Structured Dynamics in the Algorithmic Agent

Ruffini, Castaldo, Vohryzek — Entropy 27(1), 90, 2025.

Why I cared. This is the question I can’t put down: if an agent must compress and track its world, what does that requirement force the agent itself to become?

What we did. We formalised the generative world model in the language of symmetry — Lie pseudogroups, the continuous transformations that leave natural data invariant — used a generic neural network as a stand-in agent, and, by analogy with Noether’s theorem, asked what tracking that data demands of it.

What we found. Tracking forces the agent to mirror the symmetries of the world it models. That dual constraint pushes it into a hierarchical, low-dimensional organisation — the manifold hypothesis — and ties together compression (Kolmogorov complexity), symmetry (group theory), and dynamics (conservation laws, reduced manifolds).

What it opened. If the world’s symmetry prints itself onto the agent, can an agent’s structure be read as a fingerprint of its world — and does that constrain how brains, and artificial agents, must be built?