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About this paper
Tianle Wang, Jiayu Liu, Ruizhi Zhao, Ning Miao
SAPD trains reasoning models on fixed worked solutions by matching a student’s next-token distribution to a teacher guided by the corresponding solution step, while the student uses the full reference prefix and generates no training rollouts. On Qwen3-4B-Instruct-2507, its mean math Avg@12 across AIME24, AIME25, and HMMT25 is 47.87%, versus 47.50% for OPSD; it does not lead every benchmark.
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