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home / papers / 2023 / GPT Can Solve Mathematical Problems Without a Calculator

GPT Can Solve Mathematical Problems Without a Calculator

Paper · 2023 · Zhen Yang, Ming Ding, Qingsong Lv et al.

Summary

A common belief holds that LLMs cannot reliably do arithmetic without calling an external calculator, especially multiplying numbers longer than 8 digits or working with decimals and fractions. The authors test this belief with MathGLM, a family of Transformer models trained from scratch (10M to 2B parameters). The models learn from a synthetic arithmetic corpus in which every expression is solved through explicit intermediate steps. Expressions range from a single operation up to nine chained operations and mix integers, decimals, fractions, percentages, negatives, powers and brackets. A curriculum gradually raises difficulty to numbers of up to 12 digits. For word problems, they rewrote the Ape210K answers as stepwise calculations and fine-tuned several GLM backbones on the result. The 2B model nearly solves multi-digit arithmetic and far outperforms GPT-4. The GLM-10B variant roughly matches GPT-4 on Chinese math word problems. The work suggests that much arithmetic weakness comes from training data rather than model architecture.

Key points

  • On complex mixed-operation tests, MathGLM reaches 93.03% accuracy, while GPT-4 scores 18.84%. GPT-4 manages only 4.3% on multi-digit multiplication.
  • The training data spans 1-atomic to 9-atomic operations, and curriculum learning extends operand length to 12 digits.
  • Stepwise reconstruction of Ape210K raises answer accuracy substantially across all backbones:
    • GLM-10B: +42.29%
    • GLM-Large: +37.86%
    • GLM-6B: +47.97%
    • GLM2-6B: +53.96%
    • ChatGLM-6B: +40.65%
    • ChatGLM2-6B: +49.38%
  • The stepwise format causes a small drop in arithmetic accuracy on word problems, which the authors treat as a trade-off for better final answers. Misreading the question is the most frequent error type for MathGLM-GLM-10B.
  • MathGLM-GLM-10B performs close to GPT-4 on a 5,000-item Chinese test set. Code and data are released at github.com/THUDM/MathGLM.

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

🎓Tsinghua UniversityBeijing · China439 works · 94,783 citations🏢Zhipu AIBeijing · China25 works · 2,494 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksArts and Humanities · 17,959 worksLanguage and Linguistics · 17,789 worksComputational Theory and Mathematics · 496 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 4,145 worksReasoning · 1,948 works

Cite

Cite as Zhen Yang, Ming Ding, Qingsong Lv, Zhihuan Jiang, Zehai He, Yuyi Guo, Jinfeng Bai and Jie Tang. 2023. GPT Can Solve Mathematical Problems Without a Calculator. arXiv:2309.03241.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2309.03241 · arXiv 2309.03241

@misc{yang2023gpt,
  title = {{GPT Can Solve Mathematical Problems Without a Calculator}},
  author = {Zhen Yang, Ming Ding, Qingsong Lv, Zhihuan Jiang, Zehai He, Yuyi Guo, Jinfeng Bai and Jie Tang},
  year = {2023},
  doi = {10.48550/arxiv.2309.03241},
  eprint = {2309.03241},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2309.03241}
}

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