The Computational Anatomy of Visual Neglect

An Introduction to Predictive Processing Models of Perception and Decision-Making

The predictive processing framework includes a broad set of ideas, which might be articulated and developed in a variety of ways, concerning how the brain may leverage predictive models when implementing perception, cognition, decision-making, and motor control. This article provides an up-to-date introduction to the two most influential theories within this framework: predictive coding and active inference. The first half of the paper (Sections 2-5) reviews the evolution of predictive coding, from early ideas about efficient coding in the visual system to a more general model encompassing perception, cognition, and motor control. The theory is characterized in terms of the claims it makes at Marr's computational, algorithmic, and implementation levels of description, and the conceptual and mathematical connections between predictive coding, Bayesian inference, and variational free energy (a quantity jointly evaluating model accuracy and complexity) are explored. The second half of the paper (Sections 6-8) turns to recent theories of active inference. Like predictive coding, active inference models assume that perceptual and learning processes minimize variational free energy as a means of approximating Bayesian inference in a biologically plausible manner. However, these models focus primarily on planning and decision-making processes that predictive coding models were not developed to address. Under active inference, an agent evaluates potential plans (action sequences) based on their expected free energy (a quantity that combines anticipated reward and information gain). The agent is assumed to represent the world as a partially observable Markov decision process with discrete time and discrete states. Current research applications of active inference models are described, including a range of simulation work, as well as studies fitting models to empirical data. The paper concludes by considering future research directions that will be important for further development of both models.

Hierarchical psychophysiological pathways subtend perceptual asymmetries in Neglect

Stroke patients with left Hemispatial Neglect (LHN) show deficits in perceiving left contralesional stimuli with biased visuospatial perception towards the right hemifield. However, very little is known about the functional organization of the visuospatial perceptual neural network and how this can account for the profound reorganization of space representation in LHN. In the present work, we aimed at (1) identifying EEG measures that discriminate LHN patients against controls and (2) devise a causative neurophysiological model between the discriminative EEG measures. To these aims, EEG was recorded during exposure to lateralized visual stimuli which allowed for pre-and post-stimulus activity investigation across three groups: LHN patients, lesioned controls, and healthy individuals. Moreover, all participants performed a standard behavioral test assessing the perceptual asymmetry index in detecting lateralized stimuli. The between-groups discriminative EEG patterns were entered into a Structural Equation Model for the identification of causative hierarchical associations (i.e., pathways) between EEG measures and the perceptual asymmetry index. The model identified two pathways. A first pathway showed that the combined contribution of pre-stimulus frontoparietal connectivity and individual-alpha-frequency predicts post-stimulus processing, as measured by visual-evoked N100, which, in turn, predicts the perceptual asymmetry index. A second pathway directly links the inter-hemispheric distribution of alpha-amplitude with the perceptual asymmetry index. The two pathways can collectively explain 83.1% of the variance in the perceptual asymmetry index. Using causative modeling, the present study identified how psychophysiological correlates of visuospatial perception are organized and predict the degree of behavioral asymmetry in LHN patients and controls.

Disconnectomics to unravel the network underlying deficits of spatial exploration and attention

Spatial attention and exploration are related to a predominantly right hemispheric network structure. However, the areas of the brain involved and their exact role is still debated. Spatial neglect following right hemispheric stroke lesions has been frequently viewed as a model to study these processes in humans. Previous investigations on the anatomical basis on spatial neglect predominantly focused on focal brain damage and lesion-behaviour mapping analyses. This approach might not be suited to detect remote areas structurally spared but which might contribute to the behavioural deficit. In the present study of a sample of 203 right hemispheric stroke patients, we combined connectome lesion-symptom mapping with multivariate support vector regression to unravel the complex and disconnected network structure in spatial neglect. We delineated three central nodes that were extensively disconnected from other intrahemispheric areas, namely the right superior parietal lobule, the insula, and the temporal pole. Additionally, the analysis allocated central roles within this network to the inferior frontal gyrus (pars triangularis and opercularis), right middle temporal gyrus, right temporal pole and left and right orbitofrontal cortices, including interhemispheric disconnection. Our results suggest that these structures-although not necessarily directly damaged-might play a role within the network underlying spatial neglect in humans.

In the Body’s Eye: The computational anatomy of interoceptive inference

A growing body of evidence highlights the intricate linkage of exteroceptive perception to the rhythmic activity of the visceral body. In parallel, interoceptive inference theories of affective perception and self-consciousness are on the rise in cognitive science. However, thus far no formal theory has emerged to integrate these twin domains; instead, most extant work is conceptual in nature. Here, we introduce a formal model of cardiac active inference, which explains how ascending cardiac signals entrain exteroceptive sensory perception and uncertainty. Through simulated psychophysics, we reproduce the defensive startle reflex and commonly reported effects linking the cardiac cycle to affective behaviour. We further show that simulated ‘interoceptive lesions’ blunt affective expectations, induce psychosomatic hallucinations, and exacerbate biases in perceptual uncertainty. Through synthetic heart-rate variability analyses, we illustrate how the balance of arousal-priors and visceral prediction errors produces idiosyncratic patterns of physiological reactivity. Our model thus offers a roadmap for computationally phenotyping disordered brain-body interaction.

