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

• URL: http://arxiv.org/abs/2507.04023v2
• Date: Wed, 08 Oct 2025 14:20:50 GMT
• Title: Do LLMs Overthink Basic Math Reasoning? Benchmarking the Accuracy-Efficiency Tradeoff in Language Models
• Authors: Gaurav Srivastava, Aafiya Hussain, Sriram Srinivasan, Xuan Wang,
• Abstract summary: Large language models (LLMs) achieve impressive performance on complex mathematical benchmarks yet sometimes fail on basic math reasoning.<n>This paper focuses on the fundamental tradeoff between accuracy and overthinking.<n>We introduce the Overthinking Score, a harmonic-mean metric combining accuracy and token-efficiency for holistic model evaluation.
• Score: 6.312798900093575
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 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. Our findings reveal: 1) model performance on complex benchmarks does not translate directly to basic math reasoning; 2) reasoning models generate ~18 more tokens while sometimes achieving lower accuracy and exhibit catastrophic collapse when token is constrained, dropping by ~28; 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.

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