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 this https URL

通过识别推理路径的最佳集合来确定推理路径增强的能力边界，通过不同类型的数据的最佳集合的混合来累积增强模型的不同能力，以较低的建设成本实现 SOTA 性能，并提供用于鲁棒性测试和教育应用的自动问题生成器。