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. While we mostly focus on building new principled conceptual relations between syntax and the FEP, we also show through a sample of preliminary examples 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.

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 modeling 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 nontrivial 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.

Spectral dynamic causal modeling: A didactic introduction and its relationship with functional connectivity

We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive 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 modeling 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.

Cerebellar state estimation enables resilient coupling across behavioural domains

Cerebellar computations are necessary for fine behavioural control and may rely on internal models for estimation of behaviourally relevant states. Here, we propose that the central cerebellar function is to estimate how states interact with each other, and to use these estimates to coordinates extra-cerebellar neuronal dynamics underpinning a range of interconnected behaviours. To support this claim, we describe a cerebellar model for state estimation that includes state interactions, and link this model with the neuronal architecture and dynamics observed empirically. This is formalised using the free energy principle, which provides a dual perspective on a system in terms of both the dynamics of its physical-in this case neuronal-states, and the inferential process they entail. As a demonstration of this proposal, we simulate cerebellar-dependent synchronisation of whisking and respiration, which are known to be tightly coupled in rodents, as well as limb and tail coordination during locomotion. In summary, we propose that the ubiquitous involvement of the cerebellum in behaviour arises from its central role in precisely coupling behavioural domains.

Modelling cortical network dynamics

We have investigated the theoretical constraints of the interactions between coupled cortical columns. Each cortical column consists of a set of neural populations where each population is modelled as a neural mass. The existence of semi-stable states within a cortical column is dependent on the type of interaction between the neuronal populations, i.e., the form of the synaptic kernels. Current-to-current coupling has been shown, in contrast to potential-to-current coupling, to create semi-stable states within a cortical column. The interaction between semi-stable states of the cortical columns is studied where we derive the dynamics for the collected activity. For small excitations the dynamics follow the Kuramoto model; however, in contrast to previous work we derive coupled equations between phase and amplitude dynamics with the possibility of defining connectivity as a stationary and dynamic variable. The turbulent flow of phase dynamics which occurs in networks of Kuramoto oscillators would indicate turbulent changes in dynamic connectivity for coupled cortical columns which is something that has been recorded in epileptic seizures. We used the results we derived to estimate a seizure propagation model which allowed for inversions using the Laplace assumption (Dynamic Causal Modelling). The seizure propagation model was trialed on simulated data, and future work will investigate the estimation of the connectivity matrix from empirical data. This model can be used to predict changes in seizure evolution after virtual changes in the connectivity network, something that could be of clinical use when applied to epilepsy surgical cases.

Order and change in art: towards an active inference account of aesthetic experience

How to account for the power that art holds over us? Why do artworks touch us deeply, consoling, transforming or invigorating us in the process? In this paper, we argue that an answer to this question might emerge from a fecund framework in cognitive science known as predictive processing (a.k.a. active inference). We unpack how this approach connects sense-making and aesthetic experiences through the idea of an 'epistemic arc', consisting of three parts (curiosity, epistemic action and aha experiences), which we cast as aspects of active inference. We then show how epistemic arcs are built and sustained by artworks to provide us with those satisfying experiences that we tend to call 'aesthetic'. Next, we defuse two key objections to this approach; namely, that it places undue emphasis on the cognitive component of our aesthetic encounters-at the expense of affective aspects-and on closure and uncertainty minimization (order)-at the expense of openness and lingering uncertainty (change). We show that the approach offers crucial resources to account for the open-ended, free and playful behaviour inherent in aesthetic experiences. The upshot is a promising but deflationary approach, both philosophically informed and psychologically sound, that opens new empirical avenues for understanding our aesthetic encounters. This article is part of the theme issue 'Art, aesthetics and predictive processing: theoretical and empirical perspectives'.

From active affordance to active inference: vertical integration of cognition in the cerebral cortex through dual subcortical control systems

In previous papers, we proposed that the dorsal attention system's top-down control is regulated by the dorsal division of the limbic system, providing a feedforward or impulsive form of control generating expectancies during active inference. In contrast, we proposed that the ventral attention system is regulated by the ventral limbic division, regulating feedback constraints and error-correction for active inference within the neocortical hierarchy. Here, we propose that these forms of cognitive control reflect vertical integration of subcortical arousal control systems that evolved for specific forms of behavior control. The feedforward impetus to action is regulated by phasic arousal, mediated by lemnothalamic projections from the reticular activating system of the lower brainstem, and then elaborated by the hippocampus and dorsal limbic division. In contrast, feedback constraint-based on environmental requirements-is regulated by the tonic activation furnished by collothalamic projections from the midbrain arousal control centers, and then sustained and elaborated by the amygdala, basal ganglia, and ventral limbic division. In an evolutionary-developmental analysis, understanding these differing forms of active affordance-for arousal and motor control within the subcortical vertebrate neuraxis-may help explain the evolution of active inference regulating the cognition of expectancy and error-correction within the mammalian 6-layered neocortex.

