Tim Verbelen

This paper considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning, and specifically rule discovery, under a plausible set of generative models or hypotheses. In active inference, policies—i.e., combinations of actions—are selected based on their expected free energy, which comprises expected information gain and value. Information gain corresponds to the Kullback-Leibler divergence between predictive posteriors with, and without, the consequences of action. Posteriors over models can be evaluated quickly and efficiently using Bayesian Model Reduction, based upon accumulated posterior beliefs about model parameters. The ensuing information gain can then be used to select actions that disambiguate among alternative models, in the spirit of optimal experimental design. We illustrate this kind of active selection or reasoning using partially observed discrete models; namely, a three-ball paradigm used previously to describe artificial insight and aha moments via (synthetic) introspection or sleep. We focus on the sample efficiency afforded by seeking outcomes that resolve the greatest uncertainty about the world model, under which outcomes are generated.

We apply the free energy principle to free markets by treating the Market as a random dynamical system with an attracting set, i.e., some characteristic states. This licenses a normal form for stochastic dynamics that inherits from the Helmholtz–Hodge decomposition. Equipped with this functional form—and a suitable parameterization—one can create a generative model of fluctuations in the value of assets and accompanying indicator variables. This affords the opportunity for prospective (ex ante) prediction, scenario modelling and forecasting that could, in principle, be applied to any complex dynamical system exhibiting stochastic chaos. Here, we illustrate the application to portfolio management—in the context of financial services—and use the (posterior) predictive densities over future paths to evaluate the expected free energy that underwrites active inference. In this application, active inference reduces to risk-sensitive control, which can be used to model the optimal decision-making of an agent or investor. In this setting, an investor is characterized by their prior preferences for a high rate of return under drawdown constraints. Using numerical studies and historical financial data, we quantify the improvement in portfolio management, relative to baseline policies.

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a plausible set of generative models or hypotheses. In active inference, policies - i.e., combinations of actions - are selected based on their expected free energy, which comprises expected information gain and value. Information gain corresponds to the KL divergence between predictive posteriors with, and without, the consequences of action. Posteriors over models can be evaluated quickly and efficiently using Bayesian Model Reduction, based upon accumulated posterior beliefs about model parameters. The ensuing information gain can then be used to select actions that disambiguate among alternative models, in the spirit of optimal experimental design. We illustrate this kind of active selection or reasoning using partially observed discrete models; namely, a 'three-ball' paradigm used previously to describe artificial insight and 'aha moments' via (synthetic) introspection or sleep. We focus on the sample efficiency afforded by seeking outcomes that resolve the greatest uncertainty about the world model, under which outcomes are generated.

This technical note applies active inference to the problem of learning goal-directed behaviour from scratch, namely, de novo learning. By de novo learning, we mean discovering, directly from observations, the structure and parameters of a discrete generative model for sequential policy optimisation. Concretely, our procedure grows and then reduces a model until it discovers a pullback attractor over (generalised) states; this attracting set supplies paths of least action among goal states while avoiding costly states. The implicit efficiency rests upon reframing the learning problem through the lens of the free energy principle, under which it is sufficient to learn a generative model whose dynamics feature such an attracting set. For context, we briefly relate this perspective to value-based formulations (e.g., Bellman optimality) and then apply the active inference formulation to a small arcade game to illustrate de novo structure learning and ensuing agency.

Recent advances in theoretical biology suggest that key definitions of basal cognition and sentient behavior may arise as emergent properties of in vitro cell cultures and neuronal networks. Such neuronal networks reorganize activity to demonstrate structured behaviors when embodied in structured information landscapes. In this article, we characterize this kind of self-organization through the lens of the free energy principle, that is, as self-evidencing. We do this by first discussing the definitions of reactive and sentient behavior in the setting of active inference, which describes the behavior of agents that model the consequences of their actions. We then introduce a formal account of intentional behavior that describes agents as driven by a preferred end point or goal in latent state-spaces. We then investigate these forms of (reactive, sentient, and intentional) behavior using simulations. First, we simulate the in vitro experiments, in which neuronal cultures modulated activity to improve gameplay in a simplified version of Pong by implementing nested, free energy minimizing processes. The simulations are then used to deconstruct the ensuing predictive behavior, leading to the distinction between merely reactive, sentient, and intentional behavior with the latter formalized in terms of inductive inference. This distinction is further studied using simple machine learning benchmarks (navigation in a grid world and the Tower of Hanoi problem) that show how quickly and efficiently adaptive behavior emerges under an inductive form of 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.

Representing a scene and its constituent objects from raw sensory data is a core ability for enabling robots to interact with their environment. In this letter, we propose a novel approach for scene understanding, leveraging an object-centric generative model that enables an agent to infer object category and pose in an allocentric reference frame using active inference, a neuro-inspired framework for action and perception. For evaluating the behavior of an active vision agent, we also propose a new benchmark where, given a target viewpoint of a particular object, the agent needs to find the best matching viewpoint given a workspace with randomly positioned objects in 3D. We demonstrate that our active inference agent is able to balance epistemic foraging and goal-driven behavior, and quantitatively outperforms both supervised and reinforcement learning baselines by more than a factor of two in terms of success rate.

Robust evidence suggests that humans explore their environment using a combination of topological landmarks and coarse-grained path integration. This approach relies on identifiable environmental features (topological landmarks) in tandem with estimations of distance and direction (coarse-grained path integration) to construct cognitive maps of the surroundings. This cognitive map is believed to exhibit a hierarchical structure, allowing efficient planning when solving complex navigation tasks. Inspired by human behaviour, this paper presents a scalable hierarchical active inference model for autonomous navigation, exploration, and goal-oriented behaviour. The model uses visual observation and motion perception to combine curiosity-driven exploration with goal-oriented behaviour. Motion is planned using different levels of reasoning, i.e., from context to place to motion. This allows for efficient navigation in new spaces and rapid progress toward a target. By incorporating these human navigational strategies and their hierarchical representation of the environment, this model proposes a new solution for autonomous navigation and exploration. The approach is validated through simulations in a mini-grid environment.