A Dynamic Bayesian Observer Model Reveals Origins of Bias in Visual Path Integration

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

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

Context-dependence of deterministic and nondeterministic contributions to closed-loop steering control

In natural circumstances, sensory systems operate in a closed loop with motor output, whereby actions shape subsequent sensory experiences. A prime example of this is the sensorimotor processing required to align one's direction of travel, or heading, with one's goal, a behavior we refer to as steering. In steering, motor outputs work to eliminate errors between the direction of heading and the goal, modifying subsequent errors in the process. The closed-loop nature of the behavior makes it challenging to determine how deterministic and nondeterministic processes contribute to behavior. We overcome this by applying a nonparametric, linear kernel-based analysis to behavioral data of monkeys steering through a virtual environment in two experimental contexts. In a given context, the results were consistent with previous work that described the transformation as a second-order linear system. Classically, the parameters of such second-order models are associated with physical properties of the limb such as viscosity and stiffness that are commonly assumed to be approximately constant. By contrast, we found that the fit kernels differed strongly across tasks in these and other parameters, suggesting context-dependent changes in neural and biomechanical processes. We additionally fit residuals to a simple noise model and found that the form of the noise was highly conserved across both contexts and animals. Strikingly, the fitted noise also closely matched that found previously in a human steering task. Altogether, this work presents a kernel-based analysis that characterizes the context-dependence of deterministic and non-deterministic components of a closed-loop sensorimotor task.

Context-invariant beliefs are supported by dynamic reconfiguration of single unit functional connectivity in prefrontal cortex of male macaques

Natural behaviors occur in closed action-perception loops and are supported by dynamic and flexible beliefs abstracted away from our immediate sensory milieu. How this real-world flexibility is instantiated in neural circuits remains unknown. Here, we have male macaques navigate in a virtual environment by primarily leveraging sensory (optic flow) signals, or by more heavily relying on acquired internal models. We record single-unit spiking activity simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and the dorso-lateral prefrontal cortex (dlPFC). Results show that while animals were able to maintain adaptive task-relevant beliefs regardless of sensory context, the fine-grain statistical dependencies between neurons, particularly in 7a and dlPFC, dynamically remapped with the changing computational demands. In dlPFC, but not 7a, destroying these statistical dependencies abolished the area's ability for cross-context decoding. Lastly, correlational analyses suggested that the more unit-to-unit couplings remapped in dlPFC, and the less they did so in MSTd, the less were population codes and behavior impacted by the loss of sensory evidence. We conclude that dynamic functional connectivity between neurons in prefrontal cortex maintain a stable population code and context-invariant beliefs during naturalistic behavior.

Task-anchored grid cell firing is selectively associated with successful path integration-dependent behaviour

Grid firing fields have been proposed as a neural substrate for spatial localisation in general or for path integration in particular. To distinguish these possibilities, we investigate firing of grid and non-grid cells in the mouse medial entorhinal cortex during a location memory task. We find that grid firing can either be anchored to the task environment, or can encode distance travelled independently of the task reference frame. Anchoring varied between and within sessions, while spatial firing of non-grid cells was either coherent with the grid population, or was stably anchored to the task environment. We took advantage of the variability in task-anchoring to evaluate whether and when encoding of location by grid cells might contribute to behaviour. We find that when reward location is indicated by a visual cue, performance is similar regardless of whether grid cells are task-anchored or not, arguing against a role for grid representations when location cues are available. By contrast, in the absence of the visual cue, performance was enhanced when grid cells were anchored to the task environment. Our results suggest that anchoring of grid cells to task reference frames selectively enhances performance when path integration is required.

Self-motion perception and sequential decision-making: where are we heading?

To navigate and guide adaptive behaviour in a dynamic environment, animals must accurately estimate their own motion relative to the external world. This is a fundamentally multisensory process involving integration of visual, vestibular and kinesthetic inputs. Ideal observer models, paired with careful neurophysiological investigation, helped to reveal how visual and vestibular signals are combined to support perception of linear self-motion direction, or heading. Recent work has extended these findings by emphasizing the dimension of time, both with regard to stimulus dynamics and the trade-off between speed and accuracy. Both time and certainty-i.e. the degree of confidence in a multisensory decision-are essential to the ecological goals of the system: terminating a decision process is necessary for timely action, and predicting one's accuracy is critical for making multiple decisions in a sequence, as in navigation. Here, we summarize a leading model for multisensory decision-making, then show how the model can be extended to study confidence in heading discrimination. Lastly, we preview ongoing efforts to bridge self-motion perception and navigation per se, including closed-loop virtual reality and active self-motion. The design of unconstrained, ethologically inspired tasks, accompanied by large-scale neural recordings, raise promise for a deeper understanding of spatial perception and decision-making in the behaving animal. 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 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'.

