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Motor skill learning relies on neural plasticity in the motor and limbic systems. However, the spatial and temporal characteristics of these changes—and their microstructural underpinnings—remain unclear. Eighteen healthy males received 1 hour of training in a computer-based motion game, 4 times a week, for 4 consecutive weeks, while 14 untrained participants underwent scanning only. Performance improvements were observed in all trained participants. Serial myelin- and iron-sensitive multiparametric mapping at 3T during this period of intensive motor skill acquisition revealed temporally and spatially distributed, performance-related microstructural changes in the grey and white matter across a corticospinal-cerebellar-hippocampal circuit. Analysis of the trajectory of these transient changes suggested time-shifted cascades of plasticity from the dominant sensorimotor system to the contralateral hippocampus. In the cranial corticospinal tracts, changes in myelin-sensitive metrics during training in the posterior limb of the internal capsule were of greater magnitude in those who trained their upper limbs vs. lower limb trainees. Motor skill learning is associated with waves of grey and white matter plasticity, across a broad sensorimotor network.

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 variables--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.

Acknowledgements: Special thanks to Thomas Parr for our virtual conversations about Active Inference., Humans display astonishing skill in learning about the environment in which they operate. They assimilate a rich set of affordances and interrelations among different elements in particular contexts, and form flexible abstractions (i.e., concepts) that can be generalised and leveraged with ease. To capture these abilities, we present a deep hierarchical Active Inference model of goal-directed behaviour, and the accompanying belief update schemes implied by maximising model evidence. Using simulations, we elucidate the potential mechanisms that underlie and influence concept learning in a spatial foraging task. We show that the representations formed-as a result of foraging-reflect environmental structure in a way that is enhanced and nuanced by Bayesian model reduction, a special case of structure learning that typifies learning in the absence of new evidence. Synthetic agents learn associations and form concepts about environmental context and configuration as a result of inferential, parametric learning, and structure learning processes-three processes that can produce a diversity of beliefs and belief structures. Furthermore, the ensuing representations reflect symmetries for environments with identical configurations.

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.

Brain research has in recent years indisputably entered a new epoch, driven bysubstantialmethodologicaladvances and digitallyenabled data integration and modeling at multiple scales –from molecules to the whole system. Major advances are emerging at theintersection of neurosciencewith technology and computing. This new science of the brain integrates high-quality basic research,systematic data integration across multiple scales, a new culture of large-scale collaboration andtranslation into applications. A systematic approach, as pioneered in Europe’s Human Brain Project(HBP), will be essential in meeting the pressing medical andtechnological challenges of the comingdecade. The aims of this paper are To develop a concept for the coming decade of digital brain research To discuss it with the research community at large, with the aim of identifying points of convergence and common goals To provide a scientific framework for current and future development of EBRAINS To inform and engage stakeholders, funding organizations and research institutions regarding future digital brain research To identify and address key ethical and societal issues While we do not claim that there is a ‘one size fits all’ approach to addressing these aspects, we areconvinced that discussions around the theme of digital brain research will help drive progress in thebroader field of neuroscience. You can submit your comments here and be considered for co-authorship Or become a supporter by clicking here More information below Comments on this manuscript are welcome This manuscriptis a living document that is being further developed in a participatory process. The work has been initiated by the Science and Infrastructure Board of the Human Brain Project (HBP). Now, the entire research community is invited to contribute to shaping the vision by submitting comments.Comments can be submitted via an online commentary form here. All submitted comments will be considered and discussed. The final decision on whether edits or additions will be made to the next version of the manuscript based on an individual comment will be made by the Science and Infrastructure Board (SIB) of the Human Brain Project (HBP) at regular intervals. The final version of the manuscript will be prepared and published in the next months. Comments may be submitted until the end of May, 2023. Every researcher is welcome to provide comment or indicate support for the contents of this paper and jointly shape the future of brain research. Supporters of the paper: Pietro Avanzini, Marc Beyer, Maria Del Vecchio, Jitka Annen, Maurizio Mattia, Steven Laureys, Rosanne Edelenbosch, Rafael Yuste, Jean-Pierre Changeux, Linda Richards, Hye Weon Jessica Kim, Chrysoula Samara, Luis Miguel González de la Garza, Nikoleta Petalidou, Vasudha Kulkarni, Cesar David Rincon, Isabella O'Shea, Munira Tamim Electricwala, Nicola Palomero-Gallagher, Bernd Carsten Stahl, Bahar Hazal Yalcinkaya, Meysam Hashemi, Carola Sales Carbonell, Marcel Carrère, Anthony Randal McIntosh, Hiba Sheheitli, Abolfazl Ziaeemehr, Martin Breyton, Giovanna Ramos Queda, Anirudh NIhalani Vattikonda, Gyorgy Buzsaki George Ogoh, William Knight Torbjørn V Ness, MIchiel van der Vlag, Mu-ming Poo.

