Query and Response Augmentation Cannot Help Out-of-domain Math Reasoning Generalization

Chengpeng Li, Zheng Yuan, Hongyi Yuan, Guanting Dong, Keming Lu, Jiancan Wu, Chuanqi Tan, Xiang Wang, Chang Zhou

Keywords: Large Language Model; Math Reasoning; Data augmentation; Scaling relationship; Generalizability

TL;DR: This paper analyzes the scaling relationship and generalization of data augmentation in mathematical reasoning with large language models.

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 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.

Primary Area: representation learning for computer vision, audio, language, and other modalities

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Submission Number: 4983