Context-invariant beliefs are supported by dynamic reconfiguration of single unit functional connectivity in prefrontal cortex

Natural behaviors occur in closed action-perception loops and are supported by dynamic and flexible beliefs abstracted away from our immediate sensory milieu. How this real-world flexibility is instantiated in neural circuits remains unknown. Here we have macaques navigate in a virtual environment by primarily leveraging sensory (optic flow) signals, or by more heavily relying on acquired internal models. We record single-unit spiking activity simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and the dorso-lateral prefrontal cortex (dlPFC). Results show that while animals were able to maintain adaptive task-relevant beliefs regardless of sensory context, the fine-grain statistical dependencies between neurons, particularly in 7a and dlPFC, dynamically remapped with the changing computational demands. In dlPFC, but not 7a, destroying these statistical dependencies abolished the area's ability for cross-context decoding. Lastly, correlation analyses suggested that the more unit-to-unit couplings remapped in dlPFC, and the less they did so in MSTd, the less were population codes and behavior impacted by the loss of sensory evidence. We conclude that dynamic functional connectivity between prefrontal cortex neurons maintains a stable population code and context-invariant beliefs during naturalistic behavior with closed action-perception loops.

Computational cross-species views of the hippocampal formation

The discovery of place cells and head direction cells in the hippocampal formation of freely foraging rodents has led to an emphasis of its role in encoding allocentric spatial relationships. In contrast, studies in head-fixed primates have additionally found representations of spatial views. We review recent experiments in freely moving monkeys that expand upon these findings and show that postural variables such as eye/head movements strongly influence neural activity in the hippocampal formation, suggesting that the function of the hippocampus depends on where the animal looks. We interpret these results in the light of recent studies in humans performing challenging navigation tasks which suggest that depending on the context, eye/head movements serve one of two roles-gathering information about the structure of the environment (active sensing) or externalizing the contents of internal beliefs/deliberation (embodied cognition). These findings prompt future experimental investigations into the information carried by signals flowing between the hippocampal formation and the brain regions controlling postural variables, and constitute a basis for updating computational theories of the hippocampal system to accommodate the influence of eye/head movements.

Dynamical latent state computation in the male macaque posterior parietal cortex

Success in many real-world tasks depends on our ability to dynamically track hidden states of the world. We hypothesized that neural populations estimate these states by processing sensory history through recurrent interactions which reflect the internal model of the world. To test this, we recorded brain activity in posterior parietal cortex (PPC) of monkeys navigating by optic flow to a hidden target location within a virtual environment, without explicit position cues. In addition to sequential neural dynamics and strong interneuronal interactions, we found that the hidden state - monkey's displacement from the goal - was encoded in single neurons, and could be dynamically decoded from population activity. The decoded estimates predicted navigation performance on individual trials. Task manipulations that perturbed the world model induced substantial changes in neural interactions, and modified the neural representation of the hidden state, while representations of sensory and motor variables remained stable. The findings were recapitulated by a task-optimized recurrent neural network model, suggesting that task demands shape the neural interactions in PPC, leading them to embody a world model that consolidates information and tracks task-relevant hidden states.

Temporal stability of human heading perception

Humans are capable of accurately judging their heading from optic flow during straight forward self-motion. Despite the global coherence in the optic flow field, however, visual clutter and other naturalistic conditions create constant flux on the eye. This presents a problem that must be overcome to accurately perceive heading from optic flow-the visual system must maintain sensitivity to optic flow variations that correspond with actual changes in self-motion and disregard those that do not. One solution could involve integrating optic flow over time to stabilize heading signals while suppressing transient fluctuations. Stability, however, may come at the cost of sluggishness. Here, we investigate the stability of human heading perception when subjects judge their heading after the simulated direction of self-motion changes. We found that the initial heading exerted an attractive influence on judgments of the final heading. Consistent with an evolving heading representation, bias toward the initial heading increased with the size of the heading change and as the viewing duration of the optic flow consistent with the final heading decreased. Introducing periods of sensory dropout (blackouts) later in the trial increased bias whereas an earlier one did not. Simulations of a neural model, the Competitive Dynamics Model, demonstrates that a mechanism that produces an evolving heading signal through recurrent competitive interactions largely captures the human data. Our findings characterize how the visual system balances stability in heading perception with sensitivity to change and support the hypothesis that heading perception evolves over time.

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.

