Active inference and oculomotor pursuit: the dynamic causal modelling of eye movements

Active Vision in Binocular Depth Estimation: A Top-Down Perspective

Depth estimation is an ill-posed problem; objects of different shapes or dimensions, even if at different distances, may project to the same image on the retina. Our brain uses several cues for depth estimation, including monocular cues such as motion parallax and binocular cues such as diplopia. However, it remains unclear how the computations required for depth estimation are implemented in biologically plausible ways. State-of-the-art approaches to depth estimation based on deep neural networks implicitly describe the brain as a hierarchical feature detector. Instead, in this paper we propose an alternative approach that casts depth estimation as a problem of active inference. We show that depth can be inferred by inverting a hierarchical generative model that simultaneously predicts the eyes' projections from a 2D belief over an object. Model inversion consists of a series of biologically plausible homogeneous transformations based on Predictive Coding principles. Under the plausible assumption of a nonuniform fovea resolution, depth estimation favors an active vision strategy that fixates the object with the eyes, rendering the depth belief more accurate. This strategy is not realized by first fixating on a target and then estimating the depth; instead, it combines the two processes through action-perception cycles, with a similar mechanism of the saccades during object recognition. The proposed approach requires only local (top-down and bottom-up) message passing, which can be implemented in biologically plausible neural circuits.

Belief embodiment through eye movements facilitates memory-guided navigation

Neural network models optimized for task performance often excel at predicting neural activity but do not explain other properties such as the distributed representation across functionally distinct areas. Distributed representations may arise from animals' strategies for resource utilization, however, fixation-based paradigms deprive animals of a vital resource: eye movements. During a naturalistic task in which humans use a joystick to steer and catch flashing fireflies in a virtual environment lacking position cues, subjects physically track the latent task variable with their gaze. We show this strategy to be true also during an inertial version of the task in the absence of optic flow and demonstrate that these task-relevant eye movements reflect an embodiment of the subjects' dynamically evolving internal beliefs about the goal. A neural network model with tuned recurrent connectivity between oculomotor and evidence-integrating frontoparietal circuits accounted for this behavioral strategy. Critically, this model better explained neural data from monkeys' posterior parietal cortex compared to task-optimized models unconstrained by such an oculomotor-based cognitive strategy. These results highlight the importance of unconstrained movement in working memory computations and establish a functional significance of oculomotor signals for evidence-integration and navigation computations via embodied cognition.

Cognitive effort and active inference

This paper aims to integrate some key constructs in the cognitive neuroscience of cognitive control and executive function by formalising the notion of cognitive (or mental) effort in terms of active inference. To do so, we call upon a task used in neuropsychology to assess impulse inhibition-a Stroop task. In this task, participants must suppress the impulse to read a colour word and instead report the colour of the text of the word. The Stroop task is characteristically effortful, and we unpack a theory of mental effort in which, to perform this task accurately, participants must overcome prior beliefs about how they would normally act. However, our interest here is not in overt action, but in covert (mental) action. Mental actions change our beliefs but have no (direct) effect on the outside world-much like deploying covert attention. This account of effort as mental action lets us generate multimodal (choice, reaction time, and electrophysiological) data of the sort we might expect from a human participant engaging in this task. We analyse how parameters determining cognitive effort influence simulated responses and demonstrate that-when provided only with performance data-these parameters can be recovered, provided they are within a certain range.

A Bayesian computational model to investigate expert anticipation of a seemingly unpredictable ball bounce

During dynamic and time-constrained sporting tasks performers rely on both online perceptual information and prior contextual knowledge to make effective anticipatory judgments. It has been suggested that performers may integrate these sources of information in an approximately Bayesian fashion, by weighting available information sources according to their expected precision. In the present work, we extended Bayesian brain approaches to anticipation by using formal computational models to estimate how performers weighted different information sources when anticipating the bounce direction of a rugby ball. Both recreational (novice) and professional (expert) rugby players (n = 58) were asked to predict the bounce height of an oncoming rugby ball in a temporal occlusion paradigm. A computational model, based on a partially observable Markov decision process, was fitted to observed responses to estimate participants' weighting of online sensory cues and prior beliefs about ball bounce height. The results showed that experts were more sensitive to online sensory information, but that neither experts nor novices relied heavily on prior beliefs about ball trajectories in this task. Experts, but not novices, were observed to down-weight priors in their anticipatory decisions as later and more precise visual cues emerged, as predicted by Bayesian and active inference accounts of perception.

