用大模型生成的推理过程训练小模型，提升数学解题能力。
Learning to Reason: Training LLMs with GPT-OSS or DeepSeek R1 Reasoning Traces
- 用 DeepSeek-R1 和 gpt-oss 生成推理链，微调中等规模模型。
- gpt-oss 生成的推理链使模型在数学题上准确率更高。
- 该方法无需人工标注，适合资源有限的研究者快速获得推理能力。
推理时扩展（Test-time scaling）通过增加推理阶段的计算量，使大型语言模型能够通过理解目标、制定计划、执行中间步骤并自我验证来解决复杂问题。当前前沿的大模型如 DeepSeek-R1 与 OpenAI 的 gpt-oss，均采用生成中间推理轨迹的方式求解复杂问题。本文比较了使用 DeepSeek-R1 与 gpt-oss 生成的推理轨迹对中等规模语言模型在数学问题上的后训练效果，评估其在准确性与推理效率方面的差异。结果表明，基于 gpt-oss 生成的推理轨迹能显著提升模型性能，且该方法可作为低成本高效率的监督数据来源，无需昂贵的人工标注即可赋予中小模型强推理能力。
原文摘要 · Abstract (English)
Test-time scaling, which leverages additional computation during inference to improve model accuracy, has enabled a new class of Large Language Models (LLMs) that are able to reason through complex problems by understanding the goal, turning this goal into a plan, working through intermediate steps, and checking their own work before answering . Frontier large language models with reasoning capabilities, such as DeepSeek-R1 and OpenAI's gpt-oss, follow the same procedure when solving complex problems by generating intermediate reasoning traces before giving the final answer. Today, these models are being increasingly used to generate reasoning traces that serve as high-quality supervised data for post-training of small and medium-sized language models to teach reasoning capabilities without requiring expensive human curation. In this work, we compare the performance of medium-sized LLMs on Math problems after post-training on two kinds of reasoning traces. We compare the impact of reasoning traces generated by DeepSeek-R1 and gpt-oss LLMs in terms of accuracy and inference efficiency.
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