The accuracy of object motion perception during locomotion

Human observers are capable of perceiving the motion of moving objects relative to the stationary world, even while undergoing self-motion. Perceiving world-relative object motion is complicated because the local optical motion of objects is influenced by both observer and object motion, and reflects object motion in observer coordinates. It has been proposed that observers recover world-relative object motion using global optic flow to factor out the influence of self-motion. However, object-motion judgments during simulated self-motion are biased, as if the visual system cannot completely compensate for the influence of self-motion. Recently, Xie et al. demonstrated that humans are capable of accurately judging world-relative object motion when self-motion is real, actively generated by walking, and accompanied by optic flow. However, the conditions used in that study differ from those found in the real world in that the moving object was a small dot with negligible optical expansion that moved at a fixed speed in retinal (rather than world) coordinates and was only visible for 500 ms. The present study investigated the accuracy of object motion perception under more ecologically valid conditions. Subjects judged the trajectory of an object that moved through a virtual environment viewed through a head-mounted display. Judgments exhibited bias in the case of simulated self-motion but were accurate when self-motion was real, actively generated, and accompanied by optic flow. The findings are largely consistent with the conclusions of Xie et al. and demonstrate that observers are capable of accurately perceiving world-relative object motion under ecologically valid conditions.

Predictive steering: integration of artificial motor signals in self-motion estimation

The brain's computations for active and passive self-motion estimation can be unified with a single model that optimally combines vestibular and visual signals with sensory predictions based on efference copies. It is unknown whether this theoretical framework also applies to the integration of artificial motor signals, such as those that occur when driving a car, or whether self-motion estimation in this situation relies on sole feedback control. Here, we examined if training humans to control a self-motion platform leads to the construction of an accurate internal model of the mapping between the steering movement and the vestibular reafference. Participants (n = 15) sat on a linear motion platform and actively controlled the platform's velocity using a steering wheel to translate their body to a memorized visual target (motion condition). We compared their steering behavior to that of participants (n = 15) who remained stationary and instead aligned a nonvisible line with the target (stationary condition). To probe learning, the gain between the steering wheel angle and the platform or line velocity changed abruptly twice during the experiment. These gain changes were virtually undetectable in the displacement error in the motion condition, whereas clear deviations were observed in the stationary condition, showing that participants in the motion condition made within-trial changes to their steering behavior. We conclude that vestibular feedback allows not only the online control of steering but also a rapid adaptation to the gain changes to update the brain's internal model of the mapping between the steering movement and the vestibular reafference.NEW & NOTEWORTHY Perception of self-motion is known to depend on the integration of sensory signals and, when the motion is self-generated, the predicted sensory reafference based on motor efference copies. Here we show, using a closed-loop steering experiment with a direct coupling between the steering movement and the vestibular self-motion feedback, that humans are also able to integrate artificial motor signals, like the motor signals that occur when driving a car.

Naturalistic neuroscience and virtual reality

Virtual reality (VR) is one of the techniques that became particularly popular in neuroscience over the past few decades. VR experiments feature a closed-loop between sensory stimulation and behavior. Participants interact with the stimuli and not just passively perceive them. Several senses can be stimulated at once, large-scale environments can be simulated as well as social interactions. All of this makes VR experiences more natural than those in traditional lab paradigms. Compared to the situation in field research, a VR simulation is highly controllable and reproducible, as required of a laboratory technique used in the search for neural correlates of perception and behavior. VR is therefore considered a middle ground between ecological validity and experimental control. In this review, I explore the potential of VR in eliciting naturalistic perception and behavior in humans and non-human animals. In this context, I give an overview of recent virtual reality approaches used in neuroscientific research.

Coding of latent variables in sensory, parietal, and frontal cortices during closed-loop virtual navigation

We do not understand how neural nodes operate and coordinate within the recurrent action-perception loops that characterize naturalistic self-environment interactions. Here, we record single-unit spiking activity and local field potentials (LFPs) simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and dorsolateral prefrontal cortex (dlPFC) as monkeys navigate in virtual reality to 'catch fireflies'. This task requires animals to actively sample from a closed-loop virtual environment while concurrently computing continuous latent variables: (i) the distance and angle travelled (i.e., path integration) and (ii) the distance and angle to a memorized firefly location (i.e., a hidden spatial goal). We observed a patterned mixed selectivity, with the prefrontal cortex most prominently coding for latent variables, parietal cortex coding for sensorimotor variables, and MSTd most often coding for eye movements. However, even the traditionally considered sensory area (i.e., MSTd) tracked latent variables, demonstrating path integration and vector coding of hidden spatial goals. Further, global encoding profiles and unit-to-unit coupling (i.e., noise correlations) suggested a functional subnetwork composed by MSTd and dlPFC, and not between these and 7a, as anatomy would suggest. We show that the greater the unit-to-unit coupling between MSTd and dlPFC, the more the animals' gaze position was indicative of the ongoing location of the hidden spatial goal. We suggest this MSTd-dlPFC subnetwork reflects the monkeys' natural and adaptive task strategy wherein they continuously gaze toward the location of the (invisible) target. Together, these results highlight the distributed nature of neural coding during closed action-perception loops and suggest that fine-grain functional subnetworks may be dynamically established to subserve (embodied) task strategies.

