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

2026-08-10

AI Summary

Discrete active inference models struggle to scale in complex spatiotemporal domains, and their existing theoretical formulations are often compact yet tightly coupled with specific implementations, hindering reproducibility and broader application. This work proposes a hierarchical renormalized generative model (RGM) that operates across spatiotemporal scales, constructing coarse-grained causal representations of high-level objects, events, and actions from fine-grained states and trajectories. It explicitly formalizes belief updating, action selection, and inter-layer information flow. For the first time, it provides a self-contained, derivation-driven theoretical framework that clarifies discrepancies between prior formulations and their implementations, accompanied by open-sourced, independently validated code. This significantly enhances transparency, auditability, and reproducibility, establishing a modular foundation for the quantitative evaluation and extension of RGMs on standard machine learning benchmarks.

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.

Problem

• active inference
• renormalising generative models
• scalability
• reproducibility
• hierarchical modeling

Innovation

• renormalising generative models
• active inference
• hierarchical modeling
• open implementation
• multi-scale inference