Bayesian inference in ring attractor networks.

Working memories are thought to be held in attractor networks in the brain. These attractors should keep track of the uncertainty associated with each memory, so as to weigh it properly against conflicting new evidence. However, conventional attractors do not represent uncertainty. Here, we show how uncertainty could be incorporated into an attractor, specifically a ring attractor that encodes head direction. First, we introduce a rigorous normative framework (the circular Kalman filter) for benchmarking the performance of a ring attractor under conditions of uncertainty. Next, we show that the recurrent connections within a conventional ring attractor can be retuned to match this benchmark. This allows the amplitude of network activity to grow in response to confirmatory evidence, while shrinking in response to poor-quality or strongly conflicting evidence. This "Bayesian ring attractor" performs near-optimal angular path integration and evidence accumulation. Indeed, we show that a Bayesian ring attractor is consistently more accurate than a conventional ring attractor. Moreover, near-optimal performance can be achieved without exact tuning of the network connections. Finally, we use large-scale connectome data to show that the network can achieve near-optimal performance even after we incorporate biological constraints. Our work demonstrates how attractors can implement a dynamic Bayesian inference algorithm in a biologically plausible manner, and it makes testable predictions with direct relevance to the head direction system as well as any neural system that tracks direction, orientation, or periodic rhythms.

Diverse effects of gaze direction on heading perception in humans.

Gaze change can misalign spatial reference frames encoding visual and vestibular signals in cortex, which may affect the heading discrimination. Here, by systematically manipulating the eye-in-head and head-on-body positions to change the gaze direction of subjects, the performance of heading discrimination was tested with visual, vestibular, and combined stimuli in a reaction-time task in which the reaction time is under the control of subjects. We found the gaze change induced substantial biases in perceived heading, increased the threshold of discrimination and reaction time of subjects in all stimulus conditions. For the visual stimulus, the gaze effects were induced by changing the eye-in-world position, and the perceived heading was biased in the opposite direction of gaze. In contrast, the vestibular gaze effects were induced by changing the eye-in-head position, and the perceived heading was biased in the same direction of gaze. Although the bias was reduced when the visual and vestibular stimuli were combined, integration of the 2 signals substantially deviated from predictions of an extended diffusion model that accumulates evidence optimally over time and across sensory modalities. These findings reveal diverse gaze effects on the heading discrimination and emphasize that the transformation of spatial reference frames may underlie the effects.

Heuristics and optimal solutions to the breadth-depth dilemma.

In multialternative risky choice, we are often faced with the opportunity to allocate our limited information-gathering capacity between several options before receiving feedback. In such cases, we face a natural trade-off between breadth-spreading our capacity across many options-and depth-gaining more information about a smaller number of options. Despite its broad relevance to daily life, including in many naturalistic foraging situations, the optimal strategy in the breadth-depth trade-off has not been delineated. Here, we formalize the breadth-depth dilemma through a finite-sample capacity model. We find that, if capacity is small (∼10 samples), it is optimal to draw one sample per alternative, favoring breadth. However, for larger capacities, a sharp transition is observed, and it becomes best to deeply sample a very small fraction of alternatives, which roughly decreases with the square root of capacity. Thus, ignoring most options, even when capacity is large enough to shallowly sample all of them, is a signature of optimal behavior. Our results also provide a rich casuistic for metareasoning in multialternative decisions with bounded capacity using close-to-optimal heuristics.

Hierarchical structure is employed by humans during visual motion perception.

In the real world, complex dynamic scenes often arise from the composition of simpler parts. The visual system exploits this structure by hierarchically decomposing dynamic scenes: When we see a person walking on a train or an animal running in a herd, we recognize the individual's movement as nested within a reference frame that is, itself, moving. Despite its ubiquity, surprisingly little is understood about the computations underlying hierarchical motion perception. To address this gap, we developed a class of stimuli that grant tight control over statistical relations among object velocities in dynamic scenes. We first demonstrate that structured motion stimuli benefit human multiple object tracking performance. Computational analysis revealed that the performance gain is best explained by human participants making use of motion relations during tracking. A second experiment, using a motion prediction task, reinforced this conclusion and provided fine-grained information about how the visual system flexibly exploits motion structure.

Learning optimal decisions with confidence.