Shared and specialized coding across posterior cortical areas for dynamic navigation decisions

Animals adaptively integrate sensation, planning, and action to navigate toward goal locations in ever-changing environments, but the functional organization of cortex supporting these processes remains unclear. We characterized encoding in approximately 90,000 neurons across the mouse posterior cortex during a virtual navigation task with rule switching. The encoding of task and behavioral variables was highly distributed across cortical areas but differed in magnitude, resulting in three spatial gradients for visual cue, spatial position plus dynamics of choice formation, and locomotion, with peaks respectively in visual, retrosplenial, and parietal cortices. Surprisingly, the conjunctive encoding of these variables in single neurons was similar throughout the posterior cortex, creating high-dimensional representations in all areas instead of revealing computations specialized for each area. We propose that, for guiding navigation decisions, the posterior cortex operates in parallel rather than hierarchically, and collectively generates a state representation of the behavior and environment, with each area specialized in handling distinct information modalities.

Cortical Mechanisms of Multisensory Linear Self-motion Perception

Accurate self-motion perception, which is critical for organisms to survive, is a process involving multiple sensory cues. The two most powerful cues are visual (optic flow) and vestibular (inertial motion). Psychophysical studies have indicated that humans and nonhuman primates integrate the two cues to improve the estimation of self-motion direction, often in a statistically Bayesian-optimal way. In the last decade, single-unit recordings in awake, behaving animals have provided valuable neurophysiological data with a high spatial and temporal resolution, giving insight into possible neural mechanisms underlying multisensory self-motion perception. Here, we review these findings, along with new evidence from the most recent studies focusing on the temporal dynamics of signals in different modalities. We show that, in light of new data, conventional thoughts about the cortical mechanisms underlying visuo-vestibular integration for linear self-motion are challenged. We propose that different temporal component signals may mediate different functions, a possibility that requires future studies.

Sensory Evidence Accumulation Using Optic Flow in a Naturalistic Navigation Task

Sensory evidence accumulation is considered a hallmark of decision-making in noisy environments. Integration of sensory inputs has been traditionally studied using passive stimuli, segregating perception from action. Lessons learned from this approach, however, may not generalize to ethological behaviors like navigation, where there is an active interplay between perception and action. We designed a sensory-based sequential decision task in virtual reality in which humans and monkeys navigated to a memorized location by integrating optic flow generated by their own joystick movements. A major challenge in such closed-loop tasks is that subjects' actions will determine future sensory input, causing ambiguity about whether they rely on sensory input rather than expectations based solely on a learned model of the dynamics. To test whether subjects integrated optic flow over time, we used three independent experimental manipulations, unpredictable optic flow perturbations, which pushed subjects off their trajectory; gain manipulation of the joystick controller, which changed the consequences of actions; and manipulation of the optic flow density, which changed the information borne by sensory evidence. Our results suggest that both macaques (male) and humans (female/male) relied heavily on optic flow, thereby demonstrating a critical role for sensory evidence accumulation during naturalistic action-perception closed-loop tasks.SIGNIFICANCE STATEMENT The temporal integration of evidence is a fundamental component of mammalian intelligence. Yet, it has traditionally been studied using experimental paradigms that fail to capture the closed-loop interaction between actions and sensations inherent in real-world continuous behaviors. These conventional paradigms use binary decision tasks and passive stimuli with statistics that remain stationary over time. Instead, we developed a naturalistic visuomotor visual navigation paradigm that mimics the causal structure of real-world sensorimotor interactions and probed the extent to which participants integrate sensory evidence by adding task manipulations that reveal complementary aspects of the computation.

Individual beliefs about temporal continuity explain variation of perceptual biases

Perception of magnitudes such as duration or distance is often found to be systematically biased. The biases, which result from incorporating prior knowledge in the perceptual process, can vary considerably between individuals. The variations are commonly attributed to differences in sensory precision and reliance on priors. However, another factor not considered so far is the implicit belief about how successive sensory stimuli are generated: independently from each other or with certain temporal continuity. The main types of explanatory models proposed so far-static or iterative-mirror this distinction but cannot adequately explain individual biases. Here we propose a new unifying model that explains individual variation as combination of sensory precision and beliefs about temporal continuity and predicts the experimentally found changes in biases when altering temporal continuity. Thus, according to the model, individual differences in perception depend on beliefs about how stimuli are generated in the world.

