From Collective Predictive Coding to Human--AI Synergy: A Comprehensive Formulation

Yusuke Hayashi

Keywords: Hybrid Human--AI Collectives, Collective Predictive Coding, Fokker--Planck convergence

Abstract:

Collective Predictive Coding (CPC) broadens the classical framework of Predictive Coding (PC) by positing a shared external representation (e.g., language, symbols, or common knowledge) that couples agents in a multi-agent setting. Prior work has shown that both PC and CPC can be analyzed from a Bayesian perspective, with their updates expressible via Langevin equations under suitable assumptions. Notably, the CPC-derived Langevin dynamics introduce an additional potential term that can be viewed as an ``external force,'' capturing how shared symbols steer the collective.

However, to fully grasp why substituting Bayesian updates with Langevin dynamics is valid, one must recognize that the corresponding Fokker--Planck equation converges to the same posterior distribution implied by Bayesian inference. In this paper, we restore and expand the technical details linking Bayesian updating, Fokker--Planck convergence, and the emergence of the CPC-specific force term. We also offer a more thorough discussion of how each free-energy component in PC and CPC is derived, why it matters for multi-agent coordination, and what limitations arise from communication constraints and symbol emergence. These clarifications provide a stronger foundation for leveraging CPC to orchestrate hybrid human--AI collectives via shared external media.

Submission Number: 6