Diffusion decision models (DDMs) are immensely successful models for decision making under uncertainty and time pressure. In the context of perceptual decision making, these models typically start with two input units, organized in a neuron-antineuron pair. In contrast, in the brain, sensory inputs are encoded through the activity of large neuronal populations. Moreover, while DDMs are wired by hand, the nervous system must learn the weights of the network through trial and error. There is currently no normative theory of learning in DDMs and therefore no theory of how decision makers could learn to make optimal decisions in this context. Here, we derive such a rule for learning a near-optimal linear combination of DDM inputs based on trial-by-trial feedback. The rule is Bayesian in the sense that it learns not only the mean of the weights but also the uncertainty around this mean in the form of a covariance matrix. In this rule, the rate of learning is proportional (respectively, inversely proportional) to confidence for incorrect (respectively, correct) decisions. Furthermore, we show that, in volatile environments, the rule predicts a bias toward repeating the same choice after correct decisions, with a bias strength that is modulated by the previous choice's difficulty. Finally, we extend our learning rule to cases for which one of the choices is more likely a priori, which provides insights into how such biases modulate the mechanisms leading to optimal decisions in diffusion models.

Projection Filtering with Observed State Increments with Applications in Continuous-Time Circular Filtering.

Angular path integration is the ability of a system to estimate its own heading direction from potentially noisy angular velocity (or increment) observations. Non-probabilistic algorithms for angular path integration, which rely on a summation of these noisy increments, do not appropriately take into account the reliability of such observations, which is essential for appropriately weighing one's current heading direction estimate against incoming information. In a probabilistic setting, angular path integration can be formulated as a continuous-time nonlinear filtering problem (circular filtering) with observed state increments. The circular symmetry of heading direction makes this inference task inherently nonlinear, thereby precluding the use of popular inference algorithms such as Kalman filters, rendering the problem analytically inaccessible. Here, we derive an approximate solution to circular continuous-time filtering, which integrates state increment observations while maintaining a fixed representation through both state propagation and observational updates. Specifically, we extend the established projection-filtering method to account for observed state increments and apply this framework to the circular filtering problem. We further propose a generative model for continuous-time angular-valued direct observations of the hidden state, which we integrate seamlessly into the projection filter. Applying the resulting scheme to a model of probabilistic angular path integration, we derive an algorithm for circular filtering, which we term the circular Kalman filter. Importantly, this algorithm is analytically accessible, interpretable, and outperforms an alternative filter based on a Gaussian approximation.

Filtering sensory information with XCSF: improving learning robustness and robot arm control performance.

It has been shown previously that the control of a robot arm can be efficiently learned using the XCSF learning classifier system, which is a nonlinear regression system based on evolutionary computation. So far, however, the predictive knowledge about how actual motor activity changes the state of the arm system has not been exploited. In this paper, we utilize the forward velocity kinematics knowledge of XCSF to alleviate the negative effect of noisy sensors for successful learning and control. We incorporate Kalman filtering for estimating successive arm positions, iteratively combining sensory readings with XCSF-based predictions of hand position changes over time. The filtered arm position is used to improve both trajectory planning and further learning of the forward velocity kinematics. We test the approach on a simulated kinematic robot arm model. The results show that the combination can improve learning and control performance significantly. However, it also shows that variance estimates of XCSF prediction may be underestimated, in which case self-delusional spiraling effects can hinder effective learning. Thus, we introduce a heuristic parameter, which can be motivated by theory, and which limits the influence of XCSF's predictions on its own further learning input. As a result, we obtain drastic improvements in noise tolerance, allowing the system to cope with more than 10 times higher noise levels.

An opponent striatal circuit for distributional reinforcement learning.

Machine learning research has achieved large performance gains on a wide range of tasks by expanding the learning target from mean rewards to entire probability distributions of rewards - an approach known as distributional reinforcement learning (RL)1. The mesolimbic dopamine system is thought to underlie RL in the mammalian brain by updating a representation of mean value in the striatum2,3, but little is known about whether, where, and how neurons in this circuit encode information about higher-order moments of reward distributions4. To fill this gap, we used high-density probes (Neuropixels) to acutely record striatal activity from well-trained, water-restricted mice performing a classical conditioning task in which reward mean, reward variance, and stimulus identity were independently manipulated. In contrast to traditional RL accounts, we found robust evidence for abstract encoding of variance in the striatum. Remarkably, chronic ablation of dopamine inputs disorganized these distributional representations in the striatum without interfering with mean value coding. Two-photon calcium imaging and optogenetics revealed that the two major classes of striatal medium spiny neurons - D1 and D2 MSNs - contributed to this code by preferentially encoding the right and left tails of the reward distribution, respectively. We synthesize these findings into a new model of the striatum and mesolimbic dopamine that harnesses the opponency between D1 and D2 MSNs5-15 to reap the computational benefits of distributional RL.

