Replication and Information Extraction in a Minimal Agent-Environment Model

Abstract

How can information be extracted from data without explicit guidance or rewards? We investigate this question in a minimal setting where a classifying agent is exposed to a stream of structured data produced by a generative environment, and evolves by seeking consistency of its own labels in time. We find that imposing a simplicity bias on the classification rule can drive the dynamics toward label-coherent steady states, which we coin functional replicators. Remarkably, these persistent labeling rules align with the latent structure of the data. Using analytical tools from statistical mechanics, we characterize this spontaneous learning phase transition. Extending the analysis to a population of agents that pool labels from one another, we show that interaction reshapes the learning phase boundary, in some regimes enabling spontaneous learning that no isolated agent can achieve, while suppressing it in others. Our minimal framework thus opens a route to decentralized learning through label exchange alone, requiring no access to the internal weights of other agents.