The role of target-specific privilege is investigated with On-Policy Self-Distillation from Other Problems (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective.
Abstract
On-Policy Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with $\mathrm{OP}^{2}\mathrm{SD}$ (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, $\mathrm{OP}^{2}\mathrm{SD}$ improves over the base model, remains competitive with OPSD. The success of $\mathrm{OP}^{2}\mathrm{SD}$ implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.
It is found that stronger alignment attributable to the correct reference does not reliably coincide with a greater performance benefit from the reference, and performance gains and distributional alignment alone cannot determine how privileged reference information contributes to student learning in OPSD.
Experiments on challenging reasoning benchmarks show that H$^2$SD achieves the strongest overall performance among representative RLVR and self-distillation baselines, with stable optimization and a favorable accuracy-efficiency trade-off.
Qi Cai, Yi-Chuan Ma, Linyang Li et al.· arXiv.org· 2 citations
On-policy self-distillation (OPSD) improves the reasoning abilities of LLMs by internalizing privileged context into model parameters through self-distillation. Two recent research lines promote vanilla OPSD by choosing which tokens to learn from and by controlling how much privileged information the teacher receives, respectively. However, we show that each line optimizes one variable while holding the other fixed, which leads to a suboptimal solution. We argue that the two variables are coupled through the student's learning capacity: the privileged information sets the per-token divergence the teacher prescribes, while token weighting selects which of these the student must absorb. We formalize the two lines of work into a unified optimization framework, which maximizes the aggregate teacher--student divergence, subject to a budget on the aggregate learning difficulty the student can absorb. Under this modelling, we propose Unified On-Policy Self-Distillation (USD), a lightweight online algorithm to solve the Lagrangian. USD reveals that a single dual variable governs both decisions: at one price for learning difficulty, it simultaneously sets the token-selection threshold and the direction of privileged-information adjustment, keeping supervision matched to the student's evolving capacity. Through extensive experiments, USD consistently demonstrates superior performance over OPSD and token- and PI-side baselines across various model scales on various reasoning benchmarks. Code is available at https://github.com/lauvlalala/USD.
Yongkang Yang, Zhezheng Hao, Hong Zhang et al.· 1 citation
DualOPSD, an asymmetric alternating framework that adapts both policies, reduces truncation across all three scales, and makes later supervision responsive to the learner and does not require another rollout.
Yu-Tong Chen, Guangfu Guo, Zhi-Chao Xu et al.· 0 citations
DAPD is proposed, a unified framework with two levels of anchoring that significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks.
Jian-Yu Wu, Yi-Zhou Wang, Encheng Su et al.· 0 citations
This work introduces Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience.
Gui-Min Zhang, Jiayang Lyu, Ran Sun et al.· 1 citation
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