[Short] Max It or Miss It: Benchmarking LLM On Solving Extremal Problems

Binxin Gao, Jingjun Han

Keywords: AI for Math; Benchmark dataset

TL;DR: We propose a way to create dataset for benchmarking foundation model's capability of solving extremal problems.

Abstract:

Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the specific sources and mechanisms underlying these reasoning capabilities remain insufficiently understood. Optimization reasoning, $\textit{i.e.}$ finding extrema under constraints, represents a fundamental abstraction that underpins critical applications in planning, control, resource allocation, and prompt search. To systematically evaluate this capability, we introduce $\texttt{\textbf{ExtremBench}}$, a benchmark dataset for solving mathematical extremal problems, curated from inequality exercises used for Chinese Mathematical Olympiad and transformed into $93$ standardized extrema-finding problems. We conduct extensive evaluations across various state-of-the-art open-source model families, including the Qwen3, GPT-OSS, and DeepSeek. Our results reveal that LLMs' extremal-solving reasoning capabilities do not always align with those of current mathematical benchmarks such as AIME25, with some models showing strong general mathematical reasoning but poor extremal-solving skills, and vice versa. This discrepancy highlights a critical gap in current evaluation practices and suggests that existing benchmarks may not comprehensively capture the full spectrum of mathematical reasoning abilities.
Our code and dataset will be available upon acceptance.

Email Sharing: We authorize the sharing of all author emails with Program Chairs.

Data Release: We authorize the release of our submission and author names to the public in the event of acceptance.

Submission Number: 3