Understanding interactions between the brain and the body has become a topic of increased interest in computational neuroscience and psychiatry. A particular question here concerns how visceral, homeostatic rhythms such as the heart beat influence sensory, affective, and cognitive processing. To better understand these and other oscillatory brain-body interactions, we here introduce a novel computational model of interoceptive inference in which a synthetic agent’s perceptual beliefs are coupled to the rhythm of the heart. Our model both helps to explain emerging empirical data indicating that perceptual inference depends upon beat-to-beat heart rhythms, and can be used to better quantify intra- and inter-individual differences in heart-brain coupling. Using proof-of-principle simulations, we demonstrate how future empirical works could utilize our model to better understand and stratify disorders of interoception and brain-body interaction.

Left and right temporal-parietal junctions (TPJs) as "match/mismatch" hedonic machines: A unifying account of TPJ function

Experimental and theoretical studies have tried to gain insights into the involvement of the Temporal Parietal Junction (TPJ) in a broad range of cognitive functions like memory, attention, language, self-agency and theory of mind. Recent investigations have demonstrated the partition of the TPJ in discrete subsectors. Nonetheless, whether these subsectors play different roles or implement an overarching function remains debated. Here, based on a review of available evidence, we propose that the left TPJ codes both matches and mismatches between expected and actual sensory, motor, or cognitive events while the right TPJ codes mismatches. These operations help keeping track of statistical contingencies in personal, environmental, and conceptual space. We show that this hypothesis can account for the participation of the TPJ in disparate cognitive functions, including "humour", and explain: a) the higher incidence of spatial neglect in right brain damage; b) the different emotional reactions that follow left and right brain damage; c) the hemispheric lateralisation of optimistic bias mechanisms; d) the lateralisation of mechanisms that regulate routine and novelty behaviours. We propose that match and mismatch operations are aimed at approximating "free energy", in terms of the free energy principle of decision-making. By approximating "free energy", the match/mismatch TPJ system supports both information seeking to update one's own beliefs and the pleasure of being right in one's own' current choices. This renewed view of the TPJ has relevant clinical implications because the misfunctioning of TPJ-related "match" and "mismatch" circuits in unilateral brain damage can produce low-dimensional deficits of active-inference and predictive coding that can be associated with different neuropsychological disorders.

Disorders of higher visual processing in patients with acquired brain injury

BACKGROUND: Disorders of higher visual processing often impact patients with acquired brain injury. Even with treatment, these vision conditions can cause chronic challenges for patients. Understanding these conditions and their management can help improve functional independence and quality of life. OBJECTIVES: To discuss the various disorders of higher visual processing that result from acquired brain injury. Discussion to include classification, evaluation, and treatment techniques available to clinicians. METHODS: Peer reviewed journal articles were searched, primarily through PubMed. Articles spanning several decades were included in the review for historical context of these conditions, however an emphasis was placed on more recent publications for purposes of a discussion regarding clinical management of these conditions. RESULTS: Peer-reviewed articles and clinical trials from across several disciplines were included to frame a discussion of this varied group of conditions. CONCLUSION: Visual processing disorders have debilitating impacts on both the rehabilitation process as well as functional independence. Varied approaches are utilized in the treatment of these conditions with limited success. Understanding the benefits and limitations of both restorative and compensatory treatments will better help clinicians manage patients with these conditions.

Modeling the subjective perspective of consciousness and its role in the control of behaviours

Consciousness has been hypothesized to operate as a global workspace, which accesses and integrates multimodal information in a uni_ed manner, supports expectation violation monitoring and reduction, and the motivation, programming and control of action. One important yet open issue concerns how the subjective perspective at the core of consciousness, and subjective properties of manifestation of the environment in such perspective as an embodied experience, play a role in such process. We operationalised the concept of subjective perspective using the principles of the Projective Consciousness Model (PCM), based on the projective geometrical concept of Field of Consciousness. We show how these principles can account for documented relationships between appraisal and distance as an inverse distance law, yield a generative model of a_ective and epistemic drives based on purely subjective parameters, such as the apparent size of objects, and can be generalised to implement Theory of Mind, in a manner that is consistent with simulation theory. We used simulations of arti_cial agents, based on psychological rationale, to demonstrate how different model parameters could generate a variety of emergent adaptive and maladaptive behaviours that are relevant to developmental and clinical psychology: the ability to be resilient in the face of obstacles through imaginary projections, the emergence of social approach and joint attention behaviours, the ability to take advantage of false beliefs attributed to others, the emergence of avoidance behaviours as observed in social anxiety disorders, the presence of restricted interests as observed in autism spectrum disorders. The simulation of agents was applied to a speci_c robotic context, and agents' behaviours were demonstrated by controlling the corresponding robots. Our results contribute to advance the scienti_c understanding of the causal relationships between core aspects of the phenomenology of consciousness and its functions in human cybernetics.