Prior Expectations in Visual Speed Perception Predict Encoding Characteristics of Neurons in Area MT

Bayesian inference provides an elegant theoretical framework for understanding the characteristic biases and discrimination thresholds in visual speed perception. However, the framework is difficult to validate because of its flexibility and the fact that suitable constraints on the structure of the sensory uncertainty have been missing. Here, we demonstrate that a Bayesian observer model constrained by efficient coding not only well explains human visual speed perception but also provides an accurate quantitative account of the tuning characteristics of neurons known for representing visual speed. Specifically, we found that the population coding accuracy for visual speed in area MT ("neural prior") is precisely predicted by the power-law, slow-speed prior extracted from fitting the Bayesian observer model to psychophysical data ("behavioral prior") to the point that the two priors are indistinguishable in a cross-validation model comparison. Our results demonstrate a quantitative validation of the Bayesian observer model constrained by efficient coding at both the behavioral and neural levels.SIGNIFICANCE STATEMENT Statistical regularities of the environment play an important role in shaping both neural representations and perceptual behavior. Most previous work addressed these two aspects independently. Here we present a quantitative validation of a theoretical framework that makes joint predictions for neural coding and behavior, based on the assumption that neural representations of sensory information are efficient but also optimally used in generating a percept. Specifically, we demonstrate that the neural tuning characteristics for visual speed in brain area MT are precisely predicted by the statistical prior expectations extracted from psychophysical data. As such, our results provide a normative link between perceptual behavior and the neural representation of sensory information in the brain.

Influence of sensory modality and control dynamics on human path integration

Path integration is a sensorimotor computation that can be used to infer latent dynamical states by integrating self-motion cues. We studied the influence of sensory observation (visual/vestibular) and latent control dynamics (velocity/acceleration) on human path integration using a novel motion-cueing algorithm. Sensory modality and control dynamics were both varied randomly across trials, as participants controlled a joystick to steer to a memorized target location in virtual reality. Visual and vestibular steering cues allowed comparable accuracies only when participants controlled their acceleration, suggesting that vestibular signals, on their own, fail to support accurate path integration in the absence of sustained acceleration. Nevertheless, performance in all conditions reflected a failure to fully adapt to changes in the underlying control dynamics, a result that was well explained by a bias in the dynamics estimation. This work demonstrates how an incorrect internal model of control dynamics affects navigation in volatile environments in spite of continuous sensory feedback.

Cognitive, Systems, and Computational Neurosciences of the Self in Motion

Navigating by path integration requires continuously estimating one's self-motion. This estimate may be derived from visual velocity and/or vestibular acceleration signals. Importantly, these senses in isolation are ill-equipped to provide accurate estimates, and thus visuo-vestibular integration is an imperative. After a summary of the visual and vestibular pathways involved, the crux of this review focuses on the human and theoretical approaches that have outlined a normative account of cue combination in behavior and neurons, as well as on the systems neuroscience efforts that are searching for its neural implementation. We then highlight a contemporary frontier in our state of knowledge: understanding how velocity cues with time-varying reliabilities are integrated into an evolving position estimate over prolonged time periods. Further, we discuss how the brain builds internal models inferring when cues ought to be integrated versus segregated-a process of causal inference. Lastly, we suggest that the study of spatial navigation has not yet addressed its initial condition: self-location.

Vision-based speedometer regulates human walking

Can we recover self-motion from vision? This basic issue remains unsolved since, while the human visual system is known to estimate the direction of self-motion from optic flow, it remains unclear whether it also estimates the speed. Importantly, the latter requires disentangling self-motion speed and depths of objects in the scene as retinal velocity depends on both. Here we show that our automatic regulator of walking speed based on vision, which estimates and maintains the speed to its preferred range by adjusting stride length, is robust to changes in the depths. The robustness was not explained by temporal-frequency-based speed coding previously suggested to underlie depth-invariant object-motion perception. Meanwhile, it broke down, not only when the interocular distance was virtually manipulated but also when monocular depth cues were deceptive. These observations suggest that our visuomotor system embeds a speedometer that calculates self-motion speed from vision by integrating monocular/binocular depth and motion cues.

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Changes in optic flow speed triggers implicit adjustments of walking speed

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The response is invariant with respect to the depths of objects in the scene

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The invariance is not explained by temporal-frequency-based speed coding

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Both binocular and monocular depth cues contribute to the invariance

