Replication and Information Extraction in a Minimal Agent-Environment Model

We consider an unsupervised classifying agent that evolves by enforcing self-consistency of its labels under continual exposure to a data-generating environment. Because the agent's predictions feed back into its own regularized updates, the dynamics can stabilize into self-sustaining modes of operation, which we coin functional replicators. Remarkably, such replicators can spontaneously align with the latent structure of the environment, despite never being exposed to ground-truth labels or selected for adaptation. Using analytical tools from statistical mechanics and numerical experiments, we show that the onset of this regime corresponds to a transition driven by weak correlations between the agent's initial state and environmental structure. Extending the model to multiple agents, we find that their mutual influence can spontaneously break symmetry and produce consensus, illustrating a minimal setting for decentralized collective learning.