Prefrontal Computation as Active Inference

The prefrontal cortex is vital for a range of cognitive processes, including working memory, attention, and decision-making. Notably, its absence impairs the performance of tasks requiring the maintenance of information through a delay period. In this paper, we formulate a rodent task—which requires maintenance of delay-period activity—as a Markov decision process and treat optimal task performance as an (active) inference problem. We simulate the behavior of a Bayes optimal mouse presented with 1 of 2 cues that instructs the selection of concurrent visual and auditory targets on a trial-by-trial basis. Formulating inference as message passing, we reproduce features of neuronal coupling within and between prefrontal regions engaged by this task. We focus on the micro-circuitry that underwrites delay-period activity and relate it to functional specialization within the prefrontal cortex in primates. Finally, we simulate the electrophysiological correlates of inference and demonstrate the consequences of lesions to each part of our in silico prefrontal cortex. In brief, this formulation suggests that recurrent excitatory connections—which support persistent neuronal activity—encode beliefs about transition probabilities over time. We argue that attentional modulation can be understood as the contextualization of sensory input by these persistent beliefs.

Deficits of hierarchical predictive coding in left spatial neglect

Right brain-damaged patients with unilateral spatial neglect fail to explore the left side of space. Recent EEG and clinical evidence suggests that neglect patients might suffer deficits in predictive coding, i.e. in identifying and exploiting probabilistic associations among sensory stimuli in the environment. To gain direct insights on this issue, we focussed on the hierarchical components of predictive coding. We recorded EEG responses evoked by central, left-side or right-side tones that were presented at the end of sequences of four central tones. Left-side and right-side deviant tones produce a pre-attentive Mismatch Negativity that reflects a lower-order prediction error for the 'Local' deviation of the tone at the end of the sequence. Higher-order prediction errors for the frequency of these deviations in the acoustic environment, i.e. 'Global' deviation, are marked by the P3 response. We show that when neglect patients are immersed in an acoustic environment characterized by frequent left-side deviant tones, they display no pre-attentive Mismatch Negativity both for left-side deviant tones and infrequent omissions of the last tone, while they have Mismatch Negativity for infrequent right-side deviant tones. In the same condition, neglect patients show no P300 response to 'Global' prediction errors for deviant tones, including those in the non-neglected right-side, and omissions. In contrast to this, when right-side deviant tones are predominant in the acoustic environment, neglect patients have pre-attentive Mismatch Negativity both for right-side deviant tones and infrequent omissions, while they display no Mismatch Negativity for infrequent left-side deviant tones. Most importantly, in the same condition neglect patients show enhanced P300 response to infrequent left-side deviant tones, notwithstanding that these tones evoked no pre-attentive Mismatch Negativity. This latter finding indicates that 'Global' predictions are independent of 'Local' error signals provided by the Mismatch Negativity. These results qualify deficits of predictive coding in the spatial neglect syndrome and show that neglect patients base their predictive behaviour only on statistical regularities that are related to the frequent occurrence of sensory events on the right side of space.

Message Passing and Metabolism

Active inference is an increasingly prominent paradigm in theoretical biology. It frames the dynamics of living systems as if they were solving an inference problem. This rests upon their flow towards some (non-equilibrium) steady state-or equivalently, their maximisation of the Bayesian model evidence for an implicit probabilistic model. For many models, these self-evidencing dynamics manifest as messages passed among elements of a system. Such messages resemble synaptic communication at a neuronal network level but could also apply to other network structures. This paper attempts to apply the same formulation to biochemical networks. The chemical computation that occurs in regulation of metabolism relies upon sparse interactions between coupled reactions, where enzymes induce conditional dependencies between reactants. We will see that these reactions may be viewed as the movement of probability mass between alternative categorical states. When framed in this way, the master equations describing such systems can be reformulated in terms of their steady-state distribution. This distribution plays the role of a generative model, affording an inferential interpretation of the underlying biochemistry. Finally, we see that-in analogy with computational neurology and psychiatry-metabolic disorders may be characterized as false inference under aberrant prior beliefs.

Simulating the computational mechanisms of cognitive and behavioral psychotherapeutic interventions: insights from active inference

Cognitive-behavioral therapy (CBT) leverages interactions between thoughts, feelings, and behaviors. To deepen understanding of these interactions, we present a computational (active inference) model of CBT that allows formal simulations of interactions between cognitive interventions (i.e., cognitive restructuring) and behavioral interventions (i.e., exposure) in producing adaptive behavior change (i.e., reducing maladaptive avoidance behavior). Using spider phobia as a concrete example of maladaptive avoidance more generally, we show simulations indicating that when conscious beliefs about safety/danger have strong interactions with affective/behavioral outcomes, behavioral change during exposure therapy is mediated by changes in these beliefs, preventing generalization. In contrast, when these interactions are weakened, and cognitive restructuring only induces belief uncertainty (as opposed to strong safety beliefs), behavior change leads to generalized learning (i.e., "over-writing" the implicit beliefs about action-outcome mappings that directly produce avoidance). The individual is therefore equipped to face any new context, safe or dangerous, remaining in a content state without the need for avoidance behavior-increasing resilience from a CBT perspective. These results show how the same changes in behavior during CBT can be due to distinct underlying mechanisms; they predict lower rates of relapse when cognitive interventions focus on inducing uncertainty and on reducing the effects of automatic negative thoughts on behavior.

