A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts.

本研究旨在解决大型语言模型在数学推理中表现不足的问题，通过开发一种自动化方法生成高质量的监督数学数据集。该方法结合了大语言模型的直观非正式化优势和数学求解器的精确符号推理能力，生成的数据在实证实验中表现出色，使得LLaMA-2和Mistral在重新对齐后优于现有的同类模型。

神经符号数据生成用于数学推理