In math reasoning with large language models (LLMs), fine-tuning data
augmentation by query evolution and diverse reasoning paths is empirically
verified effective, profoundly narrowing the gap between open-sourced LLMs and
cutting-edge proprietary LLMs. In this paper, we conduct an investigation for
such data augmentation in math reasoning and are intended to answer: (1) What
strategies of data augmentation are more effective; (2) What is the scaling
relationship between the amount of augmented data and model performance; and
(3) Can data augmentation incentivize generalization to out-of-domain
mathematical reasoning tasks? To this end, we create a new dataset, AugGSM8K,
by complicating and diversifying the queries from GSM8K and sampling multiple
reasoning paths. We obtained a series of LLMs called MuggleMath by fine-tuning
on subsets of AugGSM8K. MuggleMath substantially achieves new state-of-the-art
on GSM8K (from 54% to 68.4% at the scale of 7B, and from 63.9% to 74.0% at the
scale of 13B). A log-linear relationship is presented between MuggleMath's
performance and the amount of augmented data. We also find that MuggleMath is
weak in out-of-domain math reasoning generalization to MATH. This is attributed
to the differences in query distribution between AugGSM8K and MATH which
suggest that augmentation on a single benchmark could not help with overall
math reasoning performance. Codes and AugGSM8K will be uploaded to
this https URL

通过问题演化和多样化推理路径的数据增强，我们验证了用于大型语言模型（LLMs）的数学推理的有效性，并深入缩小开源 LLMs 与尖端专有 LLMs 之间的差距。我们创建了一个名为 AugGSM8K 的新数据集，并使用 AugGSM8K 的子集对 MuggleMath 进行微调，实现了 GSM8K 的新的最先进水平（从 7B 规模下的 54% 到 68.4%，从 13B 规模下的 63.9% 到 74.0%）。我们也发现 MuggleMath 在 MATH 的领域外数学推理泛化方面存在困难，这归因于 AugGSM8K 和 MATH 之间问题分布的差异，暗示在单一基准上的增强无助于整体数学推理性能。