Immunoceptive inference: why are psychiatric disorders and immune responses intertwined?

There is a steadily growing literature on the role of the immune system in psychiatric disorders. So far, these advances have largely taken the form of correlations between specific aspects of inflammation (e.g. blood plasma levels of inflammatory markers, genetic mutations in immune pathways, viral or bacterial infection) with the development of neuropsychiatric conditions such as autism, bipolar disorder, schizophrenia and depression. A fundamental question remains open: why are psychiatric disorders and immune responses intertwined? To address this would require a step back from a historical mind-body dualism that has created such a dichotomy. We propose three contributions of active inference when addressing this question: translation, unification, and simulation. To illustrate these contributions, we consider the following questions. Is there an immunological analogue of sensory attenuation? Is there a common generative model that the brain and immune system jointly optimise? Can the immune response and psychiatric illness both be explained in terms of self-organising systems responding to threatening stimuli in their external environment, whether those stimuli happen to be pathogens, predators, or people? Does false inference at an immunological level alter the message passing at a psychological level (or vice versa) through a principled exchange between the two systems?

Generative Models for Active Vision

The active visual system comprises the visual cortices, cerebral attention networks, and oculomotor system. While fascinating in its own right, it is also an important model for sensorimotor networks in general. A prominent approach to studying this system is active inference-which assumes the brain makes use of an internal (generative) model to predict proprioceptive and visual input. This approach treats action as ensuring sensations conform to predictions (i.e., by moving the eyes) and posits that visual percepts are the consequence of updating predictions to conform to sensations. Under active inference, the challenge is to identify the form of the generative model that makes these predictions-and thus directs behavior. In this paper, we provide an overview of the generative models that the brain must employ to engage in active vision. This means specifying the processes that explain retinal cell activity and proprioceptive information from oculomotor muscle fibers. In addition to the mechanics of the eyes and retina, these processes include our choices about where to move our eyes. These decisions rest upon beliefs about salient locations, or the potential for information gain and belief-updating. A key theme of this paper is the relationship between "looking" and "seeing" under the brain's implicit generative model of the visual world.

Whence the Expected Free Energy?

The expected free energy (EFE) is a central quantity in the theory of active inference. It is the quantity that all active inference agents are mandated to minimize through action, and its decomposition into extrinsic and intrinsic value terms is key to the balance of exploration and exploitation that active inference agents evince. Despite its importance, the mathematical origins of this quantity and its relation to the variational free energy (VFE) remain unclear. In this letter, we investigate the origins of the EFE in detail and show that it is not simply "the free energy in the future." We present a functional that we argue is the natural extension of the VFE but actively discourages exploratory behavior, thus demonstrating that exploration does not directly follow from free energy minimization into the future. We then develop a novel objective, the free energy of the expected future (FEEF), which possesses both the epistemic component of the EFE and an intuitive mathematical grounding as the divergence between predicted and desired futures.

Active inference on discrete state-spaces: A synthesis

Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex generative models, enabling simulation of a wide range of complex behaviours. Due to successive developments in active inference, it is often difficult to see how its underlying principle relates to process theories and practical implementation. In this paper, we try to bridge this gap by providing a complete mathematical synthesis of active inference on discrete state-space models. This technical summary provides an overview of the theory, derives neuronal dynamics from first principles and relates this dynamics to biological processes. Furthermore, this paper provides a fundamental building block needed to understand active inference for mixed generative models; allowing continuous sensations to inform discrete representations. This paper may be used as follows: to guide research towards outstanding challenges, a practical guide on how to implement active inference to simulate experimental behaviour, or a pointer towards various in-silico neurophysiological responses that may be used to make empirical predictions.

Degeneracy and Redundancy in Active Inference

The notions of degeneracy and redundancy are important constructs in many areas, ranging from genomics through to network science. Degeneracy finds a powerful role in neuroscience, explaining key aspects of distributed processing and structure-function relationships in the brain. For example, degeneracy accounts for the superadditive effect of lesions on functional deficits in terms of a "many-to-one" structure-function mapping. In this paper, we offer a principled account of degeneracy and redundancy, when function is operationalized in terms of active inference, namely, a formulation of perception and action as belief updating under generative models of the world. In brief, "degeneracy" is quantified by the "entropy" of posterior beliefs about the causes of sensations, while "redundancy" is the "complexity" cost incurred by forming those beliefs. From this perspective, degeneracy and redundancy are complementary: Active inference tries to minimize redundancy while maintaining degeneracy. This formulation is substantiated using statistical and mathematical notions of degenerate mappings and statistical efficiency. We then illustrate changes in degeneracy and redundancy during the learning of a word repetition task. Finally, we characterize the effects of lesions-to intrinsic and extrinsic connections-using in silico disconnections. These numerical analyses highlight the fundamental difference between degeneracy and redundancy-and how they score distinct imperatives for perceptual inference and structure learning that are relevant to synthetic and biological intelligence.

