arXiv subjects

Karl Friston

Publications and source records attributed to Karl Friston.

71 records · Page 4Linked to original sources

arXiv2020

Anticipation in architectural experience: a computational neurophenomenology for architecture?

The perceptual experience of architecture is enacted by the sensory and motor system. When we act, we change the perceived environment according to a set of expectations that depend on our body and the built environment. The continuous process of collecting sensory information is thus based on bodily affordances. Affordances characterize the fit between the physical structure of the body and capacities for movement in the built environment. Since little has been done regarding the role of architectural design in the emergence of perceptual experience on a neuronal level, this paper offers a first step towards the role of architectural design in perceptual experience. An approach to synthesize concepts from computational neuroscience with architectural phenomenology into a computational neurophenomenology is considered. The outcome is a framework under which studies of architecture and cognitive neuroscience can be cast.

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arXiv2020

Deep active inference agents using Monte-Carlo methods

Active inference is a Bayesian framework for understanding biological intelligence. The underlying theory brings together perception and action under one single imperative: minimizing free energy. However, despite its theoretical utility in explaining intelligence, computational implementations have been restricted to low-dimensional and idealized situations. In this paper, we present a neural architecture for building deep active inference agents operating in complex, continuous state-spaces using multiple forms of Monte-Carlo (MC) sampling. For this, we introduce a number of techniques, novel to active inference. These include: i) selecting free-energy-optimal policies via MC tree search, ii) approximating this optimal policy distribution via a feed-forward `habitual' network, iii) predicting future parameter belief updates using MC dropouts and, finally, iv) optimizing state transition precision (a high-end form of attention). Our approach enables agents to learn environmental dynamics efficiently, while maintaining task performance, in relation to reward-based counterparts. We illustrate this in a new toy environment, based on the dSprites data-set, and demonstrate that active inference agents automatically create disentangled representations that are apt for modeling state transitions. In a more complex Animal-AI environment, our agents (using the same neural architecture) are able to simulate future state transitions and actions (i.e., plan), to evince reward-directed navigation - despite temporary suspension of visual input. These results show that deep active inference - equipped with MC methods - provides a flexible framework to develop biologically-inspired intelligent agents, with applications in both machine learning and cognitive science.

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arXiv2020

Is the free-energy principle a formal theory of semantics? From variational density dynamics to neural and phenotypic representations

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to assess which philosophical stance - in relation to the ontological and epistemological status of representations - is most appropriate. We focus on non-realist (deflationary and fictionalist-instrumentalist) approaches. We consider a deflationary account of mental representation, according to which the explanatorily relevant contents of neural representations are mathematical, rather than cognitive, and a fictionalist or instrumentalist account, according to which representations are scientifically useful fictions that serve explanatory (and other) aims. After reviewing the free-energy principle and active inference, we argue that the model of adaptive phenotypes under the free-energy principle can be used to furnish a formal semantics, enabling us to assign semantic content to specific phenotypic states (the internal states of a Markovian system that exists far from equilibrium). We propose a modified fictionalist account: an organism-centered fictionalism or instrumentalism. We argue that, under the free-energy principle, pursuing even a deflationary account of the content of neural representations licenses the appeal to the kind of semantic content involved in the aboutness or intentionality of cognitive systems; our position is thus coherent with, but rests on distinct assumptions from, the realist position. We argue that the free-energy principle thereby explains the aboutness or intentionality in living systems and hence their capacity to parse their sensory stream using an ontology or set of semantic factors.

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arXiv2020

Cognition coming about: self-organisation and free-energy

Wright and Bourkes compelling article rightly points out that existing models of embryogenesis fail to explain the mechanisms and functional significance of the dynamic connections among neurons. We pursue their account of Dynamic Logic by appealing to the Markov blanket formalism that underwrites the Free Energy Principle. We submit that this allows one to model embryogenesis as self-organisation in a dynamical system that minimises free-energy. The ensuing formalism may be extended to also explain the autonomous emergence of cognition, specifically in the brain, as a dynamic self-assembling process.

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arXiv2020

Sophisticated Inference

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about 'what would happen if I did that' to 'what would I believe about what would happen if I did that'. The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

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arXiv2020

Markov Blankets in the Brain

Recent characterisations of self-organising systems depend upon the presence of a Markov blanket: a statistical boundary that mediates the interactions between what is inside of and outside of a system. We leverage this idea to provide an analysis of partitions in neuronal systems. This is applicable to brain architectures at multiple scales, enabling partitions into single neurons, brain regions, and brain-wide networks. This treatment is based upon the canonical micro-circuitry used in empirical studies of effective connectivity, so as to speak directly to practical applications. This depends upon the dynamic coupling between functional units, whose form recapitulates that of a Markov blanket at each level. The nuance afforded by partitioning neural systems in this way highlights certain limitations of modular perspectives of brain function that only consider a single level of description.

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arXiv2020

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.

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arXiv2020

A World unto Itself: Human Communication as Active Inference

Work in developmental psychology suggests that humans are predisposed to align their mental states with other individuals. This manifests principally in cooperative communication, that is, intentional communication geared towards aligning mental states. This viewpoint has received ample empirical support. However, this view lacks a formal grounding, and provides no precise neuroscientific hypotheses. To remedy this, we suggest an active inference approach to cooperative communication. We suggest that humans appear to possess an evolved adaptive prior belief that their mental states are aligned with those of conspecifics. Cooperative communication emerges as the principal means to gather evidence for this belief. Our approach has implications for the study of the usage, ontogeny, and cultural evolution of human communication.

