Max It or Miss It: Benchmarking LLM On Solving Extremal Problems
This work addresses the problem of insufficient understanding of LLMs' reasoning mechanisms for optimization tasks, which is critical for applications like planning and resource allocation, but it is incremental as it focuses on benchmarking rather than novel methods.
The authors introduced ExtremBench, a benchmark of 93 extremal problems from Chinese Mathematical Olympiad, to evaluate LLMs' optimization reasoning, finding that performance on this benchmark does not align with existing mathematical benchmarks, revealing a gap in evaluation practices.
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, 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 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 and MATH-500, 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.