Structured dynamics in the algorithmic agent

Summary

The study extends the Kolmogorov Theory of Consciousness by analyzing how an agent's internal dynamics are shaped by the need to track natural data. Using group theory and Lie pseudogroups to formalize symmetry in world models, and a neural network as a proxy agent, the authors show that data tracking forces the agent to mirror the world model's symmetries. This imposes constraints on the agent's parameters and dynamics, leading to hierarchical organization consistent with the manifold hypothesis. The work connects algorithmic information theory, symmetry, and dynamics to inform AI and brain modeling.

Study at a glance

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 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.