Internal model principles

Also, good regulator theorem

2025-06-05 — 2026-02-06

Wherein the ε-transducer is introduced, by which ε-machines are extended to active inference, and Bayesian belief updating is treated as the efficient world-model, with sundry readings being listed.

adaptive
agents
AI safety
economics
evolution
extended self
game theory
gene
incentive mechanisms
learning
mind
probability
sociology
statistics
statmech
utility
wonk

Placeholder: we’ll talk about the internal model principle, the good regulator theorem, and related results.

1 Transducers

I just saw Fernando Rosas present at Rosas, Boyd, and Baltieri (2025).

The construction (the \(\epsilon\)-transducer) seems to generalize \(\epsilon\)-machines into active inference about the world, similar to how AIXI generalizes Solomonoff prior-based induction into active learning.

See also Boyd et al. (2025).

2 Incoming

Alfred Harwood, The Internal Model Principle: A Straightforward Explanation.

Jose Faustino, Distilling the Internal Model Principle.

To read: Costa-Castello, Nebot, and Grino (2005), Francis and Wonham (1976), Huang et al. (2018).

3 References

Baltieri, Biehl, Capucci, et al. 2025. “A Bayesian Interpretation of the Internal Model Principle.”
Bin, Astolfi, and Marconi. 2021. “About Robustness of Control Systems Embedding an Internal Model.”
Boyd, Nowak, Hyland, et al. 2025. “From Monoliths to Modules: Decomposing Transducers for Efficient World Modelling.”
Cao, Wang, Ouyang, et al. 2015. “The Free Energy Cost of Accurate Biochemical Oscillations.” Nature Physics.
Chirimuuta. 2025. “The Prehistory of the Idea That Thinking Is Modelling.” Human Arenas.
Cisek. 2009. “Internal Models.” In Encyclopedia of Neuroscience.
Costa-Castello, Nebot, and Grino. 2005. “Demonstration of the Internal Model Principle by Digital Repetitive Control of an Educational Laboratory Plant.” IEEE Transactions on Education.
Diester, Bartos, Bödecker, et al. 2024. “Internal World Models in Humans, Animals, and AI.” Neuron.
Duncan. 2025. “Construction and Use of Mental Models: Organizing Principles for the Science of Brain and Mind.” Neuropsychologia.
Francis, and Wonham. 1976. “The Internal Model Principle of Control Theory.” Automatica.
Hao, Gu, Ma, et al. 2023. “Reasoning with Language Model Is Planning with World Model.”
Hoel. 2017. “When the Map Is Better Than the Territory.” Entropy.
Huang, Isidori, Marconi, et al. 2018. “Internal Models in Control, Biology and Neuroscience.” In 2018 IEEE Conference on Decision and Control (CDC).
Isidori, Marconi, and Serrani. 2003. “Fundamentals of Internal-Model-Based Control Theory.” In Robust Autonomous Guidance: An Internal Model Approach.
Kawato, and Cortese. 2021. “From Internal Models Toward Metacognitive AI.”
Lewandowski, Ramesh, Meyer, et al. 2025. “The World Is Bigger: A Computationally-Embedded Perspective on the Big World Hypothesis.” In.
Rosas, Boyd, and Baltieri. 2025. “AI in a Vat: Fundamental Limits of Efficient World Modelling for Agent Sandboxing and Interpretability.” In.
Touchette, and Lloyd. 2004. “Information-Theoretic Approach to the Study of Control Systems.” Physica A: Statistical Mechanics and Its Applications.
Virgo, Biehl, Baltieri, et al. 2025. “A ‘Good Regulator Theorem’ for Embodied Agents.” In.
Wagner. 2005. Robustness and Evolvability in Living Systems. Princeton Studies in Complexity.
Wolpert, Miall, and Kawato. 1998. “Internal Models in the Cerebellum.” Trends in Cognitive Sciences.
Wonham, and Cai. 2019. Supervisory Control of Discrete-Event Systems. Communications and Control Engineering.