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JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models

Paper · 2024 · Kun Zhou, Beichen Zhang, Jiapeng Wang et al.

Summary

Specialised training data improves the mathematical reasoning of LLMs, but current approaches are costly. They either pre-train on huge math corpora or ask very large models such as GPT-4 to generate millions of problems. The authors test whether a relatively small model can be taught to synthesise useful math data cheaply.

They build a compact knowledge distillation set by having GPT-4 write problem–solution pairs from math-related texts. Prompts are tied to education stages and competitions to cover different topics and difficulty levels. Source texts for a second round are chosen by gradient-based influence estimation, which keeps the passages most beneficial for downstream tasks. DeepSeekMath-7B, trained on this set, then generates about 6M problems (4.6B tokens) covering both natural-language and Python tool-use solutions. These are used to pre-train JiuZhang3.0, which is then fine-tuned on open instruction data.

JiuZhang3.0 matches or beats state-of-the-art open models on most of 18 benchmarks, at roughly one-fifth of their estimated cost. This suggests that small distilled synthesisers are a practical route to domain data.

Key points

  • GPT-4 was called only about 9.3k times (9,335 instances). These came from 5,336 randomly sampled texts plus roughly 4k high-value texts picked via gradient similarity.
  • The prompt set covers several settings:
    • Eight natural-language prompts: Grade/Middle/High School, College, AMC 8/10/12 and AIME.
    • Two tool-manipulation prompts: Grade School and Secondary School Competitions.
  • The synthetic corpus has 5,984,584 problems (4.6B tokens). It trains JiuZhang3.0 variants at 7B, 8B and 8×7B scales; the paper mentions Mistral-7B and LLaMA-3-8B bases.
  • Reported results in the natural-language setting:
    • On MATH, JiuZhang3.0-7B scores 52.8 versus 50.2 for DeepSeekMath-7B-RL.
    • On GSM8k, JiuZhang3.0-8×7B scores 89.8 versus 86.4 for MAmmoTH2-8×7B-Plus.
  • Ablations on a 100k-sample setup show the trained synthesiser reaching 32.8 on MATH. Data from ChatGPT, Mixtral-8×7B, DeepSeekMath-RL-7B or LLaMA-3-8B-Instruct scores 26.2–27.2. Code and data are published at github.com/RUCAIBox/JiuZhang3.0.

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

 Fields, topics and concepts

📚 Shelves 7The 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 worksMathematics · 233 worksComputational Theory and Mathematics · 496 worksApplied Mathematics · 73 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,948 works

Cite

Cite as Kun Zhou, Beichen Zhang, Jiapeng Wang, Zhipeng Chen, Wayne Xin Zhao, Jing Sha, Zhichao Sheng, Shijin Wang and Ji-Rong Wen. 2024. JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models. arXiv:2405.14365.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2405.14365 · arXiv 2405.14365

@misc{zhou2024jiuzhang3,
  title = {{JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models}},
  author = {Kun Zhou, Beichen Zhang, Jiapeng Wang, Zhipeng Chen, Wayne Xin Zhao, Jing Sha, Zhichao Sheng, Shijin Wang and Ji-Rong Wen},
  year = {2024},
  doi = {10.48550/arxiv.2405.14365},
  eprint = {2405.14365},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2405.14365}
}

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