arXiv subjects

Karl Friston

Publications and source records attributed to Karl Friston.

At least 55 records · Page 3Linked to original sources

arXiv2022

Bistable perception, precision and neuromodulation

Bistable perception follows from observing a static, ambiguous, (visual) stimulus with two possible interpretations. Here, we present an active (Bayesian) inference account of bistable perception and posit that perceptual transitions between different interpretations (i.e., inferences) of the same stimulus ensue from specific eye movements that shift the focus to a different visual feature. Formally, these inferences are a consequence of precision control that determines how confident beliefs are and change the frequency with which one can perceive - and alternate between - two distinct percepts. We hypothesised that there are multiple, but distinct, ways in which precision modulation can interact to give rise to a similar frequency of bistable perception. We validated this using numerical simulations of the Necker's cube paradigm and demonstrate the multiple routes that underwrite the frequency of perceptual alternation. Our results provide an (enactive) computational account of the intricate precision balance underwriting bistable perception. Importantly, these precision parameters can be considered the computational homologues of particular neurotransmitters - i.e., acetylcholine, noradrenaline, dopamine - that have been previously implicated in controlling bistable perception, providing a computational link between the neurochemistry and perception.

q-bio.NC↗

arXiv2022

Natural Language Syntax Complies with the Free-Energy Principle

Natural language syntax yields an unbounded array of hierarchically structured expressions. We claim that these are used in the service of active inference in accord with the free-energy principle (FEP). While conceptual advances alongside modelling and simulation work have attempted to connect speech segmentation and linguistic communication with the FEP, we extend this program to the underlying computations responsible for generating syntactic objects. We argue that recently proposed principles of economy in language design - such as "minimal search" criteria from theoretical syntax - adhere to the FEP. This affords a greater degree of explanatory power to the FEP - with respect to higher language functions - and offers linguistics a grounding in first principles with respect to computability. We show how both tree-geometric depth and a Kolmogorov complexity estimate (recruiting a Lempel-Ziv compression algorithm) can be used to accurately predict legal operations on syntactic workspaces, directly in line with formulations of variational free energy minimization. This is used to motivate a general principle of language design that we term Turing-Chomsky Compression (TCC). We use TCC to align concerns of linguists with the normative account of self-organization furnished by the FEP, by marshalling evidence from theoretical linguistics and psycholinguistics to ground core principles of efficient syntactic computation within active inference.

cs.CL↗

arXiv2022

Global dynamics of neural mass models

Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations as gradient flows on a potential function of intrinsic connectivity. These results provide analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. Crucially, this work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. In principle, this formulation of cortical dynamics may improve our understanding of the itinerancy that underwrites measures of cortical activity (through EEG or MEG). Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as onset of seizure activity in epilepsy or beta bursts in Parkinsons disease.

q-bio.NC↗

arXiv2022

Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric structures to solve these problems efficiently. We show that a wide range of geometric theories emerge naturally in these fields, ranging from measure-preserving processes, information divergences, Poisson geometry, and geometric integration. Specifically, we explain how (i) leveraging the symplectic geometry of Hamiltonian systems enable us to construct (accelerated) sampling and optimisation methods, (ii) the theory of Hilbertian subspaces and Stein operators provides a general methodology to obtain robust estimators, (iii) preserving the information geometry of decision-making yields adaptive agents that perform active inference. Throughout, we emphasise the rich connections between these fields; e.g., inference draws on sampling and optimisation, and adaptive decision-making assesses decisions by inferring their counterfactual consequences. Our exposition provides a conceptual overview of underlying ideas, rather than a technical discussion, which can be found in the references herein.

stat.ML↗

arXiv2022

The Free Energy Principle drives neuromorphic development

We show how any system with morphological degrees of freedom and locally limited free energy will, under the constraints of the free energy principle, evolve toward a neuromorphic morphology that supports hierarchical computations in which each level of the hierarchy enacts a coarse-graining of its inputs, and dually a fine-graining of its outputs. Such hierarchies occur throughout biology, from the architectures of intracellular signal transduction pathways to the large-scale organization of perception and action cycles in the mammalian brain. Formally, the close formal connections between cone-cocone diagrams (CCCD) as models of quantum reference frames on the one hand, and between CCCDs and topological quantum field theories on the other, allow the representation of such computations in the fully-general quantum-computational framework of topological quantum neural networks.

