用思维结构分析大模型数学推理过程，揭示其内在思考模式。
Schoenfeld's Anatomy of Mathematical Reasoning by Language Models
- 将推理过程抽象为分析、探索、实施、验证等功能步骤
- 发现探索是影响正确性的关键分支，评估反馈常被效率策略抑制
- 适合研究模型推理机制或提升生成质量的开发者
大型语言模型日益展现推理轨迹，但其深层认知结构与步骤仍难以识别和分析，仅靠表层统计无法深入。本文采用Schoenfeld的剧集理论作为归纳性中尺度视角，提出ThinkARM（模型推理解剖）框架，将推理轨迹显式抽象为分析、探索、实施、验证等功能步骤。应用于多种模型的数学问题求解时，该抽象揭示了可复现的思维动态及推理与非推理模型间的结构性差异，这些在词元级视图下并不明显。进一步通过两个诊断案例表明：探索作为关键分支步骤与正确性密切相关；效率导向方法会刻意抑制评估反馈步骤，而非简单缩短输出。结果表明，剧集级表示使推理步骤清晰可见，支持对现代语言模型推理结构、稳定性和变化进行系统性分析。
原文摘要 · Abstract (English)
Large language models increasingly expose reasoning traces, yet their underlying cognitive structure and steps remain difficult to identify and analyze beyond surface-level statistics. We adopt Schoenfeld's Episode Theory as an inductive, intermediate-scale lens and introduce ThinkARM (Anatomy of Reasoning in Models), a scalable framework that explicitly abstracts reasoning traces into functional reasoning steps such as Analysis, Explore, Implement, Verify, etc. When applied to mathematical problem solving by diverse models, this abstraction reveals reproducible thinking dynamics and structural differences between reasoning and non-reasoning models, which are not apparent from token-level views. We further present two diagnostic case studies showing that exploration functions as a critical branching step associated with correctness, and that efficiency-oriented methods selectively suppress evaluative feedback steps rather than uniformly shortening responses. Together, our results demonstrate that episode-level representations make reasoning steps explicit, enabling systematic analysis of how reasoning is structured, stabilized, and altered in modern language models.
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