# Interpreting Dynamical Systems as Bayesian Reasoners

arXiv: https://arxiv.org/abs/2112.13523 · HTML: https://mlsanity.com/paper/2112.13523/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 27 Dec 2021.

## Builds on (most cited first, 15 of 15)

- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [Sophisticated Inference](https://mlsanity.com/paper/2006.04120/) (2020)
- [A free energy principle for a particular physics](https://mlsanity.com/paper/1906.10184/) (2019)
- [Disintegration and Bayesian Inversion via String Diagrams](https://mlsanity.com/paper/1709.00322/) (2017)
- [Agents and Devices: A Relative Definition of Agency](https://mlsanity.com/paper/1805.12387/) (2018)
- [Bayesian Mechanics for Stationary Processes](https://mlsanity.com/paper/2106.13830/) (2021)
- [A Channel-Based Perspective on Conjugate Priors](https://mlsanity.com/paper/1707.00269/) (2017)
- [How particular is the physics of the free energy principle?](https://mlsanity.com/paper/2105.11203/) (2021)
- [Towards information based spatiotemporal patterns as a foundation for agent representation in dynamical systems](https://mlsanity.com/paper/1605.05676/) (2016)
- [Some interesting observations on the free energy principle](https://mlsanity.com/paper/2002.04501/) (2020)
- [Cyber Kittens, or Some First Steps Towards Categorical Cybernetics](https://mlsanity.com/paper/2101.10483/) (2021)
- [Bayesian open games](https://mlsanity.com/paper/1910.03656/) (2019)
- [A macro agent and its actions](https://mlsanity.com/paper/2004.00058/) (2020)
- [Translating Extensive Form Games to Open Games with Agency](https://mlsanity.com/paper/2105.06763/) (2021)
- [Causal blankets: Theory and algorithmic framework](https://mlsanity.com/paper/2008.12568/) (2020)

## Built on by (most cited first, 5 of 5)

- [Interpreting systems as solving POMDPs: a step towards a formal understanding of agency](https://mlsanity.com/paper/2209.01619/) (2022)
- [Measuring Goal-Directedness](https://mlsanity.com/paper/2412.04758/) (2024)
- [A "good regulator theorem" for embodied agents](https://mlsanity.com/paper/2508.06326/) (2025)
- [Hybrid Life: Integrating Biological, Artificial, and Cognitive Systems](https://mlsanity.com/paper/2212.00285/) (2022)
- [AI in a vat: Fundamental limits of efficient world modelling for agent sandboxing and interpretability](https://mlsanity.com/paper/2504.04608/) (2025)

## Abstract (arXiv)

A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian prior or posterior. Here we begin the development of a general theory that would tell us when it is appropriate to interpret states as representing beliefs in this way. We focus on the case in which a system can be interpreted as performing either Bayesian filtering or Bayesian inference. We provide formal definitions of what it means for such an interpretation to exist, using techniques from category theory.