Renormalising Generative Models for Active Inference: Foundations, Derivations, and Verification

Active inference, a neurally-inspired model for inferring actions based on the free energy principle (FEP), has been proposed as a unifying framework for understanding perception, action, and learning in the brain. Active inference has previously been used to model ecologically important tasks such as navigation and planning, but scaling it to solve complex large-scale problems in real-world environments has remained a challenge. Inspired by the existence of multi-scale hierarchical representations in the brain, we propose a model for planning of actions based on hierarchical active inference. Our approach combines a hierarchical model of the environment with successor representations for efficient planning. We present results demonstrating (1) how lower-level successor representations can be used to learn higher-level abstract states, (2) how planning based on active inference at the lower-level can be used to bootstrap and learn higher-level abstract actions, and (3) how these learned higher-level abstract states and actions can facilitate efficient planning. We illustrate the performance of the approach on several planning and reinforcement learning (RL) problems including a variant of the well-known four rooms task, a key-based navigation task, a partially observable planning problem, the Mountain Car problem, and PointMaze, a family of navigation tasks with continuous state and action spaces. Our results represent, to our knowledge, the first application of learned hierarchical state and action abstractions to active inference in FEP-based theories of brain function.

A recent line of work measures causal emergence in reinforcement learning agents through Integrated Information Decomposition, reporting that $Φ_r$ grows with training and tracks reward improvement. For active inference, this raises the question of how reward-free predictive organization relates to such information-theoretic signatures. I test this within an active inference agent whose architecture separates a fast perception latent $z$ from a slow global latent $g$, where $g$ is driven by prediction error and structurally decoupled from policy gradients. In a reward-free environmental regime-switching protocol, $Φ_r$ concentrates in $g$; its aggregate magnitude is largely architectural and decreases with training. The substantive effect of learning becomes legible only at the atom-compositional level: decoupling flips sign from negative to positive and becomes regime-invariant under environmental change, while downward causation carries the regime-dependent adjustment. These results identify $g$ as the architectural locus of $Φ_r$-relevant temporal organization in an active inference agent, and argue against reading scalar $Φ_r$ as a direct index of learned integration.

In this paper, a novel test-time scaling law for physical artificial intelligence (AI) agents is introduced. This scaling law enables physical AI agents to reason with their world models to generalize in unforeseen scenarios at test time. The derived scaling law is grounded in the first principle of active inference, which equips agents with the general objective to survive in the real world, under which their specific task objectives are subsumed. Active inference achieves this by providing the reasoning to resolve prediction errors that arise when the agent encounters unforeseen situations outside its training distribution, enabling generalization in non-stationary environments. The proposed scaling law captures this by dynamically updating the agent's policy with this reasoning at test time. This policy update is modeled as a soft Bayesian inference process in which beliefs about the policy are updated using the reasoning that reduces expected prediction errors under allowable policies as a likelihood. The resulting posterior policy admits a biological interpretation, recovering the scaling mechanism that engages the brain's basal ganglia and prefrontal cortex at test time. To solve this analytically intractable problem, a variational inference solution minimizing free energy bounds is developed. This solution extends to enable learning beyond training by reinforcing new instances, resolved at test time, in both the policy and world model. Unlike existing scaling laws constrained by model size and training data, the derived solution scales with the continuous real-world experience of a physical AI agent. Simulation results on an autonomous driving task demonstrate that the proposed solution outperforms model-free Q-learning and model-based Bayesian reinforcement learning, achieving robust generalization to unforeseen scenarios while improving inference efficiency by over 36%.