Exploring the Mystery of Influential Data for Mathematical Reasoning
Xinzhe Ni Yeyun Gong Zhibin Gou Yelong Shen Yujiu Yang Nan Duan Weizhu Chen
Selecting influential data for fine-tuning on downstream tasks is a key
factor for both performance and computation efficiency. Recent works have shown
that training with only limited data can show a superior performance on general
tasks. However, the feasibility on mathematical reasoning tasks has not been
validated. To go further, there exist two open questions for mathematical
reasoning: how to select influential data and what is an influential data
composition. For the former one, we propose a Quality-aware Diverse Selection
(QaDS) strategy adaptable for mathematical reasoning. A comparison with other
selection strategies validates the superiority of QaDS. For the latter one, we
first enlarge our setting and explore the influential data composition. We
conduct a series of experiments and highlight: scaling up reasoning data, and
training with general data selected by QaDS is helpful. Then, we define our
optimal mixture as OpenMathMix, an influential data mixture with open-source
data selected by QaDS. With OpenMathMix, we achieve a state-of-the-art 48.8%
accuracy on MATH with 7B base model. Additionally, we showcase the use of QaDS
in creating efficient fine-tuning mixtures with various selection ratios, and
analyze the quality of a wide range of open-source datasets, which can perform
as a reference for future works on mathematical reasoning tasks.