The Σ-Model: Schema-Coherence Suppression as the Origin of Compositional Generalisation Failure — A Dynamical-Systems Framework for Generalisation Failure

Problem: Standard gradient-based training pipelines optimize parametric depth without targeting schema coherence—an agent's internal organization around governing principles rather than surface statistics. High-depth, low-coherence agents fail on OOD recombination that ID metrics miss. Existing frameworks do not specify how schema coherence forms, what suppresses it, or how it drives attentional allocation. Method: We introduce the Σ-Model, a coupled dynamical-systems framework with three contributions: (i) the σ-suppression mechanism—SGD creates a stable low-coherence equilibrium ("σ-trap"), explaining high-ID/low-OOD agents (Proposition 4.1); (ii) a grounded ODE system (Eqs. 14, 28, 29) with local existence, invariance, and bifurcation analysis (Propositions 3.1–4.4); and (iii) a five-phase training arc with empirically detectable Phase-2 entry (Prediction 9). The framework formalizes five cognitive faculty gaps with executable benchmarks and covers attentional fidelity, executive control, metacognition, social cognition, and multimodal transfer. Results: Pilot experiments (n = 15 per condition) confirm additive and multiplicative coupling significantly outperform naive SGD on OOD accuracy (d = 9.08, 7.57; p < 0.0001), with Phase 2 entry detected early in training. Conclusion: σ-suppression is the mechanistic origin of compositional failure. Capable-agent training must target dynamics explicitly — not merely scale or curriculum ordering.