Structured dynamics in the algorithmic agent

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 Noethers 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 agents 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. HighlightsO_LILie generative models are formalized using Lie pseudogroups, linking algorithmic simplicity, recursion, and compositionality with symmetry. C_LIO_LINeural networks inherit structural constraints reflecting the symmetries in Lie-generated data. C_LIO_LISimilarly, agents, instantiated as neural networks tracking world Lie-generated data, reflect Lie structure and reduced-dimensional dynamical manifolds. C_LIO_LICompositional structure in world data induces coarse-grained constraints, resulting in reduced manifolds that reflect the underlying generative process. C_LIO_LIMutual Algorithmic Information (MAI) between the agent and the world emerges as shared symmetries in their dynamical interactions. C_LIO_LIThese findings provide new insights for neuroscience, AI design, and computational brain modeling, emphasizing the interplay between data structure and agent dynamics. C_LI