Multivariate EEG activity reflects the Bayesian integration and the integrated Galilean relative velocity of sensory motion during sensorimotor behavior

Humans integrate multiple sources of information for action-taking, using the reliability of each source to allocate weight to the data. This reliability-weighted information integration is a crucial property of Bayesian inference. In this study, participants were asked to perform a smooth pursuit eye movement task in which we independently manipulated the reliability of pursuit target motion and the direction-of-motion cue. Through an analysis of pursuit initiation and multivariate electroencephalography activity, we found neural and behavioral evidence of Bayesian information integration: more attraction toward the cue direction was generated when the target motion was weak and unreliable. Furthermore, using mathematical modeling, we found that the neural signature of Bayesian information integration had extra-retinal origins, although most of the multivariate electroencephalography activity patterns during pursuit were best correlated with the retinal velocity errors accumulated over time. Our results demonstrated neural implementation of Bayesian inference in human oculomotor behavior.

Flexible intentions: An Active Inference theory

We present a normative computational theory of how the brain may support visually-guided goal-directed actions in dynamically changing environments. It extends the Active Inference theory of cortical processing according to which the brain maintains beliefs over the environmental state, and motor control signals try to fulfill the corresponding sensory predictions. We propose that the neural circuitry in the Posterior Parietal Cortex (PPC) compute flexible intentions-or motor plans from a belief over targets-to dynamically generate goal-directed actions, and we develop a computational formalization of this process. A proof-of-concept agent embodying visual and proprioceptive sensors and an actuated upper limb was tested on target-reaching tasks. The agent behaved correctly under various conditions, including static and dynamic targets, different sensory feedbacks, sensory precisions, intention gains, and movement policies; limit conditions were individuated, too. Active Inference driven by dynamic and flexible intentions can thus support goal-directed behavior in constantly changing environments, and the PPC might putatively host its core intention mechanism. More broadly, the study provides a normative computational basis for research on goal-directed behavior in end-to-end settings and further advances mechanistic theories of active biological systems.

Attentional Modulation of Vision Versus Proprioception During Action

To control our actions efficiently, our brain represents our body based on a combination of visual and proprioceptive cues, weighted according to how (un)reliable—how precise—each respective modality is in a given context. However, perceptual experiments in other modalities suggest that the weights assigned to sensory cues are also modulated “top-down” by attention. Here, we asked whether during action, attention can likewise modulate the weights (i.e., precision) assigned to visual versus proprioceptive information about body position. Participants controlled a virtual hand (VH) via a data glove, matching either the VH or their (unseen) real hand (RH) movements to a target, and thus adopting a ``visual'' or ``proprioceptive'' attentional set, under varying levels of visuo-proprioceptive congruence and visibility. Functional magnetic resonance imaging (fMRI) revealed increased activation of the multisensory superior parietal lobe (SPL) during the VH task and increased activation of the secondary somatosensory cortex (S2) during the RH task. Dynamic causal modeling (DCM) showed that these activity changes were the result of selective, diametrical gain modulations in the primary visual cortex (V1) and the S2. These results suggest that endogenous attention can balance the gain of visual versus proprioceptive brain areas, thus contextualizing their influence on multisensory areas representing the body for action.

