Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

本研究针对大型语言模型在解决数学问题时的性能不足，提出了一种新颖的方法BEATS，该方法通过设计新的提示引导模型迭代重写并基于前一步生成答案，同时引入反向验证技术检查答案的正确性。此外，采用剪枝树搜索优化搜索时间，显著提升了Qwen2-7b-Instruct在MATH基准测试中的分数。该方法为改善LLMs数学能力提供了有效的解决方案。

BEATS：通过反向验证和自适应歧义消解的高效树搜索优化大型语言模型的数学能力