Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.

本研究解决了大型语言模型（LLMs）在数学推理中应用受限于计算需求和专有限制的问题。通过创新的填补空白提示（GFP）方法，在解决过程中识别并填补问题空白，从而提高小型语言模型（SLMs）的数学推理能力。实验结果显示，GFP显著提升了SLMs的数学推理能力，具有重要的应用潜力。

填补空白的提示增强代码辅助的数学推理能力