SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation

SenseMath contains 4,800 Apply items across eight number-sense categories and four nominal digit-scale conditions, with strong, weak, and control variants. The paper's Judge setting contains exactly J1 shortcut appropriateness and J2 strategy identification. Current data version: paper-aligned-v1.

Files and Task Definitions

File	Task	Records
data/sensemath_v2_d2.json	Apply, d2	400 families / 1,200 items
data/sensemath_v2_d4.json	Apply, d4	400 families / 1,200 items
data/sensemath_v2_d8.json	Apply, d8	400 families / 1,200 items
data/sensemath_v2_d16.json	Apply, d16	400 families / 1,200 items
data/judge_j1.json	J1: is a shortcut appropriate? YES / NO	300 items
data/judge_j2.json	J2: classify a supplied solution as SHORTCUT / COMPUTATION	80 items
data/subsets/judge_j1_paper_filtered_261.json	Separate J1 reporting subset	261 of the 300 J1 items

The full J1 and filtered J1 profiles are reported separately in the paper. Do not pool their scores or add the subset to the total item count. J2 has 54 SHORTCUT and 26 COMPUTATION labels. Task identity must be determined from the manifest and task_type, not from a filename in an earlier revision.

data/manifest.json records task identities, counts, and SHA256 hashes. The GitHub repository uses the same data filenames under benchmark/ rather than data/. Questions, options, prompts and reference labels are retained from their source sets; this version alignment is not a new model evaluation or a semantic revalidation of every strategy label.

Usage

Read original JSON with Python to preserve large integer values exactly:

import json
from pathlib import Path

families = json.loads(Path("data/sensemath_v2_d4.json").read_bytes())
j1 = json.loads(Path("data/judge_j1.json").read_bytes())
j2 = json.loads(Path("data/judge_j2.json").read_bytes())

The named configurations above separate the different schemas; do not combine all JSON files into a single task. For exact arithmetic, original JSON integers are authoritative rather than any floating-point conversion by downstream tools.

Use the GitHub Judge runner with --step validate to verify hashes and task types. J1 defaults to the 300-item profile; select --j1-profile paper-filtered for the 261-item subset. The runner accepts an HF checkout via --data-dir /path/to/data.

中文说明

本版本严格对应论文的 J1、J2：J1 判断捷径是否适用，J2 判断给定解法属于捷径还是逐步计算。J1 全量 300 题与论文筛选 261 题分别使用，不能混算。完整说明见 数据版本与使用口径。

Citation

@article{zhuang2026sensemath,
  title={SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation},
  author={Zhuang, Haomin and Wang, Xiangqi and Shen, Yili and Cheng, Ying and Zhang, Xiangliang},
  journal={arXiv preprint arXiv:2604.01988},
  year={2026}
}

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