quant-ph↗

arXiv2022

Reward Maximisation through Discrete Active Inference

Active inference is a probabilistic framework for modelling the behaviour of biological and artificial agents, which derives from the principle of minimising free energy. In recent years, this framework has successfully been applied to a variety of situations where the goal was to maximise reward, offering comparable and sometimes superior performance to alternative approaches. In this paper, we clarify the connection between reward maximisation and active inference by demonstrating how and when active inference agents perform actions that are optimal for maximising reward. Precisely, we show the conditions under which active inference produces the optimal solution to the Bellman equation--a formulation that underlies several approaches to model-based reinforcement learning and control. On partially observed Markov decision processes, the standard active inference scheme can produce Bellman optimal actions for planning horizons of 1, but not beyond. In contrast, a recently developed recursive active inference scheme (sophisticated inference) can produce Bellman optimal actions on any finite temporal horizon. We append the analysis with a discussion of the broader relationship between active inference and reinforcement learning.

cs.AI↗

arXiv2022

pymdp: A Python library for active inference in discrete state spaces

Active inference is an account of cognition and behavior in complex systems which brings together action, perception, and learning under the theoretical mantle of Bayesian inference. Active inference has seen growing applications in academic research, especially in fields that seek to model human or animal behavior. While in recent years, some of the code arising from the active inference literature has been written in open source languages like Python and Julia, to-date, the most popular software for simulating active inference agents is the DEM toolbox of SPM, a MATLAB library originally developed for the statistical analysis and modelling of neuroimaging data. Increasing interest in active inference, manifested both in terms of sheer number as well as diversifying applications across scientific disciplines, has thus created a need for generic, widely-available, and user-friendly code for simulating active inference in open-source scientific computing languages like Python. The Python package we present here, pymdp (see https://github.com/infer-actively/pymdp), represents a significant step in this direction: namely, we provide the first open-source package for simulating active inference with partially-observable Markov Decision Processes or POMDPs. We review the package's structure and explain its advantages like modular design and customizability, while providing in-text code blocks along the way to demonstrate how it can be used to build and run active inference processes with ease. We developed pymdp to increase the accessibility and exposure of the active inference framework to researchers, engineers, and developers with diverse disciplinary backgrounds. In the spirit of open-source software, we also hope that it spurs new innovation, development, and collaboration in the growing active inference community.

cs.AI↗

arXiv2022

GeoSPM: Geostatistical parametric mapping for medicine

The characteristics and determinants of health and disease are often organised in space, reflecting our spatially extended nature. Understanding the influence of such factors requires models capable of capturing spatial relations. Though a mature discipline, spatial analysis is comparatively rare in medicine, arguably a consequence of the complexity of the domain and the inclemency of the data regimes that govern it. Drawing on statistical parametric mapping, a framework for topological inference well-established in the realm of neuroimaging, we propose and validate a novel approach to the spatial analysis of diverse clinical data - GeoSPM - based on differential geometry and random field theory. We evaluate GeoSPM across an extensive array of synthetic simulations encompassing diverse spatial relationships, sampling, and corruption by noise, and demonstrate its application on large-scale data from UK Biobank. GeoSPM is transparently interpretable, can be implemented with ease by non-specialists, enables flexible modelling of complex spatial relations, exhibits robustness to noise and under-sampling, offers well-founded criteria of statistical significance, and is through computational efficiency readily scalable to large datasets. We provide a complete, open-source software implementation of GeoSPM, and suggest that its adoption could catalyse the wider use of spatial analysis across the many aspects of medicine that urgently demand it.

stat.ME↗

arXiv2022

Reclaiming saliency: rhythmic precision-modulated action and perception

Computational models of visual attention in artificial intelligence and robotics have been inspired by the concept of a saliency map. These models account for the mutual information between the (current) visual information and its estimated causes. However, they fail to consider the circular causality between perception and action. In other words, they do not consider where to sample next, given current beliefs. Here, we reclaim salience as an active inference process that relies on two basic principles: uncertainty minimisation and rhythmic scheduling. For this, we make a distinction between attention and salience. Briefly, we associate attention with precision control, i.e., the confidence with which beliefs can be updated given sampled sensory data, and salience with uncertainty minimisation that underwrites the selection of future sensory data. Using this, we propose a new account of attention based on rhythmic precision-modulation and discuss its potential in robotics, providing numerical experiments that showcase advantages of precision-modulation for state and noise estimation, system identification and action selection for informative path planning.

