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. 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 cognitive dynamics is organized by slowly relaxing infrared modes embedded within a high-dimensional cognitive manifold. The resulting dynamics may be interpreted in terms of a macroscopic cognitive state continuously coupled to hierarchically organized slow-memory sectors. Integrating out these latent sectors generates retarded self-energy feedback and nonlocal memory kernels that soften the infrared response of the cognitive field. The resulting susceptibility enhancement produces a protected near-critical regime characterized by long-time contextual persistence and coherent collective dynamics. We introduce the time-scale density of states (TDOS) as a fundamental descriptor of the relaxation spectrum underlying inference, memory, and adaptive reasoning. Learning continuously reorganizes the infrared TDOS, selectively stabilizing weakly damped sectors that support contextual organization and recursive memory feedback. Near criticality, the TDOS generically develops a broad and nearly flat infrared structure associated with the accumulation of slowly relaxing modes. The resulting memory self-energy suppresses the effective forgetting gap, enhances collective susceptibility, and generates scale-free temporal organization over extended time scales. Within this framework, memory formation, adaptive reasoning, and emergent intelligence arise as hierarchical stages of infrared collective dynamical organization.