Structured Dynamics in the Algorithmic Agent.
Giulio Ruffini, Francesca Castaldo, Jakub Vohryzek
Entropy (Basel, Switzerland) January 19, 2025 Peer reviewed DOI: 10.3390/e27010090 via PubMed
Summary
Tracking natural data forces an AI agent to mirror the symmetry properties of the world model it is trying to compress. Using Lie pseudogroups to describe continuous transformations in data, and drawing an analogy to Noether's theorem, the study shows this constraint leads to a hierarchical organization in the agent's neural network, consistent with the manifold hypothesis. This bridges algorithmic information theory, symmetry, and dynamics, offering insights into the neural basis of agency and structured experience.
Study at a glance
| Design | theoretical study |
|---|---|
| Key finding | Data tracking forces an agent to mirror the symmetry properties of the generative world model, leading to a hierarchical organization consistent with the manifold hypothesis. |
Abstract
In the Kolmogorov Theory of Consciousness, algorithmic agents utilize inferred compressive models to track coarse-grained data produced by simplified world models, capturing regularities that structure subjective experience and guide action planning. Here, we study the dynamical aspects of this framework by examining how the requirement of tracking natural data drives the structural and dynamical properties of the agent. We first formalize the notion of a generative model using the language of symmetry from group theory, specifically employing Lie pseudogroups to describe the continuous transformations that characterize invariance in natural data. Then, adopting a generic neural network as a proxy for the agent dynamical system and drawing parallels to Noether's theorem in physics, we demonstrate that data tracking forces the agent to mirror the symmetry properties of the generative world model. This dual constraint on the agent's constitutive parameters and dynamical repertoire enforces a hierarchical organization consistent with the manifold hypothesis in the neural network. Our findings bridge perspectives from algorithmic information theory (Kolmogorov complexity, compressive modeling), symmetry (group theory), and dynamics (conservation laws, reduced manifolds), offering insights into the neural correlates of agenthood and structured experience in natural systems, as well as the design of artificial intelligence and computational models of the brain.