Structured dynamics in the algorithmic agent

Abstract

In the Algorithmic Information Theory of Consciousness (KT), algorithmic agents use compressive models inferred from world data to plan actions that maximize their objective function. What are the structural and dynamical consequences of tracking natural data generated by simple world models? To address this, we first propose a formalization of the concept of a generative model using the language of symmetry—Lie group theory. Then, using a generic neural network model as an agent system, we show that data tracking constrains the agent’s dynamical repertoire, forcing it to mirror the symmetry of the generative world model. This narrows down both the space of potential parameters of the agent system and its dynamical repertoire, endowing both with structure inherited from the world. Based on these insights, we examine the link between data-tracking and the manifold hypothesis, which posits that natural high-dimensional data can be compressed into a reduced number of parameters due to the presence of a low-dimensional invariant manifold within the high-dimensional phase space. This work offers a new perspective for identifying neural correlates of agenthood and structured experience in natural agents and for developing AI and computational brain models.HighlightsWe define generative models using Lie groups.We associate the algorithmic simplicity of a model with representations of Lie groups or Lie algebras with special properties such as nilpotency and compositionality (hierarchical function composition).We show that world-tracking constraints force the tracking dynamical system to mirror the symmetry in the data.In this context, we revisit the manifold hypothesis and the implications for AI design and brain modeling.

Neural Geometrodynamics, Complexity, and Plasticity: A Psychedelics Perspective

“…The fact that such a reduced space exists means that it can be generated by coordinates in a reduced latent space. The geometry and topology of this reduced space in different states provide a synthetic description of the dynamics and are of special interest [ 37 ].…”

“…World-tracking constraints force the brain as a dynamical system to mirror the symmetry in the data [ 37 ], a requirement that translates into constraints on structural and dynamical aspects of the system (and which can be analyzed using Lie group theory). This suggests leveraging the known links between topology and Lie groups [ 100 ].…”

“…The observed push of brain dynamics towards disorder and away from criticality aligns with the REBUS and FEP frameworks, which link the vividness of experience to the entropy of brain activity. At the same time, the notion that a wakeful brain exhibits dimensionality reduction and criticality features that are disrupted by the effect of psychedelics is also predicted by an algorithmic perspective on consciousness [ 16 , 36 , 37 ], where the psychedelic shift towards disorder is associated with a disruption of the world-modeling/world-tracking circuits in the brain.…”