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

Karim Zaghw; Andrew Pashea; Marc Pritsch; Wouter Nuijten; Karl Friston; Lancelot Da Costa

cs.AIAug 10, 2026

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

Authors: Karim Zaghw, Andrew Pashea, Marc Pritsch, Wouter Nuijten, Karl Friston, Lancelot Da Costa

Organizations: University of Tübingen, Tübingen, Germany · Division of the Social Sciences, University of Chicago, Chicago, IL, USA · Heidelberg University, Heidelberg, Germany · Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands · Wellcome Centre for Human Neuroimaging, UCL Queen Square Institute of Neurology, University College London, London, UK · Max Planck Institute for Intelligent Systems, Tübingen, Germany

Abstract

Active inference offers a unified framework for perception, learning, and action, but scaling discrete active-inference models to rich spatial and temporal domains remains difficult. Renormalising generative models (RGMs) address this challenge by composing discrete generative models across spatial and temporal scales, coarse-graining lower-level states and paths into higher-level causes for objects, events, and action. However, fully reproducing and adapting the framework remains difficult: the mathematical exposition is compact, and the reference implementations are deeply integrated within specialized software environments, leaving many algorithmic details implicit. This paper addresses these challenges by providing a self-contained, derivation-oriented account of RGMs together with an open, verified implementation. We explain how the hierarchy is built, how beliefs and actions are updated within it, and how information is passed between levels. Where the published equations and implementation differ in emphasis, we make those choices explicit and explain their modelling consequences. By clarifying the theory and separating it from its original implementation context, this work lowers practical barriers to entry and makes RGMs more transparent, auditable, and reproducible, providing a foundation for future quantitative evaluation and development on machine-learning benchmarks.

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Apr 17, 2026 · cs.LGJ/K move · Enter open · S save

Hierarchical Active Inference using Successor Representations

Prashant Rangarajan, Rajesh P. N. Rao

Paul G. Allen Center for Computer Science and Engineering, University of Washington, Seattle, USA

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.

Hierarchical Reinforcement Learning Classical Planning Successor Representations Abstraction Navigation

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Abstract

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