测试大模型识别复杂函数凸性的能力，发现深度增加时表现急剧下降。
ConvexBench: Can LLMs Recognize Convex Functions?
- 用符号函数复合结构构建可验证的凸性测试基准
- 深度达100时准确率从1.0降至约0.2，存在严重推理退化
- 提出分治代理框架，显著提升深层复合函数的识别能力
凸分析是现代数学的重要分支，具有广泛的应用。随着大语言模型（LLMs）开始自动化高阶数学与科学研究，理解并推理凸性能力对它们至关重要。我们引入 extit{ConvexBench}（ extit{CB}），一个可扩展且机械可验证的基准，用于测试 extit{LLMs 是否能在深层函数复合下识别符号目标的凸性}。对前沿大模型的实验揭示出明显的组合推理差距：性能随深度迅速下降，从深度2时的F1分数1.0降至深度100时约0.2。对模型推理轨迹的分析显示两种失败模式： extit{解析失败}和 extit{懒惰推理}。为解决这些局限，我们提出一种代理式分治框架，(i) 将解析任务交由外部工具生成抽象语法树（AST），(ii) 对每个中间子表达式强制递归推理并聚焦上下文。该框架有效缓解深层复合失败问题，在大深度下实现显著性能提升（例如深度100时F1分数达1.0）。
原文摘要 · Abstract (English)
Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with convexity. We introduce \cb, a scalable and mechanically verifiable benchmark for testing \textit{whether LLMs can identify the convexity of a symbolic objective under deep functional composition.} Experiments on frontier LLMs reveal a sharp compositional reasoning gap: performance degrades rapidly with increasing depth, dropping from an F1-score of $1.0$ at depth $2$ to approximately $0.2$ at depth $100$. Inspection of models' reasoning traces indicates two failure modes: \textit{parsing failure} and \textit{lazy reasoning}. To address these limitations, we propose an agentic divide-and-conquer framework that (i) offloads parsing to an external tool to construct an abstract syntax tree (AST) and (ii) enforces recursive reasoning over each intermediate sub-expression with focused context. This framework reliably mitigates deep-composition failures, achieving substantial performance improvement at large depths (e.g., F1-Score $= 1.0$ at depth $100$).
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