这篇论文解决了OPSD在长推理模型上越蒸馏越笨的问题，用PMI过滤器保留思考能力，值得做推理优化的朋友看看。
研究发现在线自蒸馏(OPSD)在长思维链推理模型上效果有限且破坏推理稳定性。通过分解教师监督信号，发现参考导致的成分驱动死记硬背，而可迁移的问题条件成分被忽略。提出两步解法：首先构建仅参考教师以隔离不可迁移成分，再用点互信息(PMI)过滤掉参考捷径。在4个长思维链模型和2个数据集上，该方法相比基线和标准OPSD均取得一致改进。
Purified OPSD: On-Policy Self-Distillation Without Losing How to Think
On-policy self-distillation (OPSD) has emerged as a promising paradigm for improving LLM reasoning, where a privileged teacher with access to reference solutions provides token-level supervision on the student's own generated trajectories. However, we find that OPSD consistently fails on long chain-of-thought (long-CoT) reasoning models, yielding at best marginal gains while destabilizing the reflective reasoning capability these models depend on. Through a novel decomposition of the teacher's supervision signal, we identify the root cause: the teacher's supervision is dominated by a reference-induced component that drives rote memorization of reference-specific shortcuts, while the question-conditioned, inference-transferable component is ignored or actively opposed. Based on this diagnosis, we propose a two-step solution. First, we construct a reference-only teacher (the same model conditioned on the reference without the question) to isolate the non-transferable component of the supervision signal; the residual after subtracting this component captures the question-conditioned, inference-transferable correction. Second, we use pointwise mutual information (PMI) as the mechanism to transform this residual into a well-formed PMI target distribution that the student can directly distill from, filtering out the reference-induced shortcut. Experiments on four long-CoT models across two datasets demonstrate consistent improvements over both the base model and standard OPSD, while preserving the models' natural epistemic behavior throughout training.