# 特权信息为 On-Policy 自蒸馏带来了什么？--基于 AMPLE-Math 的实证研究

- 来源：HuggingFace Daily Papers（社区热门论文）
- 发布时间：2026-09-17 08:00
- AIHOT 分数：39
- AIHOT 链接：https://aihot.news/items/cmu6ds2t00kq9rofj9ix05nw1
- 原文链接：https://arxiv.org/abs/2609.20612

## AI 摘要

研究构建了 AMPLE-Math 套件，包含 5,319 道数学题和六种共享同一答案的推理视图，用于分离特权信息在 on-policy 自蒸馏（OPSD）中的独立贡献。

## 正文

On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks.

Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged.

Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.