arXiv subjects

Karl Friston

Publications and source records attributed to Karl Friston.

At least 37 records · Page 2Linked to original sources

arXiv2025

SPM 25: open source neuroimaging analysis software

Statistical Parametric Mapping (SPM) is an integrated set of methods for testing hypotheses about the brain's structure and function, using data from imaging devices. These methods are implemented in an open source software package, SPM, which has been in continuous development for more than 30 years by an international community of developers. This paper reports the release of SPM 25.01, a major new version of the software that incorporates novel analysis methods, optimisations of existing methods, as well as improved practices for open science and software development.

q-bio.QM↗

arXiv2024

Active Inference Tree Search in Large POMDPs

The ability to plan ahead efficiently is key for both living organisms and artificial systems. Model-based planning and prospection are widely studied in cognitive neuroscience and artificial intelligence (AI), but from different perspectives--and with different desiderata in mind (biological realism versus scalability) that are difficult to reconcile. Here, we introduce a novel method to plan in POMDPs--Active Inference Tree Search (AcT)--that combines the normative character and biological realism of a leading planning theory in neuroscience (Active Inference) and the scalability of tree search methods in AI. This unification enhances both approaches. On the one hand, tree searches enable the biologically grounded, first principle method of active inference to be applied to large-scale problems. On the other hand, active inference provides a principled solution to the exploration-exploitation dilemma, which is often addressed heuristically in tree search methods. Our simulations show that AcT successfully navigates binary trees that are challenging for sampling-based methods, problems that require adaptive exploration, and the large POMDP problem 'RockSample'--in which AcT reproduces state-of-the-art POMDP solutions. Furthermore, we illustrate how AcT can be used to simulate neurophysiological responses (e.g., in the hippocampus and prefrontal cortex) of humans and other animals that solve large planning problems. These numerical analyses show that Active Tree Search is a principled realisation of neuroscientific and AI planning theories, which offer both biological realism and scalability.

cs.AI↗

arXiv2024

Localising the Seizure Onset Zone from Single-Pulse Electrical Stimulation Responses with a CNN Transformer

Epilepsy is one of the most common neurological disorders, often requiring surgical intervention when medication fails to control seizures. For effective surgical outcomes, precise localisation of the epileptogenic focus - often approximated through the Seizure Onset Zone (SOZ) - is critical yet remains a challenge. Active probing through electrical stimulation is already standard clinical practice for identifying epileptogenic areas. Our study advances the application of deep learning for SOZ localisation using Single-Pulse Electrical Stimulation (SPES) responses, with two key contributions. Firstly, we implement an existing deep learning model to compare two SPES analysis paradigms: divergent and convergent. These paradigms evaluate outward and inward effective connections, respectively. We assess the generalisability of these models to unseen patients and electrode placements using held-out test sets. Our findings reveal a notable improvement in moving from a divergent (AUROC: 0.574) to a convergent approach (AUROC: 0.666), marking the first application of the latter in this context. Secondly, we demonstrate the efficacy of CNN Transformers with cross-channel attention in handling heterogeneous electrode placements, increasing the AUROC to 0.730. These findings represent a significant step in modelling patient-specific intracranial EEG electrode placements in SPES. Future work will explore integrating these models into clinical decision-making processes to bridge the gap between deep learning research and practical healthcare applications.

cs.LG↗

arXiv2024

From pixels to planning: scale-free active inference

This paper describes a discrete state-space model -- and accompanying methods -- for generative modelling. This model generalises partially observed Markov decision processes to include paths as latent variables, rendering it suitable for active inference and learning in a dynamic setting. Specifically, we consider deep or hierarchical forms using the renormalisation group. The ensuing renormalising generative models (RGM) can be regarded as discrete homologues of deep convolutional neural networks or continuous state-space models in generalised coordinates of motion. By construction, these scale-invariant models can be used to learn compositionality over space and time, furnishing models of paths or orbits; i.e., events of increasing temporal depth and itinerancy. This technical note illustrates the automatic discovery, learning and deployment of RGMs using a series of applications. We start with image classification and then consider the compression and generation of movies and music. Finally, we apply the same variational principles to the learning of Atari-like games.

cs.LG↗

arXiv2024

Collective behavior from surprise minimization

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and 'social forces' such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modelling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically-observed collective phenomena, including cohesion, milling and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference -- without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal non-trivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly.

