Publications

Boltzmann entropy is a measure of the hidden information contained within a system. In the context of neuroimaging, information can be hidden within the multiple brain states that cannot be distinguished within a single image. Here, we show that information can also be hidden within multiple indistinguishable connections between neuronal regions, as quantified by a metric that we term ‘selection entropy’. We show the ways in which selection entropy behaves in comparison with the Kullback-Leibler (KL) divergence (relative entropy). Firstly, we use synthetic datasets to demonstrate that selection entropy is more sensitive to small changes in probability distributions as compared with the KL divergence. Secondly, we show that selection entropy identifies a principle gradient between sensorimotor and transmodal brain regions more definitively than the KL divergence within resting-state fMRI timeseries. As such, we introduce selection entropy as an additional asset in the analysis of neuronal functional selectivity.

Using high-density electrocorticographic recordings – from awake-behaving monkeys – and dynamic causal modelling, we characterised contrast dependent gain control in visual cortex, in terms of synaptic rate constants and intrinsic connectivity. Specifically, we used neural field models to quantify the balance of excitatory and inhibitory influences; both in terms of the strength and spatial dispersion of horizontal intrinsic connections. Our results allow us to infer that increasing contrast increases the sensitivity or gain of superficial pyramidal cells to inputs from spiny stellate populations. Furthermore, changes in the effective spatial extent of horizontal coupling nuance the spatiotemporal filtering properties of cortical laminae in V1 — effectively preserving higher spatial frequencies. These results are consistent with recent non-invasive human studies of contrast dependent changes in the gain of pyramidal cells elaborating forward connections — studies designed to test specific hypotheses about precision and gain control based on predictive coding. Furthermore, they are consistent with established results showing that the receptive fields of V1 units shrink with increasing visual contrast.

Active inference is a normative framework for generating behaviour based upon the free energy principle, a theory of self-organisation. This framework has been successfully used to solve reinforcement learning and stochastic control problems, yet, the formal relation between active inference and reward maximisation has not been fully explicated. In this paper, we consider the relation between active inference and dynamic programming under the Bellman equation, which underlies many approaches to reinforcement learning and control. We show that, on partially observable Markov decision processes, dynamic programming is a limiting case of active inference. In active inference, agents select actions to minimise expected free energy. In the absence of ambiguity about states, this reduces to matching expected states with a target distribution encoding the agent's preferences. When target states correspond to rewarding states, this maximises expected reward, as in reinforcement learning. When states are ambiguous, active inference agents will choose actions that simultaneously minimise ambiguity. This allows active inference agents to supplement their reward maximising (or exploitative) behaviour with novelty-seeking (or exploratory) behaviour. This clarifies the connection between active inference and reinforcement learning, and how both frameworks may benefit from each other.

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 Renyi divergences and their associated variational bounds. Renyi 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.

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.