# From pixels to planning: scale-free active inference

arXiv: https://arxiv.org/abs/2407.20292 · HTML: https://mlsanity.com/paper/2407.20292/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2024.

## Built on by (most cited first, 13 of 13)

- [Factorised Active Inference for Strategic Multi-Agent Interactions](https://mlsanity.com/paper/2411.07362/) (2024)
- [Possible Principles for Aligned Structure Learning Agents](https://mlsanity.com/paper/2410.00258/) (2024)
- [AXIOM: Learning to Play Games in Minutes with Expanding Object-Centric Models](https://mlsanity.com/paper/2505.24784/) (2025)
- [Active inference and artificial reasoning](https://mlsanity.com/paper/2512.21129/) (2025)
- [Toward Universal and Interpretable World Models for Open-ended Learning Agents](https://mlsanity.com/paper/2409.18676/) (2024)
- [Contemplative Artificial Intelligence](https://mlsanity.com/paper/2504.15125/) (2025)
- [Is the `Agent' Paradigm a Limiting Framework for Next-Generation Intelligent Systems?](https://mlsanity.com/paper/2509.10875/) (2025)
- [Natural Building Blocks for Structured World Models: Theory, Evidence, and Scaling](https://mlsanity.com/paper/2511.02091/) (2025)
- [EcoNet: Multiagent Planning and Control Of Household Energy Resources Using Active Inference](https://mlsanity.com/paper/2512.21343/) (2025)
- [Online Generalised Predictive Coding](https://mlsanity.com/paper/2605.02675/) (2026)
- [Renormalising Generative Models for Active Inference: Foundations, Derivations, and Verification](https://mlsanity.com/paper/2608.09512/) (2026)
- [Expected free energy as an information constraint on the Bethe Lagrangian](https://mlsanity.com/paper/2608.17167/) (2026)
- [BOBA: Dynamic Bayesian Optimization through Bayesian Active Inference](https://mlsanity.com/paper/2609.26021/) (2026)

## Abstract (arXiv)

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.