Cognitive Field Theory of Learning, Inference, and Emergence

Learning, inference, memory, and emergence in biological and artificial systems are often described using disparate theoretical frameworks ranging from neural field models to recurrent and attention-based architectures. Here we develop a cognitive field theory in which cognition emerges as a collective nonequilibrium phenomenon governed by the infrared organization of adaptive dynamical time scales. Starting from a stochastic cognitive-field equation with homeostatic stabilization and adaptive manifold geometry, we show that collective cognitive dynamics is organized by slowly relaxing infrared modes embedded within a high-dimensional cognitive manifold. Integrating out latent slow-memory sectors generates retarded self-energy feedback and nonlocal memory kernels governing long-time contextual persistence and collective cognitive coherence. We introduce the time-scale density of states (TDOS) as a fundamental descriptor characterizing the distribution of collective relaxation modes underlying inference, memory, and adaptive reasoning. Learning and adaptation continuously reorganize the infrared TDOS, selectively stabilizing weakly damped collective sectors that support contextual organization and recursive collective dynamics. Near criticality, the infrared TDOS generically develops a broad and nearly flat structure associated with the accumulation of slowly relaxing collective modes, producing scale-free temporal organization and enhanced collective coherence. Within this framework, memory formation, adaptive reasoning, and emergent intelligence arise as hierarchical stages of collective infrared dynamical organization.