An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning
This work addresses the challenge of efficiently improving math reasoning in open-source LLMs, though it appears incremental as it builds on existing supervised fine-tuning methods.
The paper tackles the problem of optimizing math reasoning in LLMs by exploring a data strategy that identifies minimal optimal sets of reasoning paths and uses a mix of these sets to cumulatively enhance abilities, achieving state-of-the-art performance on base models with lower construction costs.
Large language models (LLMs) are displaying emergent abilities for math reasoning tasks,and there is a growing attention on enhancing the ability of open-source LLMs through supervised fine-tuning (SFT).In this paper, we aim to explore a general data strategy for supervised data to help optimize and expand math reasoning ability.Firstly, we determine the ability boundary of reasoning paths augmentation by identifying these paths' minimal optimal set.Secondly, we validate that different abilities of the model can be cumulatively enhanced by Mix of Minimal Optimal Sets of corresponding types of data, while our models MMOS achieve SOTA performance on series base models under much lower construction costs.Besides, we point out GSM-HARD is not really hard and today's LLMs no longer lack numerical robustness.Also, we provide an Auto Problem Generator for robustness testing and educational applications.Our code and data are publicly available at https://github.com/cyzhh/MMOS.