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.

We consider the theoretical constraints on interactions between coupled cortical columns. Each column comprises a set of neural populations, where each population is modelled as a neural mass. The existence of semi-stable states within a cortical column has been shown to be dependent on the type of interaction between the constituent neuronal subpopulations, i.e., the form of the implicit synaptic convolution kernels. Current-to-current coupling has been shown, in contrast to potential-to-current coupling, to create semi-stable states within a cortical column. In this analytic and numerical study, the interaction between semi-stable states is characterized by equations of motion for ensemble activity. We show that for small excitations, the dynamics follow the Kuramoto model. However, in contrast to previous work, we derive coupled equations between phase and amplitude dynamics. This affords the possibility of defining connectivity as a dynamic variable. The turbulent flow of phase dynamics found in networks of Kuramoto oscillators indicate turbulent changes in dynamic connectivity for coupled cortical columns. Crucially, this is something that has been recorded in epileptic seizures. We used the results we derived to estimate a seizure propagation model, which allowed for relatively straightforward inversions using variational Laplace (a.k.a., Dynamic Causal Modelling). The face validity of the ensuing seizure propagation model was established using simulated data as a prelude to future work; which will investigate dynamic connectivity from empirical data. This model also allows predictions of seizure evolution, induced by virtual lesions to synaptic connectivity: something that could be of clinical use, when applied to epilepsy surgical cases.

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.

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.

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)., Comment: 7 pages, 2 figures

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.

This white paper lays out a vision of research and development in the field of artificial intelligence for the next decade (and beyond). Its denouement is a cyber-physical ecosystem of natural and synthetic sense-making, in which humans are integral participants$\unicode{x2014}$what we call ''shared intelligence''. This vision is premised on active inference, a formulation of adaptive behavior that can be read as a physics of intelligence, and which inherits from the physics of self-organization. In this context, we understand intelligence as the capacity to accumulate evidence for a generative model of one's sensed world$\unicode{x2014}$also known as self-evidencing. Formally, this corresponds to maximizing (Bayesian) model evidence, via belief updating over several scales: i.e., inference, learning, and model selection. Operationally, this self-evidencing can be realized via (variational) message passing or belief propagation on a factor graph. Crucially, active inference foregrounds an existential imperative of intelligent systems; namely, curiosity or the resolution of uncertainty. This same imperative underwrites belief sharing in ensembles of agents, in which certain aspects (i.e., factors) of each agent's generative world model provide a common ground or frame of reference. Active inference plays a foundational role in this ecology of belief sharing$\unicode{x2014}$leading to a formal account of collective intelligence that rests on shared narratives and goals. We also consider the kinds of communication protocols that must be developed to enable such an ecosystem of intelligences and motivate the development of a shared hyper-spatial modeling language and transaction protocol, as a first$\unicode{x2014}$and key$\unicode{x2014}$step towards such an ecology., 21+18 pages, one figure, one appendix