Dynamic causal modelling of immune heterogeneity

An interesting inference drawn by some COVID-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection-even at the start of the current pandemic. This paper introduces a model of the immune response to a virus. This is based upon the same sort of mean-field dynamics as used in epidemiology. However, in place of the location, clinical status, and other attributes of people in an epidemiological model, we consider the state of a virus, B and T-lymphocytes, and the antibodies they generate. Our aim is to formalise some key hypotheses as to the mechanism of resistance. We present a series of simple simulations illustrating changes to the dynamics of the immune response under these hypotheses. These include attenuated viral cell entry, pre-existing cross-reactive humoral (antibody-mediated) immunity, and enhanced T-cell dependent immunity. Finally, we illustrate the potential application of this sort of model by illustrating variational inversion (using simulated data) of this model to illustrate its use in testing hypotheses. In principle, this furnishes a fast and efficient immunological assay-based on sequential serology-that provides a (1) quantitative measure of latent immunological responses and (2) a Bayes optimal classification of the different kinds of immunological response (c.f., glucose tolerance tests used to test for insulin resistance). This may be especially useful in assessing SARS-CoV-2 vaccines.

The role of eye movements in manual interception: A mini-review

When we catch a moving object in mid-flight, our eyes and hands are directed toward the object. Yet, the functional role of eye movements in guiding interceptive hand movements is not yet well understood. This review synthesizes emergent views on the importance of eye movements during manual interception with an emphasis on laboratory studies published since 2015. We discuss the role of eye movements in forming visual predictions about a moving object, and for enhancing the accuracy of interceptive hand movements through feedforward (extraretinal) and feedback (retinal) signals. We conclude by proposing a framework that defines the role of human eye movements for manual interception accuracy as a function of visual certainty and object motion predictability.

Minds and Brains, Sleep and Psychiatry

Objective

This article offers a philosophical thesis for psychiatric disorders that rests upon some simple truths about the mind and brain. Specifically, it asks whether the dual aspect monism—that emerges from sleep research and theoretical neurobiology—can be applied to pathophysiology and psychopathology in psychiatry.

Methods

Our starting point is that the mind and brain are emergent aspects of the same (neuronal) dynamics; namely, the brain–mind. Our endpoint is that synaptic dysconnection syndromes inherit the same dual aspect; namely, aberrant inference or belief updating on the one hand, and a failure of neuromodulatory synaptic gain control on the other. We start with some basic considerations from sleep research that integrate the phenomenology of dreaming with the neurophysiology of sleep.

Results

We then leverage this treatment by treating the brain as an organ of inference. Our particular focus is on the role of precision (i.e., the representation of uncertainty) in belief updating and the accompanying synaptic mechanisms.

Conclusions

Finally, we suggest a dual aspect approach—based upon belief updating (i.e., mind processes) and its neurophysiological implementation (i.e., brain processes)—has a wide explanatory compass for psychiatry and various movement disorders. This approach identifies the kind of pathophysiology that underwrites psychopathology—and points to certain psychotherapeutic and psychopharmacological targets, which may stand in mechanistic relation to each other.

The ‘mind’ emerges from Bayesian belief updating in the ‘brain’

Psychopathology can be read as aberrant belief updating.

Aberrant belief updating follows from any neuromodulatory synaptopathy

Difficulties with Speech-in-Noise Perception Related to Fundamental Grouping Processes in Auditory Cortex

In our everyday lives, we are often required to follow a conversation when background noise is present (“speech-in-noise” [SPIN] perception). SPIN perception varies widely—and people who are worse at SPIN perception are also worse at fundamental auditory grouping, as assessed by figure-ground tasks. Here, we examined the cortical processes that link difficulties with SPIN perception to difficulties with figure-ground perception using functional magnetic resonance imaging. We found strong evidence that the earliest stages of the auditory cortical hierarchy (left core and belt areas) are similarly disinhibited when SPIN and figure-ground tasks are more difficult (i.e., at target-to-masker ratios corresponding to 60% rather than 90% performance)—consistent with increased cortical gain at lower levels of the auditory hierarchy. Overall, our results reveal a common neural substrate for these basic (figure-ground) and naturally relevant (SPIN) tasks—which provides a common computational basis for the link between SPIN perception and fundamental auditory grouping.