Bayesian decision theory and navigation

Spatial navigation is a complex cognitive activity that depends on perception, action, memory, reasoning, and problem-solving. Effective navigation depends on the ability to combine information from multiple spatial cues to estimate one's position and the locations of goals. Spatial cues include landmarks, and other visible features of the environment, and body-based cues generated by self-motion (vestibular, proprioceptive, and efferent information). A number of projects have investigated the extent to which visual cues and body-based cues are combined optimally according to statistical principles. Possible limitations of these investigations are that they have not accounted for navigators' prior experiences with or assumptions about the task environment and have not tested complete decision models. We examine cue combination in spatial navigation from a Bayesian perspective and present the fundamental principles of Bayesian decision theory. We show that a complete Bayesian decision model with an explicit loss function can explain a discrepancy between optimal cue weights and empirical cues weights observed by (Chen et al. Cognitive Psychology, 95, 105-144, 2017) and that the use of informative priors to represent cue bias can explain the incongruity between heading variability and heading direction observed by (Zhao and Warren 2015b, Psychological Science, 26[6], 915-924). We also discuss (Petzschner and Glasauer's , Journal of Neuroscience, 31(47), 17220-17229, 2011) use of priors to explain biases in estimates of linear displacements during visual path integration. We conclude that Bayesian decision theory offers a productive theoretical framework for investigating human spatial navigation and believe that it will lead to a deeper understanding of navigational behaviors.

The perceptual dynamics of the contrast induced speed bias

In this article we present a temporal extension of the slow motion prior model to generate predictions regarding the temporal evolution of the contrast induced speed bias. We further tested these predictions using a novel experimental paradigm that allows us to measure the dynamic perceptual difference between stimuli through a series of manual pursuit open loop tasks. Results show good agreement with our model's predictions. The main findings reveal that hand speed dynamics are affected by stimulus contrast in a way that is consistent with a dynamic model of motion perception that assumes a slow motion prior. The proposed model also confirms observations made in previous studies that suggest that motion bias persisted even at high contrast as a consequence of the dynamics of the slow motion prior.

A unifying Bayesian framework accounting for spatiotemporal interferences with a deceleration tendency

Spatial and temporal levels of information processing interfere with each other. The Kappa effect is a well-known spatiotemporal interference in which the estimated time between two lights increases as the distance between them increases, showing a deceleration tendency. A classical model attributes this interference to constant speeds and predicts a linear relation, whereas a slowness model attributes the interference to slow speeds and proposes that the tendency is due to the uncertainty of stimuli locations. This study integrated a unifying Bayesian framework with the classical model and argued that this tendency is the result of the Weber-Fechner law. This hypothesis was tested via two time discrimination tasks that manipulated the uncertainty of stimuli locations and the distance between stimuli. Experiment 1 showed that the estimated time was not modulated by the uncertainty of the stimuli locations. Experiment 2 revealed that the behavioral predictions made by the Bayesian model on logarithmic scales were more accurate than those made by the linear model. Our results suggest that the deceleration tendency in the Kappa effect is the result of the Weber-Fechner law.

Eye-Movement-Based Assessment of the Perceptual Consequences of Glaucomatous and Neuro-Ophthalmological Visual Field Defects

Purpose

Assessing the presence of visual field defects (VFD) through procedures such as perimetry is an essential aspect of the management and diagnosis of ocular disorders. However, even the latest perimetric methods have shortcomings-a high cognitive demand and requiring prolonged stable fixation and feedback through a button response. Consequently, an approach using eye movements (EM)-as a natural response-has been proposed as an alternate way to evaluate the presence of VFD. This approach has given good results for computer-simulated VFD. However, its use in patients is not well documented yet. Here we use this new approach to quantify the spatiotemporal properties (STP) of EM of various patients suffering from glaucoma and neuro-ophthalmological VFD and controls.

Methods

In total, 15 glaucoma patients, 37 patients with a neuro-ophthalmological disorder, and 21 controls performed a visual tracking task while their EM were being recorded. Subsequently, the STP of EM were quantified using a cross-correlogram analysis. Decision trees were used to identify the relevant STP and classify the populations.

Results

We achieved a classification accuracy of 94.5% (TPR/sensitivity = 96%, TNR/specificity = 90%) between patients and controls. Individually, the algorithm achieved an accuracy of 86.3% (TPR for neuro-ophthalmology [97%], glaucoma [60%], and controls [86%]). The STP of EM were highly similar across two different control cohorts.

Conclusions

In an ocular tracking task, patients with VFD due to different underlying pathology make EM with distinctive STP. These properties are interpretable based on different clinical characteristics of patients and can be used for patient classification.

Translational Relevance

Our EM-based screening tool may complement existing perimetric techniques in clinical practice.

