arXiv:2507.04023cs.CL2025-07中稿 · ACL

测试大模型在基础数学题上的过拟合现象,发现越想越错。

Do LLMs Overthink Basic Math Reasoning? Benchmarking the Accuracy-Efficiency Tradeoff in Language Models

  • 设计新评测框架,量化模型准确率与冗余输出的权衡
  • 53个模型实测显示,推理越长反而准确率下降,最高降36%
  • 揭示长推理不等于好结果,适合关注效率的开发者参考

大型语言模型(LLMs)在复杂数学任务上表现优异,但在基础数学推理中常出错且生成冗长回答。本文提出LLMThinkBench,系统评估模型推理效率,聚焦准确率与冗余之间的权衡。首先形式化准确率-冗长度权衡;其次引入综合准确率与词元效率的调和均值指标——过思考得分;第三,构建涵盖14项基础数学任务的动态数据评估协议;第四,大规模实测53个模型,包括推理与量化版本,在不同推理预算下的表现;第五,开源代码包与公开排行榜以确保可复现性。研究发现:1)复杂任务表现无法直接迁移至基础数学;2)推理模型生成约18倍更多词元,准确率反而更低,约束词元时准确率最高下降约36%;3)准确率随推理预算增加呈非单调变化,扩展推理预算收益递减(如GPT-5/o系列模型从低到高推理努力无准确率提升)。结果挑战了‘更长推理必然更好’的假设。公开排行榜见https://ctrl-gaurav.github.io/LLMThinkBench/,代码包可在https://pypi.org/project/llmthinkbench/ 获取,完整代码库位于https://github.com/ctrl-gaurav/LLMThinkBench。

原文摘要 · Abstract (English)

Large language models (LLMs) achieve impressive performance on complex mathematical benchmarks yet sometimes fail on basic math reasoning while generating unnecessarily verbose responses. In this paper, we present LLMThinkBench, a systematic benchmark and comprehensive empirical study to evaluate the efficiency of reasoning in LLMs, focusing on the fundamental tradeoff between accuracy and overthinking. First, we formalize the accuracy-verbosity tradeoff. Second, we introduce the Overthinking Score, a harmonic-mean metric combining accuracy and token-efficiency for holistic model evaluation. Third, we establish an evaluation protocol with dynamically-generated data across 14 basic math tasks. Fourth, we conduct a large-scale empirical study evaluating 53 LLMs, including reasoning and quantized variants across different reasoning budgets. Fifth, we release LLMThinkBench as an open-source Python package and public leaderboard for reproducibility. Our findings reveal: 1) model performance on complex benchmarks does not translate directly to basic math reasoning; 2) reasoning models generate ~18x more tokens while sometimes achieving lower accuracy and exhibit catastrophic collapse when tokens are constrained, dropping by up to ~36%; 3) the accuracy-verbosity relationship is non-monotonic with extended reasoning budgets yielding diminishing returns (GPT-5/o-series models show zero accuracy gain from low -> medium -> high reasoning effort). Our findings challenge the assumption that longer reasoning in LLMs necessarily improves mathematical reasoning. Our public leaderboard is available at https://ctrl-gaurav.github.io/LLMThinkBench/. Our open-source Python package is available at https://pypi.org/project/llmthinkbench/, and the codebase can be found at https://github.com/ctrl-gaurav/LLMThinkBench for easy and reproducible evaluation.

大模型评测数学推理效率优化

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