MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning

Abstract

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 two new dataset AugGSM8K and AugMATH, by complicating and diversifying the queries and sampling multiple reasoning paths from GSM8K and MATH.We obtained a series of LLMs called MuggleMath by fine-tuning LLaMA models on AugGSM8K and AugMATH. MuggleMath substantially achieves new state-of-the-art on GSM8K and MATH.A log-linear relationship and a segmented log-linear are presented between MuggleMath’s performance and the amount of augmented data on GSM8K and MATH, respectively.We also find that it is weak in out-of-domain math reasoning generalization from AugGSM8K to MATH and from AugMATH to GSM8K, which suggests that augmenting queries that cover a broader range of subjects is more beneficial for generalization.