Disconnection somewhere down the line: Multivariate lesion-symptom mapping of the line bisection error

Line Bisection is a simple task frequently used in stroke patients to diagnose disorders of spatial perception characterized by a directional bisection bias to the ipsilesional side. However, previous anatomical and behavioural findings are contradictory, and the diagnostic validity of the line bisection task has been challenged. We hereby aimed to re-analyse the anatomical basis of pathological line bisection by using multivariate lesion-symptom mapping and disconnection-symptom mapping based on support vector regression in a sample of 163 right hemispheric acute stroke patients. In line with some previous studies, we observed that pathological line bisection was related to more than a single focal lesion location. Cortical damage primarily to right parietal areas, particularly the inferior parietal lobe, including the angular gyrus, as well as damage to the right basal ganglia contributed to the pathology. In contrast to some previous studies, an involvement of frontal cortical brain areas in the line bisection task was not observed. Subcortically, damage to the right superior longitudinal fasciculus (I, II and III) and arcuate fasciculus as well as the internal capsule was associated with line bisection errors. Moreover, white matter damage of interhemispheric fibre bundles, such as the anterior commissure and posterior parts of the corpus callosum projecting into the left hemisphere, was predictive of pathological deviation in the line bisection task.

A Bayesian Account of Generalist and Specialist Formation Under the Active Inference Framework

This paper offers a formal account of policy learning, or habitual behavioral optimization, under the framework of Active Inference. In this setting, habit formation becomes an autodidactic, experience-dependent process, based upon what the agent sees itself doing. We focus on the effect of environmental volatility on habit formation by simulating artificial agents operating in a partially observable Markov decision process. Specifically, we used a "two-step" maze paradigm, in which the agent has to decide whether to go left or right to secure a reward. We observe that in volatile environments with numerous reward locations, the agents learn to adopt a generalist strategy, never forming a strong habitual behavior for any preferred maze direction. Conversely, in conservative or static environments, agents adopt a specialist strategy; forming strong preferences for policies that result in approach to a small number of previously-observed reward locations. The pros and cons of the two strategies are tested and discussed. In general, specialization offers greater benefits, but only when contingencies are conserved over time. We consider the implications of this formal (Active Inference) account of policy learning for understanding the relationship between specialization and habit formation.

Reduced effective connectivity between right parietal and inferior frontal cortex during audiospatial perception in neglect patients with a right-hemisphere lesion

A lesion to the right hemisphere of the brain in humans commonly leads to perceptual neglect of the left side of the sensorium. The clinical observation that lesions to disparate cortical and subcortical areas converge upon similar behavioural symptoms points to neglect as a dysconnection syndrome that may result from the disruption of a distributed network, rather than aberrant computations in any particular brain region. To test this hypothesis, we used Bayesian analysis of effective connectivity based on electroencephalographic recordings in ten patients (6 male, 4 female; age range 41-68) with left-sided neglect following a right-hemisphere lesion. In line with previous research, age-matched healthy controls showed a contralateral increase in connection strength between parietal and frontal cortex with respect to the laterality of audiospatial oddball stimuli. Neglect patients, however, showed a dysconnection between parietal and frontal cortex in the right hemisphere when oddballs appeared on their left side, but preserved connectivity in the left hemisphere when stimuli appeared on their right. This preserved fronto-parietal connectivity was associated with lower neglect severity. Moreover, we saw ipsilateral fronto-temporal connectivity increases for oddballs appearing on the neglected side, which might be a compensatory mechanism for residual left side awareness. No group differences were found in intrinsic (within-region) connectivity. While further validation is required in a bigger sample, our findings are in keeping with the idea that neglect results from the disruption of a distributed network, rather than a lesion to any single brain region. SIGNIFICANCE STATEMENT: Lesions to the right hemisphere of the brain commonly lead to neglect syndrome, characterized by perceptual deficits where patients are unaware of the left side of their body and environment. Using analysis of non-invasive electrophysiological recordings, we provide evidence that patients with left-sided neglect have reduced connectivity between the right parietal and frontal cortex during audiospatial stimuli, but preserved connectivity between regions in the non-lesioned left hemisphere. Moreover, for these intact connections we observed an ipsilateral fronto-temporal increase in connectivity during oddballs appearing on the neglected side, which might be a compensatory mechanism for residual perception. Crucially, we found that patients with more severe neglect symptoms had reduced connectivity between parietal and frontal cortex in the left hemisphere. This suggests that neglect may be caused by the disruption of a distributed network in the brain, rather than a lesion to any particular brain region.