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.

Active inference under visuo-proprioceptive conflict: Simulation and empirical results

It has been suggested that the brain controls hand movements via internal models that rely on visual and proprioceptive cues about the state of the hand. In active inference formulations of such models, the relative influence of each modality on action and perception is determined by how precise (reliable) it is expected to be. The ‘top-down’ affordance of expected precision to a particular sensory modality is associated with attention. Here, we asked whether increasing attention to (i.e., the precision of) vision or proprioception would enhance performance in a hand-target phase matching task, in which visual and proprioceptive cues about hand posture were incongruent. We show that in a simple simulated agent—based on predictive coding formulations of active inference—increasing the expected precision of vision or proprioception improved task performance (target matching with the seen or felt hand, respectively) under visuo-proprioceptive conflict. Moreover, we show that this formulation captured the behaviour and self-reported attentional allocation of human participants performing the same task in a virtual reality environment. Together, our results show that selective attention can balance the impact of (conflicting) visual and proprioceptive cues on action—rendering attention a key mechanism for a flexible body representation for action.

Effect of Prior Direction Expectation on the Accuracy and Precision of Smooth Pursuit Eye Movements

The integration of sensory with top–down cognitive signals for generating appropriate sensory–motor behaviors is an important issue in understanding the brain’s information processes. Recent studies have demonstrated that the interplay between sensory and high-level signals in oculomotor behavior could be explained by Bayesian inference. Specifically, prior knowledge for motion speed introduces a bias in the speed of smooth pursuit eye movements. The other important prediction of Bayesian inference is variability reduction by prior expectation; however, there is insufficient evidence in oculomotor behaviors to support this prediction. In the present study, we trained monkeys to switch the prior expectation about motion direction and independently controlled the strength of the motion stimulus. Under identical sensory stimulus conditions, we tested if prior knowledge about the motion direction reduced the variability of open-loop smooth pursuit eye movements. We observed a significant reduction when the prior expectation was strong; this was consistent with the prediction of Bayesian inference. Taking advantage of the open-loop smooth pursuit, we investigated the temporal dynamics of the effect of the prior to the pursuit direction bias and variability. This analysis demonstrated that the strength of the sensory evidence depended not only on the strength of the sensory stimulus but also on the time required for the pursuit system to form a neural sensory representation. Finally, we demonstrated that the variability and directional bias change by prior knowledge were quantitatively explained by the Bayesian observer model.

Earth-Gravity Congruent Motion Facilitates Ocular Control for Pursuit of Parabolic Trajectories

There is evidence that humans rely on an earth gravity (9.81 m/s²) prior for a series of tasks involving perception and action, the reason being that gravity helps predict future positions of moving objects. Eye-movements in turn are partially guided by predictions about observed motion. Thus, the question arises whether knowledge about gravity is also used to guide eye-movements: If humans rely on a representation of earth gravity for the control of eye movements, earth-gravity-congruent motion should elicit improved visual pursuit. In a pre-registered experiment, we presented participants (n = 10) with parabolic motion governed by six different gravities (-1/0.7/0.85/1/1.15/1.3 g), two initial vertical velocities and two initial horizontal velocities in a 3D environment. Participants were instructed to follow the target with their eyes. We tracked their gaze and computed the visual gain (velocity of the eyes divided by velocity of the target) as proxy for the quality of pursuit. An LMM analysis with gravity condition as fixed effect and intercepts varying per subject showed that the gain was lower for -1 g than for 1 g (by -0.13, SE = 0.005). This model was significantly better than a null model without gravity as fixed effect (p < 0.001), supporting our hypothesis. A comparison of 1 g and the remaining gravity conditions revealed that 1.15 g (by 0.043, SE = 0.005) and 1.3 g (by 0.065, SE = 0.005) were associated with lower gains, while 0.7 g (by 0.054, SE = 0.005) and 0.85 g (by 0.029, SE = 0.005) were associated with higher gains. This model was again significantly better than a null model (p < 0.001), contradicting our hypothesis. Post-hoc analyses reveal that confounds in the 0.7/0.85/1/1.15/1.3 g condition may be responsible for these contradicting results. Despite these discrepancies, our data thus provide some support for the hypothesis that internalized knowledge about earth gravity guides eye movements.