Brain research has in recent years indisputably entered a new epoch, driven bysubstantialmethodologicaladvances and digitallyenabled data integration and modeling at multiple scales –from molecules to the whole system. Major advances are emerging at theintersection of neurosciencewith technology and computing. This new science of the brain integrates high-quality basic research,systematic data integration across multiple scales, a new culture of large-scale collaboration andtranslation into applications. A systematic approach, as pioneered in Europe’s Human Brain Project(HBP), will be essential in meeting the pressing medical andtechnological challenges of the comingdecade. The aims of this paper are To develop a concept for the coming decade of digital brain research To discuss it with the research community at large, with the aim of identifying points of convergence and common goals To provide a scientific framework for current and future development of EBRAINS To inform and engage stakeholders, funding organizations and research institutions regarding future digital brain research To identify and address key ethical and societal issues While we do not claim that there is a ‘one size fits all’ approach to addressing these aspects, we areconvinced that discussions around the theme of digital brain research will help drive progress in thebroader field of neuroscience. You can submit your comments here and be considered for co-authorship Or become a supporter by clicking here More information below Comments on this manuscript are welcome This manuscriptis a living document that is being further developed in a participatory process. The work has been initiated by the Science and Infrastructure Board of the Human Brain Project (HBP). Now, the entire research community is invited to contribute to shaping the vision by submitting comments.Comments can be submitted via an online commentary form here. All submitted comments will be considered and discussed. The final decision on whether edits or additions will be made to the next version of the manuscript based on an individual comment will be made by the Science and Infrastructure Board (SIB) of the Human Brain Project (HBP) at regular intervals. New versions of the manuscript will be published every few months on Zenodo. Comments may be submitted until the beginning of 2023. During the Human Brain Project Summit 2023, the manuscript will be adopted by HBP and non-HBP participants, and a final version will be published shortly after. Supporters of the paper: Pietro Avanzini, Marc Beyer, Maria Del Vecchio, Jitka Annen, Maurizio Mattia, Steven Laureys, Rosanne Edelenbosch, Rafael Yuste, Jean-Pierre Changeux, Linda Richards.

For this project, we are investigating network-wide effects of induced seizures in a zebrafish model. We apply dynamic causal modelling to light-sheet microscopy data to identify synaptic dynamics that underlie the observed changes in neuronal output at the level of whole neuronal populations.

This paper presents a meta-theory of the usage of the free energy principle (FEP) and examines its scope in the modelling of physical systems. We consider the so-called `map-territory fallacy' and the fallacious reification of model properties. By showing that the FEP is a consistent, physics-inspired theory of inferences of inferences, we disprove the assertion that the map-territory fallacy contradicts the principled usage of the FEP. As such, we argue that deploying the map-territory fallacy to criticise the use of the FEP and Bayesian mechanics itself constitutes a fallacy: what we call the {\it map-territory fallacy fallacy}. In so doing, we emphasise a few key points: the uniqueness of the FEP as a model of particles or agents that model their environments; the restoration of convention to the FEP via its relation to the principle of constrained maximum entropy; the `Jaynes optimality' of the FEP under this relation; and finally, the way that this meta-theoretical approach to the FEP clarifies its utility and scope as a formal modelling tool. Taken together, these features make the FEP, uniquely, {\it the} ideal model of generic systems in statistical physics., 23 pages

This is a transcript of the proceedings of the 2nd Applied Active Inference Symposium. There are twoSymposium sessions of four hours each, starting at 4 & 16 UTC on July 31st Watch link for 1st Symposium interval, July 31st at 4 UTC: https://youtu.be/zm2d9o5n0PU Watch link for 2nd Symposium interval, July 31st at 16 UTC: https://youtu.be/dTVHHenms_Y The Program is available at:https://coda.io/@active-inference-institute/2nd-applied-active-inference-symposium

Discussion with authors of the 2022 preprint “The free energy principle made simpler but not too simple” by Karl Friston, Lancelot Da Costa, Noor Sajid, Conor Heins, Kai Ueltzhöffer, Grigorios A. Pavliotis, & Thomas Parr.https://arxiv.org/abs/2201.06387 Session 045.0, May 27, 2022https://www.youtube.com/watch?v=9MQQKaKEXs0 Session 045.1, June 1, 2022https://www.youtube.com/watch?v=V0l9fOJgbtc Session 045.2, June 8, 2022https://www.youtube.com/watch?v=S5-jXzhiG18

