PreSO: Privileged Representation Isolation for On-Policy Self-Distillation

Yuhang Yang, Mingxuan Xia, Chao Ye, Shuai Zhu, Shouqing Yang +4

On-policy self-distillation (OPSD) uses a self-teacher conditioned on privileged information to turn the sparse outcome signal of reinforcement learning with verifiable rewards (RLVR) into dense token-level supervision. Yet the teacher's advantage may depend on information unavailable to the student at inference, raising a central question: which privileged changes are worth distilling? We use cross-problem recurrence as an empirical cue for potentially reusable guidance. Comparing the representation shifts induced by full solutions and compact hints, we find that hint-induced shifts are more concentrated and directionally consistent across problems, and yield more sustained downstream gains despite revealing less information. Motivated by this association, we propose Privileged Representation Isolation for On-Policy Self-Distillation (PreSO). At the source, PreSO uses compact hints to limit the solution-specific detail entering the privileged shift. At the target, it estimates a leading low-rank subspace from shifts pooled across related problems, projects the privilege-induced correction onto this subspace, and adds it to the student's unprivileged representation to form the…