Inferring What to Do (And What Not to)

In recent years, the "planning as inference" paradigm has become central to the study of behaviour. The advance offered by this is the formalisation of motivation as a prior belief about "how I am going to act". This paper provides an overview of the factors that contribute to this prior. These are rooted in optimal experimental design, information theory, and statistical decision making. We unpack how these factors imply a functional architecture for motivated behaviour. This raises an important question: how can we put this architecture to work in the service of understanding observed neurobiological structure? To answer this question, we draw from established techniques in experimental studies of behaviour. Typically, these examine the influence of perturbations of the nervous system-which include pathological insults or optogenetic manipulations-to see their influence on behaviour. Here, we argue that the message passing that emerges from inferring what to do can be similarly perturbed. If a given perturbation elicits the same behaviours as a focal brain lesion, this provides a functional interpretation of empirical findings and an anatomical grounding for theoretical results. We highlight examples of this approach that influence different sorts of goal-directed behaviour, active learning, and decision making. Finally, we summarise their implications for the neuroanatomy of inferring what to do (and what not to).

Generalised free energy and active inference

Active inference is an approach to understanding behaviour that rests upon the idea that the brain uses an internal generative model to predict incoming sensory data. The fit between this model and data may be improved in two ways. The brain could optimise probabilistic beliefs about the variables in the generative model (i.e. perceptual inference). Alternatively, by acting on the world, it could change the sensory data, such that they are more consistent with the model. This implies a common objective function (variational free energy) for action and perception that scores the fit between an internal model and the world. We compare two free energy functionals for active inference in the framework of Markov decision processes. One of these is a functional of beliefs (i.e. probability distributions) about states and policies, but a function of observations, while the second is a functional of beliefs about all three. In the former (expected free energy), prior beliefs about outcomes are not part of the generative model (because they are absorbed into the prior over policies). Conversely, in the second (generalised free energy), priors over outcomes become an explicit component of the generative model. When using the free energy function, which is blind to future observations, we equip the generative model with a prior over policies that ensure preferred (i.e. priors over) outcomes are realised. In other words, if we expect to encounter a particular kind of outcome, this lends plausibility to those policies for which this outcome is a consequence. In addition, this formulation ensures that selected policies minimise uncertainty about future outcomes by minimising the free energy expected in the future. When using the free energy functional-that effectively treats future observations as hidden states-we show that policies are inferred or selected that realise prior preferences by minimising the free energy of future expectations. Interestingly, the form of posterior beliefs about policies (and associated belief updating) turns out to be identical under both formulations, but the quantities used to compute them are not.

Introducing a Bayesian model of selective attention based on active inference

Information gathering comprises actions whose (sensory) consequences resolve uncertainty (i.e., are salient). In other words, actions that solicit salient information cause the greatest shift in beliefs (i.e., information gain) about the causes of our sensations. However, not all information is relevant to the task at hand: this is especially the case in complex, naturalistic scenes. This paper introduces a formal model of selective attention based on active inference and contextual epistemic foraging. We consider a visual search task with a special emphasis on goal-directed and task-relevant exploration. In this scheme, attention modulates the expected fidelity (precision) of the mapping between observations and hidden states in a state-dependent or context-sensitive manner. This ensures task-irrelevant observations have little expected information gain, and so the agent - driven to reduce expected surprise (i.e., uncertainty) - does not actively seek them out. Instead, it selectively samples task-relevant observations, which inform (task-relevant) hidden states. We further show, through simulations, that the atypical exploratory behaviours in conditions such as autism and anxiety may be due to a failure to appropriately modulate sensory precision in a context-specific way.

Using machine learning-based lesion behavior mapping to identify anatomical networks of cognitive dysfunction: Spatial neglect and attention

Previous lesion behavior studies primarily used univariate lesion behavior mapping techniques to map the anatomical basis of spatial neglect after right brain damage. These studies led to inconsistent results and lively controversies. Given these inconsistencies, the idea of a wide-spread network that might underlie spatial orientation and neglect has been pushed forward. In such case, univariate lesion behavior mapping methods might have been inherently limited in detecting the presumed network due to limited statistical power. By comparing various univariate analyses with multivariate lesion-mapping based on support vector regression, we aimed to validate the network hypothesis directly in a large sample of 203 newly recruited right brain damaged patients. If the exact same correction factors and parameter combinations (FDR correction and dTLVC for lesion size control) were used, both univariate as well as multivariate approaches uncovered the same complex network pattern underlying spatial neglect. At the cortical level, lesion location dominantly affected the temporal cortex and its borders into inferior parietal and occipital cortices. Beyond, frontal and subcortical gray matter regions as well as white matter tracts connecting these regions were affected. Our findings underline the importance of a right network in spatial exploration and attention and specifically in the emergence of the core symptoms of spatial neglect.

