ConvexBench: Can LLMs Recognize Convex Functions?

• URL: http://arxiv.org/abs/2602.01075v2
• Date: Wed, 04 Feb 2026 08:09:18 GMT
• Title: ConvexBench: Can LLMs Recognize Convex Functions?
• Authors: Yepeng Liu, Yu Huang, Yu-Xiang Wang, Yingbin Liang, Yuheng Bu,
• Abstract summary: Convex analysis is a modern branch of mathematics with many applications.<n>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.<n>We introduce cb, a scalable and mechanically verifiable benchmark for testing textitwhether LLMs can identify the convexity of a symbolic objective under deep functional composition.
• Score: 70.53167848190624
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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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