SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation
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-time modules. A matched Random control preserves the structured factor's rank and nonzero spectru...
| Authors | Yunmeng Chen, Kunyu Wang, Peihan Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 September 2026 |
| Last updated at source | 11 September 2026 |
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