Nerve injury disrupts temporal processing in the spinal cord dorsal horn through alterations in PV+ interneurons.

How mechanical allodynia following nerve injury is encoded in patterns of neural activity in the spinal cord dorsal horn (DH) remains incompletely understood. We address this in mice using the spared nerve injury model of neuropathic pain and in vivo electrophysiological recordings. Surprisingly, despite dramatic behavioral over-reactivity to mechanical stimuli following nerve injury, an overall increase in sensitivity or reactivity of DH neurons is not observed. We do, however, observe a marked decrease in correlated neural firing patterns, including the synchrony of mechanical stimulus-evoked firing, across the DH. Alterations in DH temporal firing patterns are recapitulated by silencing DH parvalbumin+ (PV+) interneurons, previously implicated in mechanical allodynia, as are allodynic pain-like behaviors. These findings reveal decorrelated DH network activity, driven by alterations in PV+ interneurons, as a prominent feature of neuropathic pain and suggest restoration of proper temporal activity as a potential therapeutic strategy to treat chronic neuropathic pain.

The cost of accumulating evidence in perceptual decision making.

Decision making often involves the accumulation of information over time, but acquiring information typically comes at a cost. Little is known about the cost incurred by animals and humans for acquiring additional information from sensory variables due, for instance, to attentional efforts. Through a novel integration of diffusion models and dynamic programming, we were able to estimate the cost of making additional observations per unit of time from two monkeys and six humans in a reaction time (RT) random-dot motion discrimination task. Surprisingly, we find that the cost is neither zero nor constant over time, but for the animals and humans features a brief period in which it is constant but increases thereafter. In addition, we show that our theory accurately matches the observed reaction time distributions for each stimulus condition, the time-dependent choice accuracy both conditional on stimulus strength and independent of it, and choice accuracy and mean reaction times as a function of stimulus strength. The theory also correctly predicts that urgency signals in the brain should be independent of the difficulty, or stimulus strength, at each trial.

Competitive integration of time and reward explains value-sensitive foraging decisions and frontal cortex ramping dynamics.

The ability to make advantageous decisions is critical for animals to ensure their survival. Patch foraging is a natural decision-making process in which animals decide when to leave a patch of depleting resources to search for a new one. To study the algorithmic and neural basis of patch foraging behavior in a controlled laboratory setting, we developed a virtual foraging task for head-fixed mice. Mouse behavior could be explained by ramp-to-threshold models integrating time and rewards antagonistically. Accurate behavioral modeling required inclusion of a slowly varying "patience" variable, which modulated sensitivity to time. To investigate the neural basis of this decision-making process, we performed dense electrophysiological recordings with Neuropixels probes broadly throughout frontal cortex and underlying subcortical areas. We found that decision variables from the reward integrator model were represented in neural activity, most robustly in frontal cortical areas. Regression modeling followed by unsupervised clustering identified a subset of neurons with ramping activity. These neurons' firing rates ramped up gradually in single trials over long time scales (up to tens of seconds), were inhibited by rewards, and were better described as being generated by a continuous ramp rather than a discrete stepping process. Together, these results identify reward integration via a continuous ramping process in frontal cortex as a likely candidate for the mechanism by which the mammalian brain solves patch foraging problems.

Causal inference during closed-loop navigation: parsing of self- and object-motion.

