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SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

On-policy self-distillation (OPSD) scores student-generated prefixes with a solution-conditioned self-teacher, yet transfers supervision only through next-token probabilities. We ask whether the aligned final-layer discrepancy offers a useful second channel, and how to test that channel without confusing its geometry with auxiliary strength. SCOPE-OPSD projects the privileged teacher-student residual onto a frozen rank-64 factor estimated from residual covariance and language-model-head Fisher sensitivity. It reuses the forwards already required by OPSD and adds neither rollouts nor inference-

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