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., 30 pages, 4 figures; 42 pages including table of contents and references

The COVID-19 pandemic has shone a light on the complex relationship between science and policy. Policymakers have had to make decisions at speed in conditions of uncertainty, implementing policies that have had profound consequences for people's lives. Yet this process has sometimes been characterised by fragmentation, opacity and a disconnect between evidence and policy. In the United Kingdom, concerns about the secrecy that initially surrounded this process led to the creation of Independent SAGE, an unofficial group of scientists from different disciplines that came together to ask policy-relevant questions, review the evolving evidence, and make evidence-based recommendations. The group took a public health approach with a population perspective, worked in a holistic transdisciplinary way, and were committed to public engagement. In this paper, we review the lessons learned during its first year. These include the importance of learning from local expertise, the value of learning from other countries, the role of civil society as a critical friend to government, finding appropriate relationships between science and policy, and recognising the necessity of viewing issues through an equity lens.

How is information processed in the brain during perception? Mechanistic insight is achieved only when experiments are employed to test formal or computational models. In analogy to lesion studies, phantom perception may serve as a vehicle to understand the fundamental processing principles underlying auditory perception. With a special focus on tinnitus -- as the prime example of auditory phantom perception -- we review recent work at the intersection of artificial intelligence, psychology, and neuroscience. In particular, we discuss why everyone with tinnitus suffers from hearing loss, but not everyone with hearing loss suffers from tinnitus. We argue that the increase of sensory precision due to Bayesian inference could be caused by intrinsic neural noise and lead to a prediction error in the cerebral cortex. Hence, two fundamental processing principles - being ubiquitous in the brain - provide the most explanatory power for the emergence of tinnitus: predictive coding as a top-down, and stochastic resonance as a complementary bottom-up mechanism. We conclude that both principles play a crucial role in healthy auditory perception., Comment: arXiv admin note: substantial text overlap with arXiv:2010.01914

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., Comment: 44 pages, 9 Figures; 64 pages including graphical abstract, highlights and references

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., Comment: 33 pages (excluding references), 6 figures

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., 22 pages, 3 figures, opinion

On June 21st, 2021, Active Inference Lab (activeinference.org/) hosted its first Applied Active Inference Symposium, featuring Professor Karl Friston. The Symposium was structured in three sections, corresponding to the Organizational Units of the Active Inference Lab: Education, Communication, and Tools. This publication reflects an edited and enriched transcript of the proceedings of the Symposium.

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 R\'enyi divergences and their associated variational bounds. R\'enyi 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 $\alpha$ parameter, given fixed priors. This rests on changes in $\alpha$ 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, $\alpha \to 0^{+}$ optimisation leads to mass-covering variational estimates and increased variability in choice behaviour. Furthermore, $\alpha \to + \infty$ 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 $\alpha$ 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., Comment: 23 pages, 5 figures

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.

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.

Background Disturbances in N-methyl-D-aspartate receptors (NMDARs)—as implicated in patients with schizophrenia—can cause regionally specific electrophysiological effects. Both animal models of NMDAR blockade and clinical studies in patients with schizophrenia have suggested that behavioral phenotypes are associated with reduction in inhibition within the frontal cortex. Methods Here we investigate event-related potentials to a roving auditory oddball paradigm under ketamine in healthy human volunteers (N= 18; double-blind, placebo-controlled, crossover design). Using recent advances in Bayesian modeling of group effects in dynamic causal modeling, we fit biophysically plausible network models of the auditory processing hierarchy to whole-scalp event-related potential recordings. This allowed us to identify regionally specific effects of ketamine in a distributed network of interacting cortical sources. Results We show that the effect of ketamine is best explained as a selective change in intrinsic inhibition, with a pronounced ketamine-induced reduction of inhibitory interneuron connectivity in frontal sources, compared with temporal sources. Simulations of these changes in an integrated microcircuit model shows that they are associated with a reduction in superficial pyramidal cell activity that can explain drug effects observed in the event-related potential. Conclusions These results are consistent with findings from invasive recordings in animal models exposed to NMDAR blockers, and provide evidence that inhibitory interneuron–specific NMDAR dysfunction may be sufficient to explain electrophysiological abnormalities induced by NMDAR blockade in human subjects.