cs.RO↗

arXiv2022

Action and Perception as Divergence Minimization

To learn directed behaviors in complex environments, intelligent agents need to optimize objective functions. Various objectives are known for designing artificial agents, including task rewards and intrinsic motivation. However, it is unclear how the known objectives relate to each other, which objectives remain yet to be discovered, and which objectives better describe the behavior of humans. We introduce the Action Perception Divergence (APD), an approach for categorizing the space of possible objective functions for embodied agents. We show a spectrum that reaches from narrow to general objectives. While the narrow objectives correspond to domain-specific rewards as typical in reinforcement learning, the general objectives maximize information with the environment through latent variable models of input sequences. Intuitively, these agents use perception to align their beliefs with the world and use actions to align the world with their beliefs. They infer representations that are informative of past inputs, explore future inputs that are informative of their representations, and select actions or skills that maximally influence future inputs. This explains a wide range of unsupervised objectives from a single principle, including representation learning, information gain, empowerment, and skill discovery. Our findings suggest leveraging powerful world models for unsupervised exploration as a path toward highly adaptive agents that seek out large niches in their environments, rendering task rewards optional.

cs.AI↗

arXiv2021

A free energy principle for generic quantum systems

The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on surprisal (a.k.a., self-information). This upper bound can be read as a Bayesian prediction error. Equivalently, its negative is a lower bound on Bayesian model evidence (a.k.a., marginal likelihood). In short, certain random dynamical systems evince a kind of self-evidencing. Here, we reformulate the FEP in the formal setting of spacetime-background free, scale-free quantum information theory. We show how generic quantum systems can be regarded as observers, which with the standard freedom of choice assumption become agents capable of assigning semantics to observational outcomes. We show how such agents minimize Bayesian prediction error in environments characterized by uncertainty, insufficient learning, and quantum contextuality. We show that in its quantum-theoretic formulation, the FEP is asymptotically equivalent to the Principle of Unitarity. Based on these results, we suggest that biological systems employ quantum coherence as a computational resource and - implicitly - as a communication resource. We summarize a number of problems for future research, particularly involving the resources required for classical communication and for detecting and responding to quantum context switches.

quant-ph↗

arXiv2021

Insula Interoception, Active Inference and Feeling Representation

The body sends interoceptive visceral information through deep brain structures to the cerebral cortex. The insula cortex, organized in hierarchical modules, is the major cortical region receiving interoceptive afferents and contains visceral topographic maps. Yet, the biological significance of the insula's modular architecture in relation to deep brain regions remains unsolved. In this opinion, we propose the Insula Hierarchical Modular Adaptive Interoception Control (IMAC) model to suggest that insula modules (granular, dysgranular and agranular subregions), forming networks with prefrontal (supplementary motor area, dorsolateral and ventromedial cortices) and striatum (posterior, dorsomedial and ventromedial) subregions, are specialized for higher-order interoceptive representations, recruited in a context-dependent manner to support habitual, model-based and exploratory adaptive behavior. We then discuss how insula interoceptive representations, or metaceptions, could give rise to conscious interoceptive feelings built up from low-order visceral representations and associated basic emotions located in deep interoceptive brain structures.

q-bio.NC↗

arXiv2021

Bayesian Mechanics for Stationary Processes

This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady-state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.

math-ph↗

arXiv2021

Active inference, Bayesian optimal design, and expected utility

Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference combines Bayesian decision theory and optimal Bayesian design principles under a single imperative to minimize expected free energy. It is this aspect of active inference that allows for the natural emergence of information-seeking behavior. When removing prior outcomes preferences from expected free energy, active inference reduces to optimal Bayesian design, i.e., information gain maximization. Conversely, active inference reduces to Bayesian decision theory in the absence of ambiguity and relative risk, i.e., expected utility maximization. Using these limiting cases, we illustrate how behaviors differ when agents select actions that optimize expected utility, expected information gain, and expected free energy. Our T-maze simulations show optimizing expected free energy produces goal-directed information-seeking behavior while optimizing expected utility induces purely exploitive behavior and maximizing information gain engenders intrinsically motivated behavior.