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arXiv2020

Some interesting observations on the free energy principle

Biehl et al (2020) present some interesting observations on an early formulation of the free energy principle in (Friston, 2013). We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various (subsets of) states in sparsely coupled systems that possess a Markov blanket - and the distinction between exact and approximate Bayesian inference, implied by the ensuing Bayesian mechanics.

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arXiv2019

Bayesian model reduction

This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in their priors. In the setting of variational Bayes this has an analytical solution, which finesses the problem of scoring large model spaces in model comparison or structure learning. In this technical note, we review Bayesian model reduction and provide the relevant equations for several discrete and continuous probability distributions. We provide worked examples in the context of multivariate linear regression, Gaussian mixture models and dynamical systems (dynamic causal modelling). These examples are accompanied by the Matlab scripts necessary to reproduce the results. Finally, we briefly review recent applications in the fields of neuroimaging and neuroscience. Specifically, we consider structure learning and hierarchical or empirical Bayes that can be regarded as a metaphor for neurobiological processes like abductive reasoning.

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arXiv2019

Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems.

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arXiv2019

A free energy principle for a particular physics

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of things) at increasingly higher spatiotemporal scales. This decomposition provides a description of small things; e.g., quantum mechanics - via the Schrodinger equation, ensembles of small things - via statistical mechanics and related fluctuation theorems, through to big things - via classical mechanics. These descriptions are complemented with a Bayesian mechanics for autonomous or active things. Although this work provides a formulation of every thing, its main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In brief, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states of something as representing or making inferences about its external states. The ensuing Bayesian mechanics is compatible with quantum, statistical and classical mechanics and may offer a formal description of lifelike particles.

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arXiv2017

Bayesian Belief Updating of Spatiotemporal Seizure Dynamics

Epileptic seizure activity shows complicated dynamics in both space and time. To understand the evolution and propagation of seizures spatially extended sets of data need to be analysed. We have previously described an efficient filtering scheme using variational Laplace that can be used in the Dynamic Causal Modelling (DCM) framework [Friston, 2003] to estimate the temporal dynamics of seizures recorded using either invasive or non-invasive electrical recordings (EEG/ECoG). Spatiotemporal dynamics are modelled using a partial differential equation -- in contrast to the ordinary differential equation used in our previous work on temporal estimation of seizure dynamics [Cooray, 2016]. We provide the requisite theoretical background for the method and test the ensuing scheme on simulated seizure activity data and empirical invasive ECoG data. The method provides a framework to assimilate the spatial and temporal dynamics of seizure activity, an aspect of great physiological and clinical importance.

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arXiv2017

Approximate Bayesian inference as a gauge theory

In a published paper [Sengupta, 2016], we have proposed that the brain (and other self-organized biological and artificial systems) can be characterized via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we have shown that a gauge theory for neuronal dynamics -- based on approximate Bayesian inference -- has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception. Here, we describe the technical apparatus that enables such a variational inference on manifolds. Particularly, the novel contribution of this paper is an algorithm that utlizes a Schild's ladder for parallel transport of sufficient statistics (means, covariances, etc.) on a statistical manifold.

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arXiv2017

Sentient Self-Organization: Minimal dynamics and circular causality

Theoretical arguments and empirical evidence in neuroscience suggests that organisms represent or model their environment by minimizing a variational free-energy bound on the surprise associated with sensory signals from the environment. In this paper, we study phase transitions in coupled dissipative dynamical systems (complex Ginzburg-Landau equations) under a variety of coupling conditions to model the exchange of a system (agent) with its environment. We show that arbitrary coupling between sensory signals and the internal state of a system -- or those between its action and external (environmental) states -- do not guarantee synchronous dynamics between external and internal states: the spatial structure and the temporal dynamics of sensory signals and action (that comprise the system's Markov blanket) have to be pruned to produce synchrony. This synchrony is necessary for an agent to infer environmental states -- a pre-requisite for survival. Therefore, such sentient dynamics, relies primarily on approximate synchronization between the agent and its niche.

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arXiv2016

Active inference, eye movements and oculomotor delays

This paper considers the problem of sensorimotor delays in the optimal control of (smooth) eye movements under uncertainty. Specifically, we consider delays in the visuo-oculomotor loop and their implications for active inference. Active inference uses a generalisation of Kalman filtering to provide Bayes optimal estimates of hidden states and action in generalized coordinates of motion. Representing hidden states in generalized coordinates provides a simple way of compensating for both sensory and oculomotor delays. The efficacy of this scheme is illustrated using neuronal simulations of pursuit initiation responses, with and without compensation. We then consider an extension of the gener-ative model to simulate smooth pursuit eye movements - in which the visuo-oculomotor system believes both the target and its centre of gaze are attracted to a (hidden) point moving in the visual field. Finally, the generative model is equipped with a hierarchical structure, so that it can recognise and remember unseen (occluded) trajectories and emit anticipatory responses. These simulations speak to a straightforward and neurobiologically plausible solution to the generic problem of integrating information from different sources with different temporal delays and the particular difficulties encountered when a system - like the oculomotor system - tries to control its environment with delayed signals.

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arXiv2016

The connected brain: Causality, models and intrinsic dynamics

Recently, there have been several concerted international efforts - the BRAIN initiative, European Human Brain Project and the Human Connectome Project, to name a few - that hope to revolutionize our understanding of the connected brain. Over the past two decades, functional neuroimaging has emerged as the predominant technique in systems neuroscience. This is foreshadowed by an ever increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. In this article, we summarize pedagogically the (deep) history of brain mapping. We will highlight the theoretical advances made in the (dynamic) causal modelling of brain function - that may have escaped the wider audience of this article - and provide a brief overview of recent developments and interesting clinical applications. We hope that this article will engage the signal processing community by showcasing the inherently multidisciplinary nature of this important topic and the intriguing questions that are being addressed.

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