given brain area? Information may be distributed roughly evenly across neuronal populations, so that total information scales linearly with the number of recorded neurons. Alternatively, the neural code might be highly redundant, meaning that total information saturates. Here we investigate how sensory information about the direction of a moving visual stimulus is distributed across hundreds of simultaneously recorded neurons in mouse primary visual cortex. We show that information scales sublinearly due to correlated noise in these populations. We compartmentalized noise correlations into information-limiting and nonlimiting components, then extrapolate to predict how information grows with even larger neural populations. We predict that tens of thousands of neurons encode 95% of the information about visual stimulus direction, much less than the number of neurons in primary visual cortex. These findings suggest that the brain uses a widely distributed, but nonetheless redundant code that supports recovering most sensory information from smaller subpopulations.