Supporting generalization in non-human primate behavior by tapping into structural knowledge: Examples from sensorimotor mappings, inference, and decision-making

The complex behaviors we ultimately wish to understand are far from those currently used in systems neuroscience laboratories. A salient difference are the closed loops between action and perception prominently present in natural but not laboratory behaviors. The framework of reinforcement learning and control naturally wades across action and perception, and thus is poised to inform the neurosciences of tomorrow, not only from a data analyses and modeling framework, but also in guiding experimental design. We argue that this theoretical framework emphasizes active sensing, dynamical planning, and the leveraging of structural regularities as key operations for intelligent behavior within uncertain, time-varying environments. Similarly, we argue that we may study natural task strategies and their neural circuits without over-training animals when the tasks we use tap into our animal's structural knowledge. As proof-of-principle, we teach animals to navigate through a virtual environment - i.e., explore a well-defined and repetitive structure governed by the laws of physics - using a joystick. Once these animals have learned to 'drive', without further training they naturally (i) show zero- or one-shot learning of novel sensorimotor contingencies, (ii) infer the evolving path of dynamically changing latent variables, and (iii) make decisions consistent with maximizing reward rate. Such task designs allow for the study of flexible and generalizable, yet controlled, behaviors. In turn, they allow for the exploitation of pillars of intelligence - flexibility, prediction, and generalization -, properties whose neural underpinning have remained elusive.

Vestibular cues improve landmark-based route navigation: A simulated driving study

It is well established that humans use self-motion and landmark cues to successfully navigate their environment. Existing research has demonstrated a critical role of the vestibular system in supporting navigation across many species. However, less is known about how vestibular cues interact with landmarks to promote successful navigation in humans. In the present study, we used a motion simulator to manipulate the presence or absence of vestibular cues during a virtual navigation task. Participants learned routes to a target destination in three different landmark blocks in a virtual town: one with proximal landmarks, one with distal landmarks, and one with no landmarks present. Afterwards, they were tested on their ability to retrace the route and find the target destination. We observed a significant interaction between vestibular cues and proximal landmarks, demonstrating that the potential for vestibular cues to improve route navigation is dependent on landmarks that are present in the environment. In particular, vestibular cues significantly improved route navigation when proximal landmarks were present, but this was not significant when distal landmarks or no landmarks were present. Overall, our results indicate that landmarks play an important role in the successful incorporation of vestibular cues to human spatial navigation.

Retrosplenial Segregation Reflects the Navigation Load During Ambulatory Movement

Spatial navigation is a complex cognitive process based on vestibular, proprioceptive, and visualcues that are integrated and processed by an extensive network of brain areas. The retrosplenial complex (RSC) is an integral part of coordination and translation between spatial reference frames. Previous studies have demonstrated that the RSC is active during a spatial navigation tasks. The specifics of RSC activity under various navigation loads, however, are still not characterized. This study investigated the local information processed by the RSC under various navigation load conditions manipulated by the number of turns in the physical navigation setup. The results showed that the local information processed via the RSC, which was reflected by the segregation network, was higher when the number of turns increased, suggesting that RSC activity is associated with the navigation task load. The present findings shed light on how the brain processes spatial information in a physical navigation task.

Inverse Rational Control with Partially Observable Continuous Nonlinear Dynamics

A fundamental question in neuroscience is how the brain creates an internal model of the world to guide actions using sequences of ambiguous sensory information. This is naturally formulated as a reinforcement learning problem under partial observations, where an agent must estimate relevant latent variables in the world from its evidence, anticipate possible future states, and choose actions that optimize total expected reward. This problem can be solved by control theory, which allows us to find the optimal actions for a given system dynamics and objective function. However, animals often appear to behave suboptimally. Why? We hypothesize that animals have their own flawed internal model of the world, and choose actions with the highest expected subjective reward according to that flawed model. We describe this behavior as rational but not optimal. The problem of Inverse Rational Control (IRC) aims to identify which internal model would best explain an agent's actions. Our contribution here generalizes past work on Inverse Rational Control which solved this problem for discrete control in partially observable Markov decision processes. Here we accommodate continuous nonlinear dynamics and continuous actions, and impute sensory observations corrupted by unknown noise that is private to the animal. We first build an optimal Bayesian agent that learns an optimal policy generalized over the entire model space of dynamics and subjective rewards using deep reinforcement learning. Crucially, this allows us to compute a likelihood over models for experimentally observable action trajectories acquired from a suboptimal agent. We then find the model parameters that maximize the likelihood using gradient ascent. Our method successfully recovers the true model of rational agents. This approach provides a foundation for interpreting the behavioral and neural dynamics of animal brains during complex tasks.

Visual and Vestibular Selectivity for Self-Motion in Macaque Posterior Parietal Area 7a

We examined the responses of neurons in posterior parietal area 7a to passive rotational and translational self-motion stimuli, while systematically varying the speed of visually simulated (optic flow cues) or actual (vestibular cues) self-motion. Contrary to a general belief that responses in area 7a are predominantly visual, we found evidence for a vestibular dominance in self-motion processing. Only a small fraction of neurons showed multisensory convergence of visual/vestibular and linear/angular self-motion cues. These findings suggest possibly independent neuronal population codes for visual versus vestibular and linear versus angular self-motion. Neural responses scaled with self-motion magnitude (i.e., speed) but temporal dynamics were diverse across the population. Analyses of laminar recordings showed a strong distance-dependent decrease for correlations in stimulus-induced (signal correlation) and stimulus-independent (noise correlation) components of spike-count variability, supporting the notion that neurons are spatially clustered with respect to their sensory representation of motion. Single-unit and multiunit response patterns were also correlated, but no other systematic dependencies on cortical layers or columns were observed. These findings describe a likely independent multimodal neural code for linear and angular self-motion in a posterior parietal area of the macaque brain that is connected to the hippocampal formation.

