Han, Huiwen: Mean Reversion or Innovation Collapse? Stability Analysis of Closed-Loop Social Communication Systems with AI-Agent Mediators

We model the Expansion–Compression (EC) loop introduced in the DECO series as a discrete-time closed-loop control system, with the LLM expansion operator E as a forward gain element and the LLM compression operator C as a feedback element. Using the transfer-function formalism of linear systems theory and its nonlinear extensions, we analyse the stability, convergence properties, and phase transitions of a population of N such loops coupled through a shared semantic environment. We establish fou