Cognitive Representations through Rational Field Equilibrium: A Gradient-Free Framework for Adaptive Structure

Cognitive representations are commonly modeled either as symbolic structures or as parameters optimized through iterative learning.This paper proposes Rational Field Equilibrium, a training-free computational framework in which cognitive representations emerge from locally bounded relational interactions within a conceptual space.Each representation interacts only with elements within a fixed rational neighborhood defined by a distance threshold, which constrains perceptual and conceptual interaction and provides a stable relational geometry for equilibrium formation. Representational adaptation arises analytically from weighted relational consistency rather than error-driven optimization.Unlike gradient-based learning, the proposed framework does not rely on iterative training or backpropagation. Instead, coherent conceptual structure emerges directly from relational equilibrium within perception and conceptual spaces.Experiments on geometric and semantic representations demonstrate spontaneous self-organization and deterministic convergence in a single forward pass, suggesting that adaptive cognitive structure can arise from stable relational geometry alone.