A key computation in building adaptive internal models of the external world is to ascribe sensory signals to their likely cause(s), a process of causal inference (CI). CI is well studied within the framework of two-alternative forced-choice tasks, but less well understood within the cadre of naturalistic action-perception loops. Here, we examine the process of disambiguating retinal motion caused by self- and/or object-motion during closed-loop navigation. First, we derive a normative account specifying how observers ought to intercept hidden and moving targets given their belief about (i) whether retinal motion was caused by the target moving, and (ii) if so, with what velocity. Next, in line with the modelling results, we show that humans report targets as stationary and steer towards their initial rather than final position more often when they are themselves moving, suggesting a putative misattribution of object-motion to the self. Further, we predict that observers should misattribute retinal motion more often: (i) during passive rather than active self-motion (given the lack of an efference copy informing self-motion estimates in the former), and (ii) when targets are presented eccentrically rather than centrally (given that lateral self-motion flow vectors are larger at eccentric locations during forward self-motion). Results support both of these predictions. Lastly, analysis of eye movements show that, while initial saccades toward targets were largely accurate regardless of the self-motion condition, subsequent gaze pursuit was modulated by target velocity during object-only motion, but not during concurrent object- and self-motion. These results demonstrate CI within action-perception loops, and suggest a protracted temporal unfolding of the computations characterizing CI. This article is part of the theme issue 'Decision and control processes in multisensory perception'.

Causal inference during closed-loop navigation: parsing of self- and object-motion.

A key computation in building adaptive internal models of the external world is to ascribe sensory signals to their likely cause(s), a process of Bayesian Causal Inference (CI). CI is well studied within the framework of two-alternative forced-choice tasks, but less well understood within the cadre of naturalistic action-perception loops. Here, we examine the process of disambiguating retinal motion caused by self- and/or object-motion during closed-loop navigation. First, we derive a normative account specifying how observers ought to intercept hidden and moving targets given their belief over (i) whether retinal motion was caused by the target moving, and (ii) if so, with what velocity. Next, in line with the modeling results, we show that humans report targets as stationary and steer toward their initial rather than final position more often when they are themselves moving, suggesting a misattribution of object-motion to the self. Further, we predict that observers should misattribute retinal motion more often: (i) during passive rather than active self-motion (given the lack of an efference copy informing self-motion estimates in the former), and (ii) when targets are presented eccentrically rather than centrally (given that lateral self-motion flow vectors are larger at eccentric locations during forward self-motion). Results confirm both of these predictions. Lastly, analysis of eye-movements show that, while initial saccades toward targets are largely accurate regardless of the self-motion condition, subsequent gaze pursuit was modulated by target velocity during object-only motion, but not during concurrent object- and self-motion. These results demonstrate CI within action-perception loops, and suggest a protracted temporal unfolding of the computations characterizing CI.

Nerve injury disrupts temporal processing in the spinal cord dorsal horn through alterations in PV + interneurons.

How mechanical allodynia following nerve injury is encoded in patterns of neural activity in the spinal cord dorsal horn (DH) is not known. We addressed this using the spared nerve injury model of neuropathic pain and in vivo electrophysiological recordings. Surprisingly, despite dramatic behavioral over-reactivity to mechanical stimuli following nerve injury, an overall increase in sensitivity or reactivity of DH neurons was not observed. We did, however, observe a marked decrease in correlated neural firing patterns, including the synchrony of mechanical stimulus-evoked firing, across the DH. Alterations in DH temporal firing patterns were recapitulated by silencing DH parvalbumin + (PV + ) inhibitory interneurons, previously implicated in mechanical allodynia, as were allodynic pain-like behaviors in mice. These findings reveal decorrelated DH network activity, driven by alterations in PV + interneurons, as a prominent feature of neuropathic pain, and suggest that restoration of proper temporal activity is a potential treatment for chronic neuropathic pain.

A large majority of awake hippocampal sharp-wave ripples feature spatial trajectories with momentum.

During periods of rest, hippocampal place cells feature bursts of activity called sharp-wave ripples (SWRs). Heuristic approaches have revealed that a small fraction of SWRs appear to "simulate" trajectories through the environment, called awake hippocampal replay. However, the functional role of a majority of these SWRs remains unclear. We find, using Bayesian model comparison of state-space models to characterize the spatiotemporal dynamics embedded in SWRs, that almost all SWRs of foraging rodents simulate such trajectories. Furthermore, these trajectories feature momentum, or inertia in their velocities, that mirrors the animals' natural movement, in contrast to replay events during sleep, which lack such momentum. Last, we show that past analyses of replayed trajectories for navigational planning were biased by the heuristic SWR sub-selection. Our findings thus identify the dominant function of awake SWRs as simulating trajectories with momentum and provide a principled foundation for future work on their computational function.

