Recent work has shown the immense potential of synthetically generated
datasets for training large language models (LLMs), especially for acquiring
targeted skills. Current large-scale math instruction tuning datasets such as
MetaMathQA (Yu et al., 2024) and MAmmoTH (Yue et al., 2024) are constructed
using outputs from closed-source LLMs with commercially restrictive licenses. A
key reason limiting the use of open-source LLMs in these data generation
pipelines has been the wide gap between the mathematical skills of the best
closed-source LLMs, such as GPT-4, and the best open-source LLMs. Building on
the recent progress in open-source LLMs, our proposed prompting novelty, and
some brute-force scaling, we construct OpenMathInstruct-1, a math instruction
tuning dataset with 1.8M problem-solution pairs. The dataset is constructed by
synthesizing code-interpreter solutions for GSM8K and MATH, two popular math
reasoning benchmarks, using the recently released and permissively licensed
Mixtral model. Our best model, OpenMath-CodeLlama-70B, trained on a subset of
OpenMathInstruct-1, achieves a score of 84.6% on GSM8K and 50.7% on MATH, which
is competitive with the best gpt-distilled models. We release our code, models,
and the OpenMathInstruct-1 dataset under a commercially permissive license.

利用合成数据集训练大型语言模型（LLMs）的巨大潜力已被展示，尤其是用于获得有针对性的技能。本研究基于开源 LLMs 的最新进展和引导创新，通过某些粗暴的扩展构建了一个包含 180 万个问题 - 解决方案对的数学指导调整数据集 OpenMathInstruct-1，并在 GSM8K 和 MATH 两个热门数学推理基准上取得了与最佳 gpt - 蒸馏模型相竞争的成绩。我们以商业许可证发布了我们的代码、模型和 OpenMathInstruct-1 数据集。