arXiv 2510.257762025-10-27cs.CLcs.LG

StreetMath：大语言模型近似行为研究

StreetMath: Study of LLMs' Approximation Behaviors

LuxMuse AI（LuxMuse人工智能公司）；Department of Electrical and Computer Engineering, North Carolina State University（北卡罗来纳州立大学电气与计算机工程系）；Department of Mathematics, University of Waterloo（滑铁卢大学数学系）；Vokram Group（Vokram集团）；Department of Computer Science, Saint Louis University（圣路易斯大学计算机科学系）

Chiung-Yi Tseng, Somshubhra Roy, Maisha Thasin, Danyang Zhang, Blessing Effiong

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AI总结：

本研究提出StreetMath基准评估LLM的近似推理能力，通过多模型评测与机制可解释性分析发现LLM近似任务中仍倾向精确计算、两类运算依赖不同神经组件，且不具备人类的认知吝啬特征。

摘要：

已有大量文献围绕大语言模型（LLM）的数学推理能力展开研究，尤其关注其在自回归架构下的精确算术运算表现。然而，针对LLM在非正式、快节奏数学运算中的近似推理能力，尤其是非自回归解码器模型的相关能力，研究关注度仍远远不足。为填补这一空白，我们提出了StreetMath基准，用于评估模型在真实近似场景下的近似能力。我们对多种架构的LLM开展了广泛评估，包括Qwen3-4B-Instruct-2507、Qwen3-4B-Thinking-2507、Dream-v0-Instruct-7B、Falcon-Mamba-7B-Instruct以及Mamba-GPT-3B，还运用机制可解释性技术探查模型的内部计算状态。分析显示，即便在需要近似的任务中，LLM通常也会尝试计算精确值或调用外部工具；此外，模型有时会在早期层或步骤就得到正确答案，但求解近似任务时仍会消耗更多token。补充实验表明，精确算术运算和近似算术运算依赖的神经组件大体相互独立。结合认知心理学研究，我们认为在街头数学场景下，LLM并不像人类那样表现出认知吝啬特征。我们已将研究成果开源，地址为https://github.com/ctseng777/StreetMath。

英文摘要：

There is a substantial body of literature examining the mathematical reasoning capabilities of large language models (LLMs), particularly their performance on precise arithmetic operations in autoregressive architectures. However, their ability to perform approximate reasoning in informal, fast-paced mathematical operations has received far less attention, especially among non-autoregressive decoder models. Our work addresses this gap by introducing StreetMath, a benchmark designed to evaluate models' approximation abilities under real-world approximation scenarios. We conduct extensive evaluations across different LLM architectures: Qwen3-4B-Instruct-2507, Qwen3-4B-Thinking-2507, Dream-v0-Instruct-7B, Falcon-Mamba-7B-Instruct, and Mamba-GPT-3B. Furthermore, we apply mechanistic interpretability techniques to probe their internal computational states. Our analysis reveals that LLMs generally attempt to compute exact values or invoke external tools even in tasks that call for approximation. Moreover, while models sometimes reach the correct answer in early layers or steps, they still consume more tokens when solving approximation tasks. Additional experiments indicate that exact and approximate arithmetic operations rely on largely separate neural components. Drawing upon research on cognitive psychology, we argue that LLMs do not exhibit cognitive miserliness in the same way humans do in street math settings. We open source our work https://github.com/ctseng777/StreetMath

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