Thomas Parr

Deep temporal models and active inference

Highlights • Active inference provides a principled account of epistemic behaviour.• Active inference rests upon hierarchical or deep generative models.• Deep generative models of state transitions embody nested temporal structure.• Reading can be simulated via active inference with deep models.• These simulations appear to have a high degree of biological plausibility.

The graphical brain: Belief propagation and active inference

This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models. Crucially, these models can entertain both discrete and continuous states, leading to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to elucidate the requisite message passing in terms of its form and scheduling. To accommodate mixed generative models (of discrete and continuous states), one also has to consider link nodes or factors that enable discrete and continuous representations to talk to each other. When mapping the implicit computational architecture onto neuronal connectivity, several interesting features emerge. For example, Bayesian model averaging and comparison, which link discrete and continuous states, may be implemented in thalamocortical loops. These and other considerations speak to a computational connectome that is inherently state dependent and self-organizing in ways that yield to a principled (variational) account. We conclude with simulations of reading that illustrate the implicit neuronal message passing, with a special focus on how discrete (semantic) representations inform, and are informed by, continuous (visual) sampling of the sensorium. Author Summary This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain.

The active construction of the visual world

ABSTRACT What we see is fundamentally dependent on where we look. Despite this seemingly obvious statement, many accounts of the neurobiology underpinning visual perception fail to consider the active nature of how we sample our sensory world. This review offers an overview of the neurobiology of visual perception, which begins with the control of saccadic eye movements. Starting from here, we can follow the anatomy backwards, to try to understand the functional architecture of neuronal networks that support the interrogation of a visual scene. Many of the principles encountered in this exercise are equally applicable to other perceptual modalities. For example, the somatosensory system, like the visual system, requires the sampling of data through mobile receptive epithelia. Analysis of a somatosensory scene depends on what is palpated, in much the same way that visual analysis relies on what is foveated. The discussion here is structured around the anatomical systems involved in active vision and visual scene construction, but will use these systems to introduce some general theoretical considerations. We will additionally highlight points of contact between the biology and the pathophysiology that has been proposed to cause a clinical disorder of scene construction – spatial hemineglect. HIGHLIGHTSThe neuroanatomy of active vision is reviewed.Saccadic eye movements are controlled by the oculomotor brainstem system.The brainstem system is influenced by the basal ganglia and cortical networks.Hemineglect can result from deficits in networks that select saccadic targets.Memory processes support the temporal continuity of visual experience.

Working memory, attention, and salience in active inference

The psychological concepts of working memory and attention are widely used in the cognitive and neuroscientific literatures. Perhaps because of the interdisciplinary appeal of these concepts, the same terms are often used to mean very different things. Drawing on recent advances in theoretical neurobiology, this paper tries to highlight the correspondence between these established psychological constructs and the formal processes implicit in mathematical descriptions of brain function. Here, we consider attention and salience from the perspective offered by active inference. Using variational principles and simulations, we use active inference to demonstrate how attention and salience can be disambiguated in terms of message passing between populations of neurons in cortical and subcortical structures. In brief, we suggest that salience is something that is afforded to actions that realise epistemic affordance, while attention per se is afforded to precise sensory evidence – or beliefs about the causes of sensations.

Uncertainty, epistemics and active inference

Biological systems—like ourselves—are constantly faced with uncertainty. Despite noisy sensory data, and volatile environments, creatures appear to actively maintain their integrity. To account for this remarkable ability to make optimal decisions in the face of a capricious world, we propose a generative model that represents the beliefs an agent might possess about their own uncertainty. By simulating a noisy and volatile environment, we demonstrate how uncertainty influences optimal epistemic (visual) foraging. In our simulations, saccades were deployed less frequently to regions with a lower sensory precision, while a greater volatility led to a shorter inhibition of return. These simulations illustrate a principled explanation for some cardinal aspects of visual foraging—and allow us to propose a correspondence between the representation of uncertainty and ascending neuromodulatory systems, complementing that suggested by Yu & Dayan (Yu & Dayan 2005 Neuron 46, 681–692. (doi:10.1016/j.neuron.2005.04.026)).

The Markov blankets of life: autonomy, active inference and the free energy principle

This work addresses the autonomous organization of biological systems. It does so by considering the boundaries of biological systems, from individual cells to Home sapiens, in terms of the presence of Markov blankets under the active inference scheme—a corollary of the free energy principle. A Markov blanket defines the boundaries of a system in a statistical sense. Here we consider how a collective of Markov blankets can self-assemble into a global system that itself has a Markov blanket; thereby providing an illustration of how autonomous systems can be understood as having layers of nested and self-sustaining boundaries. This allows us to show that: (i) any living system is a Markov blanketed system and (ii) the boundaries of such systems need not be co-extensive with the biophysical boundaries of a living organism. In other words, autonomous systems are hierarchically composed of Markov blankets of Markov blankets—all the way down to individual cells, all the way up to you and me, and all the way out to include elements of the local environment.

The Computational Anatomy of Visual Neglect

Abstract Visual neglect is a debilitating neuropsychological phenomenon that has many clinical implications and—in cognitive neuroscience—offers an important lesion deficit model. In this article, we describe a computational model of visual neglect based upon active inference. Our objective is to establish a computational and neurophysiological process theory that can be used to disambiguate among the various causes of this important syndrome; namely, a computational neuropsychology of visual neglect. We introduce a Bayes optimal model based upon Markov decision processes that reproduces the visual searches induced by the line cancellation task (used to characterize visual neglect at the bedside). We then consider 3 distinct ways in which the model could be lesioned to reproduce neuropsychological (visual search) deficits. Crucially, these 3 levels of pathology map nicely onto the neuroanatomy of saccadic eye movements and the systems implicated in visual neglect.

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.

Generalised free energy and active inference: can the future cause the past?

We compare two free energy functionals for active inference under Markov decision processes. One of these is a functional of beliefs 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 counterfactual (i.e., 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, 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 counterfactual 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.

Active inference and the anatomy of oculomotion

ABSTRACT Given that eye movement control can be framed as an inferential process, how are the requisite forces generated to produce anticipated or desired fixation? Starting from a generative model based on simple Newtonian equations of motion, we derive a variational solution to this problem and illustrate the plausibility of its implementation in the oculomotor brainstem. We show, through simulation, that the Bayesian filtering equations that implement ‘planning as inference’ can generate both saccadic and smooth pursuit eye movements. Crucially, the associated message passing maps well onto the known connectivity and neuroanatomy of the brainstem – and the changes in these messages over time are strikingly similar to single unit recordings of neurons in the corresponding nuclei. Furthermore, we show that simulated lesions to axonal pathways reproduce eye movement patterns of neurological patients with damage to these tracts. HIGHLIGHTSEye movement control is cast as an inferential process that induces Newtonian rotational forces.A plausible computational anatomy of Bayesian filtering in the brainstem is proposed.Smooth pursuit and saccadic eye movements are simulated.Lesions to the model cause similar patterns of eye movements to those found in neurological patients.