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 hypothesized 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 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 homologs 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.

Predictive coding and stochastic resonance as fundamental principles of auditory phantom perception

Mechanistic insight is achieved only when experiments are employed to test formal or computational models. Furthermore, in analogy to lesion studies, phantom perception may serve as a vehicle to understand the fundamental processing principles underlying healthy 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 (at least hidden) hearing loss, but not everyone with hearing loss suffers from tinnitus. We argue that intrinsic neural noise is generated and amplified along the auditory pathway as a compensatory mechanism to restore normal hearing based on adaptive stochastic resonance. The neural noise increase can then be misinterpreted as auditory input and perceived as tinnitus. This mechanism can be formalized in the Bayesian brain framework, where the percept (posterior) assimilates a prior prediction (brain's expectations) and likelihood (bottom-up neural signal). A higher mean and lower variance (i.e. enhanced precision) of the likelihood shifts the posterior, evincing a misinterpretation of sensory evidence, which may be further confounded by plastic changes in the brain that underwrite prior predictions. Hence, two fundamental processing principles provide the most explanatory power for the emergence of auditory phantom perceptions: predictive coding as a top-down and adaptive stochastic resonance as a complementary bottom-up mechanism. We conclude that both principles also play a crucial role in healthy auditory perception. Finally, in the context of neuroscience-inspired artificial intelligence, both processing principles may serve to improve contemporary machine learning techniques.

Inferring Trajectories of Psychotic Disorders Using Dynamic Causal Modeling

Introduction

Illness course plays a crucial role in delineating psychiatric disorders. However, existing nosologies consider only its most basic features (e.g., symptom sequence, duration). We developed a Dynamic Causal Model (DCM) that characterizes course patterns more fully using dense timeseries data. This foundational study introduces the new modeling approach and evaluates its validity using empirical and simulated data.

Methods

A three-level DCM was constructed to model how latent dynamics produce symptoms of depression, mania, and psychosis. This model was fit to symptom scores of nine patients collected prospectively over four years, following first hospitalization. Simulated subjects based on these empirical data were used to evaluate model parameters at the subject-level. At the group-level, we tested the accuracy with which the DCM can estimate the latent course patterns using Parametric Empirical Bayes (PEB) and leave-one-out cross-validation.

Results

Analyses of empirical data showed that DCM accurately captured symptom trajectories for all nine subjects. Simulation results showed that parameters could be estimated accurately (correlations between generative and estimated parameters >= 0.76). Moreover, the model could distinguish different latent course patterns, with PEB correctly assigning simulated patients for eight of nine course patterns. When testing any pair of two specific course patterns using leave-one-out cross-validation, 30 out of 36 pairs showed a moderate or high out-of-samples correlation between the true group-membership and the estimated group-membership values.

Conclusion

DCM has been widely used in neuroscience to infer latent neuronal processes from neuroimaging data. Our findings highlight the potential of adopting this methodology for modeling symptom trajectories to explicate nosologic entities, temporal patterns that define them, and facilitate personalized treatment.

On Bayesian mechanics: a physics of and by beliefs

The aim of this paper is to introduce a field of study that has emerged over the last decade, called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a particular partition (i.e. into particles), where the internal states (or the trajectories of internal states) of a particular system encode the parameters of beliefs about external states (or their trajectories). These tools allow us to write down mechanical theories for systems that look as if they are estimating posterior probability distributions over the causes of their sensory states. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on a space of beliefs (i.e. on a statistical manifold). Here, we will review the state of the art in the literature on the free energy principle, distinguishing between three ways in which Bayesian mechanics has been applied to particular systems (i.e. path-tracking, mode-tracking and mode-matching). We go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.

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 slow changes in the type of cortical activity, i.e. 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 in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. 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. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy.

An insula hierarchical network architecture for active interoceptive inference

In the brain, the insular cortex receives a vast amount of interoceptive information, ascending through deep brain structures, from multiple visceral organs. The unique hierarchical and modular architecture of the insula suggests specialization for processing interoceptive afferents. Yet, the biological significance of the insula's neuroanatomical architecture, in relation to deep brain structures, remains obscure. In this opinion piece, we propose the Insula Hierarchical Modular Adaptive Interoception Control (IMAC) model to suggest that insula modules (granular, dysgranular and agranular), forming parallel networks with the prefrontal cortex and striatum, are specialized to form higher order interoceptive representations. These interoceptive representations are recruited in a context-dependent manner to support habitual, model-based and exploratory control of visceral organs and physiological processes. We discuss how insula interoceptive representations may give rise to conscious feelings that best explain lower order deep brain interoceptive representations, and how the insula may serve to defend the body and mind against pathological depression.