Recovering Event-Conditioned Local Symmetry Projectors for Hybrid Reinforcement Learning

Exploiting symmetry allows reinforcement learning to share information across related states and actions. In contact-rich environments, some transformation directions remain compatible with the dynamics while others are broken. Scalar gates cannot represent these surviving subspaces, whereas fixed-basis diagonal gates discard the cross terms of rotated subspaces. We recover event-conditioned local symmetry projectors from paired reset-and-step simulator queries. Hybrid-flow residuals and typed-event information define a Gram operator whose low-defect eigenspace yields a full projector subject to finite compatibility checks. In a direct-wrench MuJoCo orbital-contact task, the projector's translation–rotation cross terms recover the orbit pivot and define a quotient shared by the actor, critics, target networks, and action transport. One projector recovered at a canonical condition per geometry was reused across eight task conditions, reducing recovery calls by 87.5% relative to condition-specific recovery. Out-of-distribution (OOD) evaluation used obstacle centers withheld from policy optimization but independently certified before training. Across 20 paired seeds, sparse recovered full improved OOD regulation AUC over no-op SAC by 0.131. It also outperformed diagonal and spectrum-matched orthogonal controls while closely matching oracle full. With matched MLPs, direct-pivot features did not reproduce the quotient benefit. After charging all recovery calls, recovered full retained a +0.037 total-call OOD AUC advantage over no-op.