Pressure and Generalization: A General Theory of Learning

Why do some systems generalize while others merely memorize? This paper presents a general theory of learning: pressure (P) — any constraint, limitation, or stress that makes the free storage of information costly during learning — is the mechanism that transforms memorization into generalization. The theory is formalized as four axioms: (1) memorization is the default, (2) without pressure, no system generalizes on tasks where memorization and generalization are structurally distinct, (3) memorization and generalization coexist as superposed signals in the same medium, and (4) systems that cannot memorize cannot generalize. Three properties follow: pressure exploits the dimensionality asymmetry between memorization (high-dimensional, specific) and generalization (low-dimensional, abstract); pressure has a viable range bounded by insufficiency and catastrophic collapse; and the transition from memorization to generalization is qualitative, not continuous. The theory is substrate-independent. It is tested through over 60 experimental configurations comprising over 3,000 runs on neural networks, where zero pressure produces zero generalization on structurally distinct tasks without exception. Without modification, the same theory explains thirty established findings across seven domains — cognitive psychology, neuroscience, motor learning, creativity research, evolutionary biology, immunology, and machine learning. The theory makes strong, falsifiable predictions and provides specific criteria for its own refutation.