stat.ML↗

arXiv2021

Exploration and preference satisfaction trade-off in reward-free learning

Biological agents have meaningful interactions with their environment despite the absence of immediate reward signals. In such instances, the agent can learn preferred modes of behaviour that lead to predictable states -- necessary for survival. In this paper, we pursue the notion that this learnt behaviour can be a consequence of reward-free preference learning that ensures an appropriate trade-off between exploration and preference satisfaction. For this, we introduce a model-based Bayesian agent equipped with a preference learning mechanism (pepper) using conjugate priors. These conjugate priors are used to augment the expected free energy planner for learning preferences over states (or outcomes) across time. Importantly, our approach enables the agent to learn preferences that encourage adaptive behaviour at test time. We illustrate this in the OpenAI Gym FrozenLake and the 3D mini-world environments -- with and without volatility. Given a constant environment, these agents learn confident (i.e., precise) preferences and act to satisfy them. Conversely, in a volatile setting, perpetual preference uncertainty maintains exploratory behaviour. Our experiments suggest that learnable (reward-free) preferences entail a trade-off between exploration and preference satisfaction. Pepper offers a straightforward framework suitable for designing adaptive agents when reward functions cannot be predefined as in real environments.

cs.AI↗

arXiv2021

Bayesian brains and the Rényi divergence

Under the Bayesian brain hypothesis, behavioural variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioural preferences when confronted with similar choices. For example, greedy preferences are a consequence of confident (or precise) beliefs over certain outcomes. Here, we offer an alternative account of behavioural variability using Rényi divergences and their associated variational bounds. Rényi bounds are analogous to the variational free energy (or evidence lower bound) and can be derived under the same assumptions. Importantly, these bounds provide a formal way to establish behavioural differences through an $α$ parameter, given fixed priors. This rests on changes in $α$ that alter the bound (on a continuous scale), inducing different posterior estimates and consequent variations in behaviour. Thus, it looks as if individuals have different priors, and have reached different conclusions. More specifically, $α\to 0^{+}$ optimisation leads to mass-covering variational estimates and increased variability in choice behaviour. Furthermore, $α\to + \infty$ optimisation leads to mass-seeking variational posteriors and greedy preferences. We exemplify this formulation through simulations of the multi-armed bandit task. We note that these $α$ parameterisations may be especially relevant, i.e., shape preferences, when the true posterior is not in the same family of distributions as the assumed (simpler) approximate density, which may be the case in many real-world scenarios. The ensuing departure from vanilla variational inference provides a potentially useful explanation for differences in behavioural preferences of biological (or artificial) agents under the assumption that the brain performs variational Bayesian inference.

q-bio.NC↗

arXiv2021

Neural dynamics under active inference: plausibility and efficiency of information processing

Active inference is a normative framework for explaining behaviour under the free energy principle -- a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on (variational) free energy -- a measure of the fit between an internal (generative) model and sensory observations. The free energy gradient is a prediction error -- plausibly encoded in the average membrane potentials of neuronal populations. Conversely, the expected probability of a state can be expressed in terms of neuronal firing rates. We show that this is consistent with current models of neuronal dynamics and establish face validity by synthesising plausible electrophysiological responses. We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating in both schemes, a measure of the distance traveled in information space that has a direct interpretation in terms of metabolic cost. We show that neural dynamics under active inference are metabolically efficient and suggest that neural representations in biological agents may evolve by approximating steepest descent in information space towards the point of optimal inference.

q-bio.NC↗

arXiv2020

Neural and phenotypic representation under the free-energy principle

The aim of this paper is to leverage the free-energy principle and its corollary process theory, active inference, to develop a generic, generalizable model of the representational capacities of living creatures; that is, a theory of phenotypic representation. Given their ubiquity, we are concerned with distributed forms of representation (e.g., population codes), whereby patterns of ensemble activity in living tissue come to represent the causes of sensory input or data. The active inference framework rests on the Markov blanket formalism, which allows us to partition systems of interest, such as biological systems, into internal states, external states, and the blanket (active and sensory) states that render internal and external states conditionally independent of each other. In this framework, the representational capacity of living creatures emerges as a consequence of their Markovian structure and nonequilibrium dynamics, which together entail a dual-aspect information geometry. This entails a modest representational capacity: internal states have an intrinsic information geometry that describes their trajectory over time in state space, as well as an extrinsic information geometry that allows internal states to encode (the parameters of) probabilistic beliefs about (fictive) external states. Building on this, we describe here how, in an automatic and emergent manner, information about stimuli can come to be encoded by groups of neurons bound by a Markov blanket; what is known as the neuronal packet hypothesis. As a concrete demonstration of this type of emergent representation, we present numerical simulations showing that self-organizing ensembles of active inference agents sharing the right kind of probabilistic generative model are able to encode recoverable information about a stimulus array.

q-bio.NC↗