发表机构
University of Tübingen; University of Chicago; Heidelberg University; Eindhoven University of Technology; University College London; Max Planck Institute for Intelligent Systems（蒂宾根大学; 芝加哥大学; 海德堡大学; 埃因霍温理工大学; 伦敦大学学院; 马克斯·普朗克智能系统研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对主动推理模型扩展难题，提供重正化生成模型（RGMs）的自包含推导说明及开源验证实现，降低其应用门槛，为后续机器学习基准研究奠定基础。
AI 中文摘要
主动推理为感知、学习和行动提供了统一框架，但将离散主动推理模型扩展到丰富的时空领域仍存在困难。重正化生成模型（RGMs）通过跨时空尺度组合离散生成模型，将低层状态和路径粗粒化为物体、事件和行动的高层原因，解决了这一挑战。然而，完整复现和适配该框架仍具难度：数学阐述紧凑，参考实现深度集成于专业软件环境，许多算法细节隐含。本文通过提供自包含、面向推导的RGMs说明及开源、已验证的实现，解决了这些挑战。我们解释了层级如何构建、信念和行动如何在其中更新、信息如何在层级间传递。当已发表方程与实现侧重点不同时，我们明确这些选择并解释其建模后果。通过厘清理论并将其与原始实现环境分离，本工作降低了实践入门门槛，使RGMs更透明、可审计、可复现，为机器学习基准上的未来定量评估和开发奠定基础。
英文摘要
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.
Comments25 pages, 1 figure. Accepted as a full paper at the 7th International Workshop on Active Inference (IWAI 2026). Supplementary material: https://doi.org/10.5281/zenodo.20533539. Code: https://github.com/atomresearch/RGMs