nlin.AO↗

arXiv2024

Mortal Computation: A Foundation for Biomimetic Intelligence

This review motivates and synthesizes research efforts in neuroscience-inspired artificial intelligence and biomimetic computing in terms of mortal computation. Specifically, we characterize the notion of mortality by recasting ideas in biophysics, cybernetics, and cognitive science in terms of a theoretical foundation for sentient behavior. We frame the mortal computation thesis through the Markov blanket formalism and the circular causality entailed by inference, learning, and selection. The ensuing framework -- underwritten by the free energy principle -- could prove useful for guiding the construction of unconventional connectionist computational systems, neuromorphic intelligence, and chimeric agents, including sentient organoids, which stand to revolutionize the long-term future of embodied, enactive artificial intelligence and cognition research.

q-bio.NC↗

arXiv2024

The inner screen model of consciousness: applying the free energy principle directly to the study of conscious experience

This paper presents a model of consciousness that follows directly from the free-energy principle (FEP). We first rehearse the classical and quantum formulations of the FEP. In particular, we consider the inner screen hypothesis that follows from the quantum information theoretic version of the FEP. We then review applications of the FEP to the known sparse (nested and hierarchical) neuro-anatomy of the brain. We focus on the holographic structure of the brain, and how this structure supports (overt and covert) action.

q-bio.NC↗

arXiv2023

Neural representation in active inference: using generative models to interact with -- and understand -- the lived world

This paper considers neural representation through the lens of active inference, a normative framework for understanding brain function. It delves into how living organisms employ generative models to minimize the discrepancy between predictions and observations (as scored with variational free energy). The ensuing analysis suggests that the brain learns generative models to navigate the world adaptively, not (or not solely) to understand it. Different living organisms may possess an array of generative models, spanning from those that support action-perception cycles to those that underwrite planning and imagination; namely, from "explicit" models that entail variables for predicting concurrent sensations, like objects, faces, or people - to "action-oriented models" that predict action outcomes. It then elucidates how generative models and belief dynamics might link to neural representation and the implications of different types of generative models for understanding an agent's cognitive capabilities in relation to its ecological niche. The paper concludes with open questions regarding the evolution of generative models and the development of advanced cognitive abilities - and the gradual transition from "pragmatic" to "detached" neural representations. The analysis on offer foregrounds the diverse roles that generative models play in cognitive processes and the evolution of neural representation.

q-bio.NC↗

arXiv2023

Spectral Dynamic Causal Modelling: A Didactic Introduction and its Relationship with Functional Connectivity

We present a didactic introduction to spectral Dynamic Causal Modelling (DCM), a Bayesian state-space modelling approach used to infer effective connectivity from non-invasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modelling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements--at all time lags--including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

q-bio.NC↗

arXiv2023

Canonical Cortical Field Theories

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

q-bio.NC↗

arXiv2023

Hierarchical generative modelling for autonomous robots

Humans can produce complex whole-body motions when interacting with their surroundings, by planning, executing and combining individual limb movements. We investigated this fundamental aspect of motor control in the setting of autonomous robotic operations. We approach this problem by hierarchical generative modelling equipped with multi-level planning-for autonomous task completion-that mimics the deep temporal architecture of human motor control. Here, temporal depth refers to the nested time scales at which successive levels of a forward or generative model unfold, for example, delivering an object requires a global plan to contextualise the fast coordination of multiple local movements of limbs. This separation of temporal scales also motivates robotics and control. Specifically, to achieve versatile sensorimotor control, it is advantageous to hierarchically structure the planning and low-level motor control of individual limbs. We use numerical and physical simulation to conduct experiments and to establish the efficacy of this formulation. Using a hierarchical generative model, we show how a humanoid robot can autonomously complete a complex task that necessitates a holistic use of locomotion, manipulation, and grasping. Specifically, we demonstrate the ability of a humanoid robot that can retrieve and transport a box, open and walk through a door to reach the destination, approach and kick a football, while showing robust performance in presence of body damage and ground irregularities. Our findings demonstrated the effectiveness of using human-inspired motor control algorithms, and our method provides a viable hierarchical architecture for the autonomous completion of challenging goal-directed tasks.

cs.RO↗

arXiv2023

Brain in the Dark: Design Principles for Neuro-mimetic Learning and Inference

Even though the brain operates in pure darkness, within the skull, it can infer the most likely causes of its sensory input. An approach to modelling this inference is to assume that the brain has a generative model of the world, which it can invert to infer the hidden causes behind its sensory stimuli, that is, perception. This assumption raises key questions: how to formulate the problem of designing brain-inspired generative models, how to invert them for the tasks of inference and learning, what is the appropriate loss function to be optimised, and, most importantly, what are the different choices of mean field approximation (MFA) and their implications for variational inference (VI).

