SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation
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Computer Science > Machine Learning
arXiv:2609.12579 (cs)
[Submitted on 11 Sep 2026]
Title:SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation
Authors:Yunmeng Chen (1), Kunyu Wang (2), Peihan Li (1), Yi Wang (1), Shuyin Xia (3), Yi Liu (1), Xinyong Cheng (2), Dehui Wang (2), Xiangyong Zhai (2), Yanxing Liu (1), Song Liu (1) ((1) Chongqing Ant Consumer Finance Co., Ltd., (2) Alibaba Cloud Computing Co., Ltd., (3) Chongqing University of Posts and Telecommunications)
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Abstract: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 spectrum and uses per-arm gradient-RMS calibration, isolating the effect of the data-dependent orientation. Across the complete 25/50/75/100-step trajectories for Qwen3-1.7B, 4B, and 8B, Structured is never below Pure OPSD, with strict gains in 11 of the 12 model-checkpoint combinations and an exact tie at 4B step 25. Structured also exceeds matched Random in 10 of the 12 combinations. At step 75 on Qwen3-1.7B, Structured exceeds matched Random by 1.39 Macro Avg@12 points in each of two independent training reruns. A cross-fitted diagnostic also shows 4.40 times greater held-out privileged-gap capture than the matched random orientation. The results support a compact, Fisher-conditioned privileged subspace for short-budget OPSD.
| Comments: | 16 pages, 3 figures. Yunmeng Chen, Kunyu Wang, and Peihan Li contributed equally. Corresponding author: Song Liu |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2609.12579 [cs.LG] |
| (or arXiv:2609.12579v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.12579
arXiv-issued DOI via DataCite (pending registration)
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