用神经符号方法生成高质量数学题，让大模型推理能力大幅提升
Neuro-Symbolic Data Generation for Math Reasoning
- 结合大模型与数学求解器，智能生成多样且有效的数学题
- 在生成数据上微调后，LLaMA-2和Mistral超越现有最优模型
- 适合提升数学推理能力的模型训练与数据构建研究者
大型语言模型（LLMs）在数学推理上的表现不足是其固有缺陷，还是因缺乏高质量数学数据所致？为探究此问题，我们提出一种自动化生成高质量监督数学数据集的方法。该方法通过精心变异现有数学题，确保生成题目的多样性与正确性，采用神经符号框架融合大模型的直观泛化能力与数学求解器的精确符号推理，并结合投影马尔可夫链蒙特卡洛采样处理高度不规则的符号空间。实验证明，所生成数据质量高，使用这些数据微调后的LLaMA-2与Mistral模型性能超越当前最优水平。
原文摘要 · Abstract (English)
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.
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