Neural Networks & AI

This theoretical study introduces a novel 'cognitive field theory' to unify the disparate frameworks currently used to describe learning, inference, memory, and emergence in both biological and artificial systems. The methodology establishes a stochastic cognitive-field equation incorporating homeostatic stabilization and adaptive manifold geometry, demonstrating that cognitive dynamics are organized by slowly relaxing infrared modes embedded within a high-dimensional cognitive manifold. By integrating out latent sectors, the model generates retarded self-energy feedback and nonlocal memory kernels that soften the infrared response of the cognitive field. A key innovation of this research is the introduction of the time-scale density of states (TDOS) as a fundamental descriptor of the relaxation spectrum underlying inference, memory, and adaptive reasoning. The results show that learning continuously reorganizes the infrared TDOS, selectively stabilizing weakly damped sectors to support contextual organization and recursive memory feedback. Near criticality, the TDOS develops a broad, nearly flat infrared structure that suppresses the effective forgetting gap, enhances collective susceptibility, and generates scale-free temporal organization over extended time scales. Consequently, memory formation, adaptive reasoning, and emergent intelligence are mathematically framed as hierarchical stages of infrared collective dynamical organization. Because this is a purely theoretical framework, limitations include a lack of empirical validation in clinical or biological neural networks, and future directions must focus on testing these mathematical predictions against real-world neurophysiological data.