This paper addresses the challenges faced by multiscale formulations of the variational (free energy) approach to dynamics that obtain for large-scale ensembles. We review a framework for modelling complex adaptive control systems for multiscale free energy bounding organism–niche dynamics, thereby integrating the modelling strategies and heuristics of variational neuroethology with a broader perspective on the ecological nestedness of biotic systems. We extend the multiscale variational formulation beyond the action–perception loops of individual organisms by appealing to the variational approach to niche construction to explain the dynamics of coupled systems constituted by organisms and their ecological niche. We suggest that the statistical robustness of living systems is inherited, in part, from their eco-niches, as niches help coordinate dynamical patterns across larger spatiotemporal scales. We call this approach variational ecology. We argue that, when applied to cultural animals such as humans, variational ecology enables us to formulate not just a physics of individual minds, but also a physics of interacting minds across spatial and temporal scales – a physics of sentient systems that range from cells to societies., Highlights • We extend the multiscale variational free energy approach to large-scale ensembles. • We integrate multiscale modelling with a broad perspective on ecological nestedness. • We argue that the statistical robustness of living systems is ecologically inherited. • We propose variational ecology as a physics of sentient systems.

This article proposes a formal model that integrates cognitive and psychodynamic psychotherapeutic models of psychopathy to show how two major psychopathic traits called lacks remorse and self-aggrandizing can be understood as a form of abnormal Bayesian inference about the self. This model draws on the predictive coding (i.e., active inference) framework, a neurobiologically plausible explanatory framework for message passing in the brain that is formalized in terms of hierarchical Bayesian inference. In summary, this model proposes that these two cardinal psychopathic traits reflect entrenched maladaptive Bayesian inferences about the self, which defend against the experience of deep-seated, self-related negative emotions, specifically shame and worthlessness. Support for the model in extant research on the neurobiology of psychopathy and quantitative simulations are provided. Finally, we offer a preliminary overview of a novel treatment for psychopathy that rests on our Bayesian formulation.

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., 50 pages, 9 figures, 1 Appendix of two sections with pseudocodes and one encoding example , submitted preprint

When someone masters a skill, their performance looks to us like second nature: it looks as if their actions are smoothly performed without explicit, knowledge-driven, online monitoring of their performance. Contemporary computational models in motor control theory, however, are instructionist: that is, they cast skillful performance as a knowledge-driven process. Optimal motor control theory (OMCT), as representative par excellence of such approaches, casts skillful performance as an instruction, instantiated in the brain, that needs to be executed—a motor command. This paper aims to show the limitations of such instructionist approaches to skillful performance. We specifically address the question of whether the assumption of control-theoretic models is warranted. The first section of this paper examines the instructionist assumption, according to which skillful performance consists of the execution of theoretical instructions harnessed in motor representations. The second and third sections characterize the implementation of motor representations as motor commands, with a special focus on formulations from OMCT. The final sections of this paper examine predictive coding and active inference—behavioral modeling frameworks that descend, but are distinct, from OMCT—and argue that the instructionist, control-theoretic assumptions are ill-motivated in light of new developments in active inference.

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., Comment: 19 pages; 3 figures

To interact seamlessly with robots, users must infer the causes of a robot's behavior and be confident about that inference. Hence, trust is a necessary condition for human-robot collaboration (HRC). Despite its crucial role, it is largely unknown how trust emerges, develops, and supports human interactions with nonhuman artefacts. Here, we review the literature on trust, human-robot interaction, human-robot collaboration, and human interaction at large. Early models of trust suggest that trust entails a trade-off between benevolence and competence, while studies of human-to-human interaction emphasize the role of shared behavior and mutual knowledge in the gradual building of trust. We then introduce a model of trust as an agent's best explanation for reliable sensory exchange with an extended motor plant or partner. This model is based on the cognitive neuroscience of active inference and suggests that, in the context of HRC, trust can be cast in terms of virtual control over an artificial agent. In this setting, interactive feedback becomes a necessary component of the trustor's perception-action cycle. The resulting model has important implications for understanding human-robot interaction and collaboration, as it allows the traditional determinants of human trust to be defined in terms of active inference, information exchange and empowerment. Furthermore, this model suggests that boredom and surprise may be used as markers for under and over-reliance on the system. Finally, we examine the role of shared behavior in the genesis of trust, especially in the context of dyadic collaboration, suggesting important consequences for the acceptability and design of human-robot collaborative systems.