cs.NE↗

arXiv2023

Path integrals, particular kinds, and strange things

This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time. The main results are a method or principle of least action that can be used to emulate the behaviour of particles in open exchange with their external milieu. Particles are defined by a particular partition, in which internal states are individuated from external states by active and sensory blanket states. The variational principle at hand allows one to interpret internal dynamics - of certain kinds of particles - as inferring external states that are hidden behind blanket states. We consider different kinds of particles, and to what extent they can be imbued with an elementary form of inference or sentience. Specifically, we consider the distinction between dissipative and conservative particles, inert and active particles and, finally, ordinary and strange particles. Strange particles can be described as inferring their own actions, endowing them with apparent autonomy or agency. In short - of the kinds of particles afforded by a particular partition - strange kinds may be apt for describing sentient behaviour.

nlin.AO↗

arXiv2023

Designing explainable artificial intelligence with active inference: A framework for transparent introspection and decision-making

This paper investigates the prospect of developing human-interpretable, explainable artificial intelligence (AI) systems based on active inference and the free energy principle. We first provide a brief overview of active inference, and in particular, of how it applies to the modeling of decision-making, introspection, as well as the generation of overt and covert actions. We then discuss how active inference can be leveraged to design explainable AI systems, namely, by allowing us to model core features of ``introspective'' processes and by generating useful, human-interpretable models of the processes involved in decision-making. We propose an architecture for explainable AI systems using active inference. This architecture foregrounds the role of an explicit hierarchical generative model, the operation of which enables the AI system to track and explain the factors that contribute to its own decisions, and whose structure is designed to be interpretable and auditable by human users. We outline how this architecture can integrate diverse sources of information to make informed decisions in an auditable manner, mimicking or reproducing aspects of human-like consciousness and introspection. Finally, we discuss the implications of our findings for future research in AI, and the potential ethical considerations of developing AI systems with (the appearance of) introspective capabilities.

cs.AI↗

arXiv2023

The free energy principle made simpler but not too simple

This paper provides a concise description of the free energy principle, starting from a formulation of random dynamical systems in terms of a Langevin equation and ending with a Bayesian mechanics that can be read as a physics of sentience. It rehearses the key steps using standard results from statistical physics. These steps entail (i) establishing a particular partition of states based upon conditional independencies that inherit from sparsely coupled dynamics, (ii) unpacking the implications of this partition in terms of Bayesian inference and (iii) describing the paths of particular states with a variational principle of least action. Teleologically, the free energy principle offers a normative account of self-organisation in terms of optimal Bayesian design and decision-making, in the sense of maximising marginal likelihood or Bayesian model evidence. In summary, starting from a description of the world in terms of random dynamical systems, we end up with a description of self-organisation as sentient behaviour that can be interpreted as self-evidencing; namely, self-assembly, autopoiesis or active inference.

cond-mat.stat-mech↗

arXiv2023

Curvature-Sensitive Predictive Coding with Approximate Laplace Monte Carlo

Predictive coding (PC) accounts of perception now form one of the dominant computational theories of the brain, where they prescribe a general algorithm for inference and learning over hierarchical latent probabilistic models. Despite this, they have enjoyed little export to the broader field of machine learning, where comparative generative modelling techniques have flourished. In part, this has been due to the poor performance of models trained with PC when evaluated by both sample quality and marginal likelihood. By adopting the perspective of PC as a variational Bayes algorithm under the Laplace approximation, we identify the source of these deficits to lie in the exclusion of an associated Hessian term in the PC objective function, which would otherwise regularise the sharpness of the probability landscape and prevent over-certainty in the approximate posterior. To remedy this, we make three primary contributions: we begin by suggesting a simple Monte Carlo estimated evidence lower bound which relies on sampling from the Hessian-parameterised variational posterior. We then derive a novel block diagonal approximation to the full Hessian matrix that has lower memory requirements and favourable mathematical properties. Lastly, we present an algorithm that combines our method with standard PC to reduce memory complexity further. We evaluate models trained with our approach against the standard PC framework on image benchmark datasets. Our approach produces higher log-likelihoods and qualitatively better samples that more closely capture the diversity of the data-generating distribution.

cs.LG↗

arXiv2023

A variational synthesis of evolutionary and developmental dynamics

This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain - and are constrained by - fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (bayesian model selection). The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations - and nested meta-populations - of different natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses - and identify points of contact with related mathematical formulations of evolution.

q-bio.PE↗

arXiv2023

Control flow in active inference systems

Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. We show here that when systems are described as executing active inference driven by the free-energy principle (and hence can be considered Bayesian prediction-error minimizers), their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implmented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.

q-bio.NC↗