Metric-Topology Factorization: A Computational Framework for Hippocampal-Neocortical Intelligence

Abstract: The brain achieves stability and plasticity in a topologically complex, shifting world through Metric-Topology Factorization (MTF), separating discrete topological indexing for context selection from continuous metric condensation for local inference. Semantically rich environments defy single globally contractive geometries, causing obstructions under shifts, so intelligence factorizes these: the hippocampus provides sparse signatures indexing manifold identity, while the neocortex untangles geometry hierarchically. In the ventral stream, a dynamic-programming-like process quotients symmetries (e.g., translation, scale), transforming non-convex sensory mazes into separable bowls. Offline replay and consolidation amortize transformations for rapid task switching. Dreaming in REM involves stochastic hippocampal traversal to expose and regularize latent structures. Consciousness arises from resolving topological uncertainty into stable embeddings, with awareness for unamortized states. Evolutionarily, transitions like sensorimotor control to language expand topological complexity, demanding advanced indexing-metric separation. Intelligence emerges via recalibrating context-specific geometries, converting global navigation into local dynamics, not deeper search.