Dynamic Causal Modelling of Active Vision

In this paper, we draw from recent theoretical work on active perception, which suggests that the brain makes use of an internal (i.e., generative) model to make inferences about the causes of sensations. This view treats visual sensations as consequent on action (i.e., saccades) and implies that visual percepts must be actively constructed via a sequence of eye movements. Oculomotor control calls on a distributed set of brain sources that includes the dorsal and ventral frontoparietal (attention) networks. We argue that connections from the frontal eye fields to ventral parietal sources represent the mapping from “where”, fixation location to information derived from “what” representations in the ventral visual stream. During scene construction, this mapping must be learned, putatively through changes in the effective connectivity of these synapses. Here, we test the hypothesis that the coupling between the dorsal frontal cortex and the right temporoparietal cortex is modulated during saccadic interrogation of a simple visual scene. Using dynamic causal modeling for magnetoencephalography with (male and female) human participants, we assess the evidence for changes in effective connectivity by comparing models that allow for this modulation with models that do not. We find strong evidence for modulation of connections between the two attention networks; namely, a disinhibition of the ventral network by its dorsal counterpart.

SIGNIFICANCE STATEMENT This work draws from recent theoretical accounts of active vision and provides empirical evidence for changes in synaptic efficacy consistent with these computational models. In brief, we used magnetoencephalography in combination with eye-tracking to assess the neural correlates of a form of short-term memory during a dot cancellation task. Using dynamic causal modeling to quantify changes in effective connectivity, we found evidence that the coupling between the dorsal and ventral attention networks changed during the saccadic interrogation of a simple visual scene. Intuitively, this is consistent with the idea that these neuronal connections may encode beliefs about “what I would see if I looked there”, and that this mapping is optimized as new data are obtained with each fixation.

Neuronal message passing using Mean-field, Bethe, and Marginal approximations

Neuronal computations rely upon local interactions across synapses. For a neuronal network to perform inference, it must integrate information from locally computed messages that are propagated among elements of that network. We review the form of two popular (Bayesian) message passing schemes and consider their plausibility as descriptions of inference in biological networks. These are variational message passing and belief propagation - each of which is derived from a free energy functional that relies upon different approximations (mean-field and Bethe respectively). We begin with an overview of these schemes and illustrate the form of the messages required to perform inference using Hidden Markov Models as generative models. Throughout, we use factor graphs to show the form of the generative models and of the messages they entail. We consider how these messages might manifest neuronally and simulate the inferences they perform. While variational message passing offers a simple and neuronally plausible architecture, it falls short of the inferential performance of belief propagation. In contrast, belief propagation allows exact computation of marginal posteriors at the expense of the architectural simplicity of variational message passing. As a compromise between these two extremes, we offer a third approach - marginal message passing - that features a simple architecture, while approximating the performance of belief propagation. Finally, we link formal considerations to accounts of neurological and psychiatric syndromes in terms of aberrant message passing.

Computational mechanisms of curiosity and goal-directed exploration

Successful behaviour depends on the right balance between maximising reward and soliciting information about the world. Here, we show how different types of information-gain emerge when casting behaviour as surprise minimisation. We present two distinct mechanisms for goal-directed exploration that express separable profiles of active sampling to reduce uncertainty. 'Hidden state' exploration motivates agents to sample unambiguous observations to accurately infer the (hidden) state of the world. Conversely, 'model parameter' exploration, compels agents to sample outcomes associated with high uncertainty, if they are informative for their representation of the task structure. We illustrate the emergence of these types of information-gain, termed active inference and active learning, and show how these forms of exploration induce distinct patterns of 'Bayes-optimal' behaviour. Our findings provide a computational framework for understanding how distinct levels of uncertainty systematically affect the exploration-exploitation trade-off in decision-making.

The Anatomy of Inference: Generative Models and Brain Structure

To infer the causes of its sensations, the brain must call on a generative (predictive) model. This necessitates passing local messages between populations of neurons to update beliefs about hidden variables in the world beyond its sensory samples. It also entails inferences about how we will act. Active inference is a principled framework that frames perception and action as approximate Bayesian inference. This has been successful in accounting for a wide range of physiological and behavioral phenomena. Recently, a process theory has emerged that attempts to relate inferences to their neurobiological substrates. In this paper, we review and develop the anatomical aspects of this process theory. We argue that the form of the generative models required for inference constrains the way in which brain regions connect to one another. Specifically, neuronal populations representing beliefs about a variable must receive input from populations representing the Markov blanket of that variable. We illustrate this idea in four different domains: perception, planning, attention, and movement. In doing so, we attempt to show how appealing to generative models enables us to account for anatomical brain architectures. Ultimately, committing to an anatomical theory of inference ensures we can form empirical hypotheses that can be tested using neuroimaging, neuropsychological, and electrophysiological experiments.

