Diagnosing Faults in Reinforcement Learning Simulators and World Models with Canonical Polynomial Invariants

תקציר מקורי באנגליתarXiv:2609.13194v1 Announce Type: cross Abstract: A large literature builds physical structure into learned dynamics on the premise that models respecting the underlying physics predict better. We test that premise using exact polynomial invariants recovered from trajectories and canonicalised as reduced Gr\"obner bases over $\mathbb{Q}$. On Acrobot, exactness provides little benefit for prediction: a consistency regulariser reduces algebraic residual while leaving rollout fidelity essentially unchanged, and a shaping potential recovered from a system with a 100% mass error accelerates learning as effectively as the correct potential. Exact canonical invariants instead prove valuable for diagnosis. We develop two procedures: screening, which identifies the violated physical constraint, and