The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to Rt estimation, resulting in the state-of-the-art DARt system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in revealing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for accurate and timely estimating transmission dynamics from reported data., Comment: Xian Yang, Shuo Wang and Yuting Xing contribute equally

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., Comment: 23 pages, 15 figures

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 R��nyi divergences and their associated variational bounds. R��nyi 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 $��$ parameter, given fixed priors. This rests on changes in $��$ 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, $��\to 0^{+}$ optimisation leads to mass-covering variational estimates and increased variability in choice behaviour. Furthermore, $��\to + \infty$ 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 $��$ 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., 23 pages, 5 figures

The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and hence with the principle of stationary action. Taking the Dynamic Causal Modelling neuronal state equation, Hodgkin-Huxley model, and the Leaky Integrate-and-Fire model as examples, we show that it is possible to write complex oscillatory forms of these equations in terms of a single Lagrangian. We therefore bring mathematical descriptions in computational neuroscience under the remit of the principle of stationary action and use this reformulation to express symmetries and associated conservation laws arising in neural systems.

Twenty years have passed since the dysconnection hypothesis was first proposed (Friston and Frith, 1995; Weinberger, 1993). In that time, neuroscience has witnessed tremendous advances: we now live in a world of non-invasive neuroanatomy, computational neuroimaging and the Bayesian brain. The genomics era has come and gone. Connectomics and large-scale neuroinformatics initiatives are emerging everywhere. So where is the dysconnection hypothesis now? This article considers how the notion of schizophrenia as a dysconnection syndrome has developed – and how it has been enriched by recent advances in clinical neuroscience. In particular, we examine the dysconnection hypothesis in the context of (i) theoretical neurobiology and computational psychiatry; (ii) the empirical insights afforded by neuroimaging and associated connectomics – and (iii) how bottom-up (molecular biology and genetics) and top-down (systems biology) perspectives are converging on the mechanisms and nature of dysconnections in schizophrenia., Schizophrenia Research, 176 (2-3), ISSN:0920-9964, ISSN:1573-2509

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., 18 pages, 3 figures (main text); 37 pages including references and appendix

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., 30 pages; 6 figures

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., 25 pages, 5 figures, 1 table, Glossary

By equipping a previously reported dynamic causal model of COVID-19 with an isolation state, we modelled the effects of self-isolation consequent on tracking and tracing. Specifically, we included a quarantine or isolation state occupied by people who believe they might be infected but are asymptomatic, and only leave if they test negative. We recovered maximum posteriori estimates of the model parameters using time series of new cases, daily deaths, and tests for the UK. These parameters were used to simulate the trajectory of the outbreak in the UK over an 18-month period. Several clear-cut conclusions emerged from these simulations. For example, under plausible (graded) relaxations of social distancing, a rebound of infections within weeks is unlikely. The emergence of a later second wave depends almost exclusively on the rate at which we lose immunity, inherited from the first wave. There exists no testing strategy that can attenuate mortality rates, other than by deferring or delaying a second wave. A sufficiently powerful tracking and tracing policy--implemented at the time of writing (10th May 2020)--will defer any second wave beyond a time horizon of 18 months. Crucially, this deferment is within current testing capabilities (requiring an efficacy of tracing and tracking of about 20% of asymptomatic infected cases, with less than 50,000 tests per day). These conclusions are based upon a dynamic causal model for which we provide some construct and face validation, using a comparative analysis of the United Kingdom and Germany, supplemented with recent serological studies., 31 pages, 12 figures, one table. Technical report

This technical note introduces parametric dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.