SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation
This work addresses the problem of evaluating and understanding the limitations of LLMs in numerical reasoning for AI researchers and developers, highlighting incremental insights into model behavior without proposing new methods.
The paper tackled the question of whether large language models (LLMs) exhibit human-like number sense by evaluating their ability to recognize numerical structure, apply shortcuts appropriately, and avoid them when misleading, using the SenseMath benchmark. The results showed that while models can achieve up to 15% accuracy gains when explicitly prompted to use shortcuts, they spontaneously employ them in fewer than 40% of cases under standard prompting and fail to judge applicability or generate valid shortcut-bearing problems.
Large language models often default to step-by-step computation even when efficient numerical shortcuts are available. This raises a basic question: do they exhibit number sense in a human-like behavioral sense, i.e., the ability to recognize numerical structure, apply shortcuts when appropriate, and avoid them when they are not? We introduce SenseMath, a controlled benchmark for evaluating structure-sensitive numerical reasoning in LLMs. SenseMath contains 4,800 items spanning eight shortcut categories and four digit scales, with matched strong-shortcut, weak-shortcut, and control variants. It supports three evaluation settings of increasing cognitive demand: Shortcut Use (whether models can apply shortcuts on shortcut-amenable problems); Applicability Judgment (whether they can recognize when a shortcut is appropriate or misleading); and Problem Generation (whether they can generate new problem items that correctly admit a given type of shortcut). Our evaluation across five LLMs, ranging from GPT-4o-mini to Llama-3.1-8B, shows a consistent pattern: when explicitly prompted, models readily adopt shortcut strategies and achieve substantial accuracy gains on shortcut-amenable items (up to 15%), yet under standard chain-of-thought prompting they spontaneously employ such strategies in fewer than 40% of cases, even when they demonstrably possess the requisite capability. Moreover, this competence is confined to the Use level; models systematically over-generalise shortcuts to problems where they do not apply, and fail to generate valid shortcut-bearing problems from scratch. Together, these results suggest that current LLMs exhibit procedural shortcut fluency without the structural understanding of when and why shortcuts work that underlies human number sense.