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Self-Error-Instruct: Generalizing from Errors for LLMs Mathematical Reasoning

Paper · 2025 · Erxin Yu, Jing Li, Ming Liao et al.

Summary

LLMs still make many mistakes on math problems. Earlier error-driven methods build new training data from single failed examples, so the data tends to stay tied to those instances. Self-Error-Instruct (SEI) instead groups failures by error type. First, a target model is run on the GSM8K and MATH training sets to collect its wrong answers. GPT-4o, acting as the instructor, labels each failure with an error keyphrase, and these keyphrases are clustered into error categories. For each category, a few bad cases are sampled as seeds, and GPT-4o generates new problems in a self-instruct fashion. A one-shot-learning filter keeps only examples that help the model fix its bad cases without breaking its existing correct answers. The selected data is used to fine-tune the target model, and the cycle repeats. Gains appear on both in-domain and out-of-domain benchmarks. This suggests that targeting categories of weakness, rather than individual errors, gives more transferable supervision for math reasoning.

Key points

  • Models and benchmarks:
    • Target models are LLaMA3-8B-Instruct, Qwen2.5-Math-7B and Mathstral-7B-v0.1; GPT-4o is the instructor.
    • In-domain evaluation uses the GSM8K and MATH test sets; out-of-domain evaluation uses TAL, GaoKao, SAT and College.
  • Average gains: about 1.72% for LLaMA3, 24.94% for Qwen2.5 and 0.98% for Mathstral.
  • Data selection: the one-shot selector beats random selection, the gradient-based LESS method, and training on all synthesized data. Only the top 5% is kept each round.
  • Qwen2.5-Math over iterations:
    • The bad-case fix rate reached roughly 39% on GSM8K and 41% on MATH.
    • Test scores rose from 55.50 to 87.79 on GSM8K and from 32.32 to 59.18 on MATH.
    • Retraining once from scratch on all accumulated data beat continued iterative fine-tuning.
  • Limitations: GPT-4o is costly, and errors are mined only from GSM8K and MATH. The one-shot filter is compute-heavy, since it scores about 30,000 samples against a 100-example validation set. Code is available at github.com/ErxinYu/SEI.

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

🎓Chinese University of Hong KongHong Kong · China126 works · 14,073 citations🏢Huawei TechnologiesShenzhen · China75 works · 12,975 citations🎓Hong Kong Polytechnic UniversityHong Kong · China84 works · 4,956 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksComputational Theory and Mathematics · 252 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 3,320 worksReasoning · 1,426 works

Cite

Cite as Erxin Yu, Jing Li, Ming Liao, Qi Zhu, Boyang Xue, Minghui Xu, Baojun Wang, Lanqing Hong, Fei Mi and Lifeng Shang. 2025. Self-Error-Instruct: Generalizing from Errors for LLMs Mathematical Reasoning. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.acl-long.417

@inproceedings{yu2025self,
  title = {{Self-Error-Instruct: Generalizing from Errors for LLMs Mathematical Reasoning}},
  author = {Erxin Yu, Jing Li, Ming Liao, Qi Zhu, Boyang Xue, Minghui Xu, Baojun Wang, Lanqing Hong, Fei Mi and Lifeng Shang},
  booktitle = {Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.acl-long.417},
  url = {https://doi.org/10.18653/v1/2025.acl-long.417}
}

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