# A "good regulator theorem" for embodied agents

arXiv: https://arxiv.org/abs/2508.06326 · HTML: https://mlsanity.com/paper/2508.06326/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [Meta-learning of Sequential Strategies](https://mlsanity.com/paper/1905.03030/) (2019)
- [A free energy principle for a particular physics](https://mlsanity.com/paper/1906.10184/) (2019)
- [Causal Inference by String Diagram Surgery](https://mlsanity.com/paper/1811.08338/) (2018)
- [General agents contain world models](https://mlsanity.com/paper/2506.01622/) (2025)
- [The d-separation criterion in Categorical Probability](https://mlsanity.com/paper/2207.05740/) (2022)
- [Bayesian Mechanics for Stationary Processes](https://mlsanity.com/paper/2106.13830/) (2021)
- [Interpreting systems as solving POMDPs: a step towards a formal understanding of agency](https://mlsanity.com/paper/2209.01619/) (2022)
- [A Channel-Based Perspective on Conjugate Priors](https://mlsanity.com/paper/1707.00269/) (2017)
- [Interpreting Dynamical Systems as Bayesian Reasoners](https://mlsanity.com/paper/2112.13523/) (2021)
- [A Bayesian Interpretation of the Internal Model Principle](https://mlsanity.com/paper/2503.00511/) (2025)
- [Formalising the intentional stance 1: attributing goals and beliefs to stochastic processes](https://mlsanity.com/paper/2405.16490/) (2024)
- [Formalising the intentional stance 2: a coinductive approach](https://mlsanity.com/paper/2501.09173/) (2025)

## Built on by (most cited first, 4 of 4)

- [From Runtime Records to Legal Findings: An Evidentiary-Adequacy Criterion for Agentic AI Oversight](https://mlsanity.com/paper/2607.00941/) (2026)
- [Verifying Good Regulator Conditions for Hypergraph Observers: Natural Gradient Learning from Causal Invariance via Established Theorems](https://mlsanity.com/paper/2603.09067/) (2026)
- [A Matter of Time: Towards a General Theory of Agency](https://mlsanity.com/paper/2606.23122/) (2026)
- [The Anatomy of a Blind Spot: What an LLM Judge Must Be Shown, and How Much](https://mlsanity.com/paper/2610.15938/) (2026)

## Abstract (arXiv)

In a classic paper, Conant and Ashby claimed that "every good regulator of a system must be a model of that system." Artificial Life has produced many examples of systems that perform tasks with apparently no model in sight; these suggest Conant and Ashby's theorem doesn't easily generalise beyond its restricted setup. Nevertheless, here we show that a similar intuition can be fleshed out in a different way: whenever an agent is able to perform a regulation task, it is possible for an observer to interpret it as having "beliefs" about its environment, which it "updates" in response to sensory input. This notion of belief updating provides a notion of model that is more sophisticated than Conant and Ashby's, as well as a theorem that is more broadly applicable. However, it necessitates a change in perspective, in that the observer plays an essential role in the theory: models are not a mere property of the system but are imposed on it from outside. Our theorem holds regardless of whether the system is regulating its environment in a classic control theory setup, or whether it's regulating its own internal state; the model is of its environment either way. The model might be trivial, however, and this is how the apparent counterexamples are resolved.