这篇论文用老师模型和基础模型的差值做蒸馏信号，比直接模仿老师更强，数学代码推理都更好，训练时间还短。
On-Policy Delta Distillation (OPD²) 引入delta信号，定义为教师模型与其未经推理指令微调的基础模型之间的差异。该方法在数学、科学和代码推理基准上一致优于传统on-policy蒸馏。实验表明，仅需短期后训练即可使推理LLM达到强性能。代码已在GitHub开源。
On-Policy Delta Distillation
On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD$^2$). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD$^2$ consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2