Cognitive Field Theory of Learning, Inference, and Emergence

Abstract

Learning, inference, memory, and emergence in biological and artificial systems are often described using disparate theoretical frameworks. Here we develop a cognitive field theory in which cognition is described as a collective nonequilibrium phenomenon governed by the geometry and collective spectrum of a learned cognitive manifold. Starting from a stochastic cognitive-field equation on an adaptive Riemannian manifold, we derive an effective cognitive field theory incorporating nonlocal memory kernels and retarded self-energy feedback. The learned cognitive geometry generates a complex collective spectrum characterized by the time-scale density of states $ρ(λ,ω)$, whose relaxation and circulation sectors govern memory persistence and temporal coherence. Integrating out latent slow collective modes produces non-Markovian memory feedback that renormalizes the cognitive forgetting gap $r_{\rm cog}$, enhances collective susceptibility, and drives the system toward a protected near-critical regime characterized by long-time contextual persistence and scale-free temporal organization. The observable cognitive field emerges as a macroscopic order parameter, $ϕ=Ae^{iψ}$, whose amplitude encodes collective cognitive organization and whose phase encodes temporal coherence across distributed collective modes. Within this framework, learning organizes cognitive geometry, cognitive geometry generates a collective spectrum, and the resulting memory feedback stabilizes a memory-dressed cognitive field. The theory provides a unified dynamical description of learning, memory, inference, selfhood, and emergent intelligence in terms of the infrared organization of collective cognitive dynamics.