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home / papers / 2026 / GSM-Noise: Exploring and Enhancing Large Language Models' Reasoning under Noisy Inputs

GSM-Noise: Exploring and Enhancing Large Language Models' Reasoning under Noisy Inputs

Paper · 2026 · Zhengxin Zhang, Chengyu Huang, Xufu Liu et al.

Summary

LLMs that score well on clean math benchmarks often fail when real users send messy prompts. The authors first examined long English prompts from WildChat-1M, using QwQ-32B as a checker. Grammar slips, symbol errors, misordered statements and irrelevant content were all common, and longer prompts contained more of them. They then built GSM-Noise, a benchmark derived from GSM8K and R-GSM. Its templates can generate many variants that mix several kinds of noise at controllable difficulty levels.

Tests on LLaMA3, Qwen2.5, Claude and ChatGPT models showed accuracy drops of roughly 5–25% under noise. Closed-source and long-CoT models held up best. As a remedy, the authors have the model first rewrite the problem into a cleaner form and only then reason step by step. They teach this "refine before CoT" behavior through prompt engineering, SFT and RL, and all three improve robustness. The work matters because it shows that an explicit cleanup step, which lowers input entropy, makes reasoning more reliable on realistic inputs.

Key points

  • GSM-Noise contains 220 math problem templates with four kinds of noise: statement shuffling, injected irrelevant information, symbol errors and grammatical errors. The highest difficulty setting is Level 5.
  • Refinement improved results by 2–12% under PE, while SFT yielded 4–13% and RL yielded 3–25%.
  • On Level 5, SFT followed by RL lifted LLaMA3.2-1B from 1.36% to 13.00% and LLaMA3.2-3B from 12.50% to 48.41%. Qwen2.5-7B reached the best accuracy at 65.21%.
  • In the ablation, post-training without the refinement step cost about 6 accuracy points, roughly a 16% relative drop.
  • Refined problems had much lower perplexity than the noisy originals:
    • LLaMA3.2-3B: 67.15 → 10.33 after SFT, 14.17 after RL.
    • Qwen2.5-3B: 62.00 → 10.69 after SFT, 36.64 after RL.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Cornell UniversityIthaca · United States134 works · 65,159 citations🎓Pennsylvania State UniversityState College · United States67 works · 5,865 citations🔬Peng Cheng LaboratoryShenzhen · China47 works · 2,699 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 3,894 worksReasoning · 1,685 works

Cite

Cite as Zhengxin Zhang, Chengyu Huang, Xufu Liu, Dan Zhao, Jinyan Su and Claire Cardie. 2026. GSM-Noise: Exploring and Enhancing Large Language Models' Reasoning under Noisy Inputs. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.findings-acl.1748

@inproceedings{zhang2026gsm,
  title = {{GSM-Noise: Exploring and Enhancing Large Language Models' Reasoning under Noisy Inputs}},
  author = {Zhengxin Zhang, Chengyu Huang, Xufu Liu, Dan Zhao, Jinyan Su and Claire Cardie},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1748},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1748}
}

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