Co-registration of eye movements and neuroimaging for studying contextual predictions in natural reading

Sixteen years ago, Sereno and Rayner (2003. Measuring word recognition in reading: eye movements and event-related potentials. Trends in Cognitive Sciences, 7(11), 489-493) illustrated how "by means of review and comparison" eye movement (EM) and event-related potential (ERP) studies may advance our understanding of visual word recognition. Attempts to simultaneously record EMs and ERPs soon followed. Recently, this co-registration approach has also been transferred to fMRI and oscillatory EEG. With experimental settings close to natural reading, co-registration enables us to directly integrate insights from EM and neuroimaging studies. This should extend current experimental paradigms by moving the field towards studying sentence-level processing including effects of context and parafoveal preview. This article will introduce the basic principles and applications of co-registration and selectively review how this approach may shed light on one of the most controversially discussed issues in reading research, contextual predictions in online language processing.

A Bayesian Account of the Sensory-Motor Interactions Underlying Symptoms of Tourette Syndrome

Tourette syndrome is a hyperkinetic movement disorder. Characteristic features include tics, recurrent movements that are experienced as compulsive and "unwilled"; uncomfortable premonitory sensations that resolve through tic release; and often, the ability to suppress tics temporarily. We demonstrate how these symptoms and features can be understood in terms of aberrant predictive (Bayesian) processing in hierarchical neural systems, explaining specifically: why tics arise, their "unvoluntary" nature, how premonitory sensations emerge, and why tic suppression works-sometimes. In our model, premonitory sensations and tics are generated through over-precise priors for sensation and action within somatomotor regions of the striatum. Abnormally high precision of priors arises through the dysfunctional synaptic integration of cortical inputs. These priors for sensation and action are projected into primary sensory and motor areas, triggering premonitory sensations and tics, which in turn elicit prediction errors for unexpected feelings and movements. We propose experimental paradigms to validate this Bayesian account of tics. Our model integrates behavioural, neuroimaging, and computational approaches to provide mechanistic insight into the pathophysiological basis of Tourette syndrome.

Knowing when to stop: Aberrant precision and evidence accumulation in schizophrenia

Predictive coding and active inference formulations of the dysconnection hypothesis suggest that subjects with schizophrenia (SZ) hold unduly precise prior beliefs to compensate for a failure of sensory attenuation. This implies that SZ subjects should both initiate responses prematurely during evidence-accumulation tasks and fail to inhibit their responses at long stop-signal delays. SZ and healthy control subjects were asked to report the timing of billiards-ball collisions and were occasionally required to withhold their responses. SZ subjects showed larger temporal estimation errors, which were associated with premature responses and decreased response inhibition. To account for these effects, we used hierarchical (Bayesian) drift-diffusion models (HDDM) and model selection procedures to adjudicate among four hypotheses. HDDM revealed that the precision of prior beliefs (i.e., starting point) rather than increased sensory precision (i.e., drift rate) drove premature responses and impaired response inhibition in patients with SZ. From the perspective of active inference, we suggest that premature predictions in SZ are responses that, heuristically, are traded off against accuracy to ensure action execution. On the basis of previous work, we suggest that the right insular cortex might mediate this trade-off.