Visual motion perception as online hierarchical inference.

Identifying the structure of motion relations in the environment is critical for navigation, tracking, prediction, and pursuit. Yet, little is known about the mental and neural computations that allow the visual system to infer this structure online from a volatile stream of visual information. We propose online hierarchical Bayesian inference as a principled solution for how the brain might solve this complex perceptual task. We derive an online Expectation-Maximization algorithm that explains human percepts qualitatively and quantitatively for a diverse set of stimuli, covering classical psychophysics experiments, ambiguous motion scenes, and illusory motion displays. We thereby identify normative explanations for the origin of human motion structure perception and make testable predictions for future psychophysics experiments. The proposed online hierarchical inference model furthermore affords a neural network implementation which shares properties with motion-sensitive cortical areas and motivates targeted experiments to reveal the neural representations of latent structure.

Efficient stabilization of imprecise statistical inference through conditional belief updating.

Statistical inference is the optimal process for forming and maintaining accurate beliefs about uncertain environments. However, human inference comes with costs due to its associated biases and limited precision. Indeed, biased or imprecise inference can trigger variable beliefs and unwarranted changes in behaviour. Here, by studying decisions in a sequential categorization task based on noisy visual stimuli, we obtained converging evidence that humans reduce the variability of their beliefs by updating them only when the reliability of incoming sensory information is judged as sufficiently strong. Instead of integrating the evidence provided by all stimuli, participants actively discarded as much as a third of stimuli. This conditional belief updating strategy shows good test-retest reliability, correlates with perceptual confidence and explains human behaviour better than previously described strategies. This seemingly suboptimal strategy not only reduces the costs of imprecise computations but also, counterintuitively, increases the accuracy of resulting decisions.

Controllability boosts neural and cognitive signatures of changes-of-mind in uncertain environments.

In uncertain environments, seeking information about alternative choice options is essential for adaptive learning and decision-making. However, information seeking is usually confounded with changes-of-mind about the reliability of the preferred option. Here, we exploited the fact that information seeking requires control over which option to sample to isolate its behavioral and neurophysiological signatures. We found that changes-of-mind occurring with control require more evidence against the current option, are associated with reduced confidence, but are nevertheless more likely to be confirmed on the next decision. Multimodal neurophysiological recordings showed that these changes-of-mind are preceded by stronger activation of the dorsal attention network in magnetoencephalography, and followed by increased pupil-linked arousal during the presentation of decision outcomes. Together, these findings indicate that information seeking increases the saliency of evidence perceived as the direct consequence of one's own actions.

Optimal policy for attention-modulated decisions explains human fixation behavior.

Traditional accumulation-to-bound decision-making models assume that all choice options are processed with equal attention. In real life decisions, however, humans alternate their visual fixation between individual items to efficiently gather relevant information (Yang et al., 2016). These fixations also causally affect one's choices, biasing them toward the longer-fixated item (Krajbich et al., 2010). We derive a normative decision-making model in which attention enhances the reliability of information, consistent with neurophysiological findings (Cohen and Maunsell, 2009). Furthermore, our model actively controls fixation changes to optimize information gathering. We show that the optimal model reproduces fixation-related choice biases seen in humans and provides a Bayesian computational rationale for this phenomenon. This insight led to additional predictions that we could confirm in human data. Finally, by varying the relative cognitive advantage conferred by attention, we show that decision performance is benefited by a balanced spread of resources between the attended and unattended items.

Human visual motion perception shows hallmarks of Bayesian structural inference.

Motion relations in visual scenes carry an abundance of behaviorally relevant information, but little is known about how humans identify the structure underlying a scene's motion in the first place. We studied the computations governing human motion structure identification in two psychophysics experiments and found that perception of motion relations showed hallmarks of Bayesian structural inference. At the heart of our research lies a tractable task design that enabled us to reveal the signatures of probabilistic reasoning about latent structure. We found that a choice model based on the task's Bayesian ideal observer accurately matched many facets of human structural inference, including task performance, perceptual error patterns, single-trial responses, participant-specific differences, and subjective decision confidence-especially, when motion scenes were ambiguous and when object motion was hierarchically nested within other moving reference frames. Our work can guide future neuroscience experiments to reveal the neural mechanisms underlying higher-level visual motion perception.