  In this paper, we investigate the underlying factors that potentially enhance
the mathematical reasoning capabilities of large language models (LLMs). We
argue that the data scaling law for math reasoning capabilities in modern LLMs
is far from being saturated, highlighting how the model's quality improves with
increases in data quantity. To support this claim, we introduce the
Skywork-Math model series, supervised fine-tuned (SFT) on common 7B LLMs using
our proposed 2.5M-instance Skywork-MathQA dataset. Skywork-Math 7B has achieved
impressive accuracies of 51.2% on the competition-level MATH benchmark and
83.9% on the GSM8K benchmark using only SFT data, outperforming an early
version of GPT-4 on MATH. The superior performance of Skywork-Math models
contributes to our novel two-stage data synthesis and model SFT pipelines,
which include three different augmentation methods and a diverse seed problem
set, ensuring both the quantity and quality of Skywork-MathQA dataset across
varying difficulty levels. Most importantly, we provide several practical
takeaways to enhance math reasoning abilities in LLMs for both research and
industry applications.