Information fusion control with time delay for smooth pursuit eye movement

Smooth pursuit eye movement depends on prediction and learning, and is subject to time delays in the visual pathways. In this paper, an information fusion control method with time delay is presented, implementing smooth pursuit eye movement with prediction and learning as well as solving the problem of time delays in the visual pathways. By fusing the soft constraint information of the target trajectory of eyes and the ideal control strategy, and the hard constraint information of the eye system state equation and the output equation, optimal estimations of the co-state sequence and the control variable are obtained. The proposed control method can track not only constant velocity, sinusoidal target motion, but also arbitrary moving targets. Moreover, the absolute value of the retinal slip reaches steady state after 0.1 sec. Information fusion control method elegantly describes in a function manner how the brain may deal with arbitrary target velocities, how it implements the smooth pursuit eye movement with prediction, learning, and time delays. These two principles allowed us to accurately describe visually guided, predictive and learning smooth pursuit dynamics observed in a wide variety of tasks within a single theoretical framework. The tracking control performance of the proposed information fusion control with time delays is verified by numerical simulation results.

Dynamic causal modelling of eye movements during pursuit: Confirming precision-encoding in V1 using MEG

This paper shows that it is possible to estimate the subjective precision (inverse variance) of Bayesian beliefs during oculomotor pursuit. Subjects viewed a sinusoidal target, with or without random fluctuations in its motion. Eye trajectories and magnetoencephalographic (MEG) data were recorded concurrently. The target was periodically occluded, such that its reappearance caused a visual evoked response field (ERF). Dynamic causal modelling (DCM) was used to fit models of eye trajectories and the ERFs. The DCM for pursuit was based on predictive coding and active inference, and predicts subjects' eye movements based on their (subjective) Bayesian beliefs about target (and eye) motion. The precisions of these hierarchical beliefs can be inferred from behavioural (pursuit) data. The DCM for MEG data used an established biophysical model of neuronal activity that includes parameters for the gain of superficial pyramidal cells, which is thought to encode precision at the neuronal level. Previous studies (using DCM of pursuit data) suggest that noisy target motion increases subjective precision at the sensory level: i.e., subjects attend more to the target's sensory attributes. We compared (noisy motion-induced) changes in the synaptic gain based on the modelling of MEG data to changes in subjective precision estimated using the pursuit data. We demonstrate that imprecise target motion increases the gain of superficial pyramidal cells in V1 (across subjects). Furthermore, increases in sensory precision – inferred by our behavioural DCM – correlate with the increase in gain in V1, across subjects. This is a step towards a fully integrated model of brain computations, cortical responses and behaviour that may provide a useful clinical tool in conditions like schizophrenia.

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The brain encodes states of the world probabilistically with means and precisions.

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Precision (inverse variance) may be encoded by the synaptic gain of pyramidal cells.

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We estimate subjects' sensory precision using a model of oculomotor pursuit and DCM.

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We estimate subjects' synaptic gain in V1 using DCM of MEG data during pursuit.

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Estimates of synaptic gain in V1 and sensory precision are significantly correlated.

Computational Psychiatry: towards a mathematically informed understanding of mental illness

Computational Psychiatry aims to describe the relationship between the brain's neurobiology, its environment and mental symptoms in computational terms. In so doing, it may improve psychiatric classification and the diagnosis and treatment of mental illness. It can unite many levels of description in a mechanistic and rigorous fashion, while avoiding biological reductionism and artificial categorisation. We describe how computational models of cognition can infer the current state of the environment and weigh up future actions, and how these models provide new perspectives on two example disorders, depression and schizophrenia. Reinforcement learning describes how the brain can choose and value courses of actions according to their long-term future value. Some depressive symptoms may result from aberrant valuations, which could arise from prior beliefs about the loss of agency ('helplessness'), or from an inability to inhibit the mental exploration of aversive events. Predictive coding explains how the brain might perform Bayesian inference about the state of its environment by combining sensory data with prior beliefs, each weighted according to their certainty (or precision). Several cortical abnormalities in schizophrenia might reduce precision at higher levels of the inferential hierarchy, biasing inference towards sensory data and away from prior beliefs. We discuss whether striatal hyperdopaminergia might have an adaptive function in this context, and also how reinforcement learning and incentive salience models may shed light on the disorder. Finally, we review some of Computational Psychiatry's applications to neurological disorders, such as Parkinson's disease, and some pitfalls to avoid when applying its methods.