Sources of path integration error in young and aging humans

Path integration plays a vital role in navigation: it enables the continuous tracking of one's position in space by integrating self-motion cues. Path integration abilities vary widely across individuals, and tend to deteriorate in old age. The specific causes of path integration errors, however, remain poorly characterized. Here, we combine tests of path integration performance in participants of different ages with an analysis based on the Langevin equation for diffusive dynamics, which allows us to decompose errors into distinct causes that can corrupt path integration computations. We show that, across age groups, the dominant error source is unbiased noise that accumulates with travel distance not elapsed time, suggesting that the noise originates in the velocity input rather than within the integrator. Age-related declines are primarily traced to a growth in this noise. These findings shed light on the contributors to path integration error and the mechanisms underlying age-related navigational deficits.

Tracking the Mind's Eye: Primate Gaze Behavior during Virtual Visuomotor Navigation Reflects Belief Dynamics

To take the best actions, we often need to maintain and update beliefs about variables that cannot be directly observed. To understand the principles underlying such belief updates, we need tools to uncover subjects' belief dynamics from natural behavior. We tested whether eye movements could be used to infer subjects' beliefs about latent variables using a naturalistic navigation task. Humans and monkeys navigated to a remembered goal location in a virtual environment that provided optic flow but lacked explicit position cues. We observed eye movements that appeared to continuously track the goal location even when no visible target was present there. Accurate goal tracking was associated with improved task performance, and inhibiting eye movements in humans impaired navigation precision. These results suggest that gaze dynamics play a key role in action selection during challenging visuomotor behaviors and may possibly serve as a window into the subject's dynamically evolving internal beliefs.

Increased variability but intact integration during visual navigation in Autism Spectrum Disorder

Autism Spectrum Disorder (ASD) is a common neurodevelopmental disturbance afflicting a variety of functions. The recent computational focus suggesting aberrant Bayesian inference in ASD has yielded promising but conflicting results in attempting to explain a wide variety of phenotypes by canonical computations. Here, we used a naturalistic visual path integration task that combines continuous action with active sensing and allows tracking of subjects' dynamic belief states. Both groups showed a previously documented bias pattern by overshooting the radial distance and angular eccentricity of targets. For both control and ASD groups, these errors were driven by misestimated velocity signals due to a nonuniform speed prior rather than imperfect integration. We tracked participants' beliefs and found no difference in the speed prior, but there was heightened variability in the ASD group. Both end point variance and trajectory irregularities correlated with ASD symptom severity. With feedback, variance was reduced, and ASD performance approached that of controls. These findings highlight the need for both more naturalistic tasks and a broader computational perspective to understand the ASD phenotype and pathology.

Causal inference for spatial constancy across whole body motion

The brain uses self-motion information to internally update egocentric representations of locations of remembered world-fixed visual objects. If a discrepancy is observed between this internal update and reafferent visual feedback, this could be either due to an inaccurate update or because the object has moved during the motion. To optimally infer the object's location it is therefore critical for the brain to estimate the probabilities of these two causal structures and accordingly integrate and/or segregate the internal and sensory estimates. To test this hypothesis, we designed a spatial updating task involving passive whole body translation. Participants, seated on a vestibular sled, had to remember the world-fixed position of a visual target. Immediately after the translation, the reafferent visual feedback was provided by flashing a second target around the estimated "updated" target location, and participants had to report the initial target location. We found that the participants' responses were systematically biased toward the position of the second target position for relatively small but not for large differences between the "updated" and the second target location. This pattern was better captured by a Bayesian causal inference model than by alternative models that would always either integrate or segregate the internally updated target location and the visual feedback. Our results suggest that the brain implicitly represents the posterior probability that the internally updated estimate and the visual feedback come from a common cause and uses this probability to weigh the two sources of information in mediating spatial constancy across whole body motion. NEW & NOTEWORTHY When we move, egocentric representations of object locations require internal updating to keep them in register with their true world-fixed locations. How does this mechanism interact with reafferent visual input, given that objects typically do not disappear from view? Here we show that the brain implicitly represents the probability that both types of information derive from the same object and uses this probability to weigh their contribution for achieving spatial constancy across whole body motion.