Impulsivity and Active Inference

This paper characterizes impulsive behavior using a patch-leaving paradigm and active inference-a framework for describing Bayes optimal behavior. This paradigm comprises different environments (patches) with limited resources that decline over time at different rates. The challenge is to decide when to leave the current patch for another to maximize reward. We chose this task because it offers an operational characterization of impulsive behavior, namely, maximizing proximal reward at the expense of future gain. We use a Markov decision process formulation of active inference to simulate behavioral and electrophysiological responses under different models and prior beliefs. Our main finding is that there are at least three distinct causes of impulsive behavior, which we demonstrate by manipulating three different components of the Markov decision process model. These components comprise (i) the depth of planning, (ii) the capacity to maintain and process information, and (iii) the perceived value of immediate (relative to delayed) rewards. We show how these manipulations change beliefs and subsequent choices through variational message passing. Furthermore, we appeal to the process theories associated with this message passing to simulate neuronal correlates. In future work, we will use this scheme to identify the prior beliefs that underlie different sorts of impulsive behavior-and ask whether different causes of impulsivity can be inferred from the electrophysiological correlates of choice behavior.

Precision and False Perceptual Inference

Accurate perceptual inference fundamentally depends upon accurate beliefs about the reliability of sensory data. In this paper, we describe a Bayes optimal and biologically plausible scheme that refines these beliefs through a gradient descent on variational free energy. To illustrate this, we simulate belief updating during visual foraging and show that changes in estimated sensory precision (i.e., confidence in visual data) are highly sensitive to prior beliefs about the contents of a visual scene. In brief, confident prior beliefs induce an increase in estimated precision when consistent with sensory evidence, but a decrease when they conflict. Prior beliefs held with low confidence are rapidly updated to posterior beliefs, determined by sensory data. These induce much smaller changes in beliefs about sensory precision. We argue that pathologies of scene construction may be due to abnormal priors, and show that these can induce a reduction in estimated sensory precision. Having previously associated this precision with cholinergic signaling, we note that several neurodegenerative conditions are associated with visual disturbances and cholinergic deficits; notably, the synucleinopathies. On relating the message passing in our model to the functional anatomy of the ventral visual stream, we find that simulated neuronal loss in temporal lobe regions induces confident, inaccurate, empirical prior beliefs at lower levels in the visual hierarchy. This provides a plausible, if speculative, computational mechanism for the loss of cholinergic signaling and the visual disturbances associated with temporal lobe Lewy body pathology. This may be seen as an illustration of the sorts of hypotheses that may be expressed within this computational framework.

The Discrete and Continuous Brain: From Decisions to Movement-And Back Again

To act upon the world, creatures must change continuous variables such as muscle length or chemical concentration. In contrast, decision making is an inherently discrete process, involving the selection among alternative courses of action. In this article, we consider the interface between the discrete and continuous processes that translate our decisions into movement in a Newtonian world-and how movement informs our decisions. We do so by appealing to active inference, with a special focus on the oculomotor system. Within this exemplar system, we argue that the superior colliculus is well placed to act as a discrete-continuous interface. Interestingly, when the neuronal computations within the superior colliculus are formulated in terms of active inference, we find that many aspects of its neuroanatomy emerge from the computations it must perform in this role.

The Discrete and Continuous Brain: From Decisions to Movement-And Back Again

To act upon the world, creatures must change continuous variables such as muscle length or chemical concentration. In contrast, decision making is an inherently discrete process, involving the selection among alternative courses of action. In this article, we consider the interface between the discrete and continuous processes that translate our decisions into movement in a Newtonian world—and how movement informs our decisions. We do so by appealing to active inference, with a special focus on the oculomotor system. Within this exemplar system, we argue that the superior colliculus is well placed to act as a discrete-continuous interface. Interestingly, when the neuronal computations within the superior colliculus are formulated in terms of active inference, we find that many aspects of its neuroanatomy emerge from the computations it must perform in this role.

Computational Neuropsychology and Bayesian Inference

Computational theories of brain function have become very influential in neuroscience. They have facilitated the growth of formal approaches to disease, particularly in psychiatric research. In this paper, we provide a narrative review of the body of computational research addressing neuropsychological syndromes, and focus on those that employ Bayesian frameworks. Bayesian approaches to understanding brain function formulate perception and action as inferential processes. These inferences combine ‘prior’ beliefs with a generative (predictive) model to explain the causes of sensations. Under this view, neuropsychological deficits can be thought of as false inferences that arise due to aberrant prior beliefs (that are poor fits to the real world). This draws upon the notion of a Bayes optimal pathology – optimal inference with suboptimal priors – and provides a means for computational phenotyping. In principle, any given neuropsychological disorder could be characterized by the set of prior beliefs that would make a patient’s behavior appear Bayes optimal. We start with an overview of some key theoretical constructs and use these to motivate a form of computational neuropsychology that relates anatomical structures in the brain to the computations they perform. Throughout, we draw upon computational accounts of neuropsychological syndromes. These are selected to emphasize the key features of a Bayesian approach, and the possible types of pathological prior that may be present. They range from visual neglect through hallucinations to autism. Through these illustrative examples, we review the use of Bayesian approaches to understand the link between biology and computation that is at the heart of neuropsychology.