Large language models (LLMs) have shown increasing proficiency in solving mathematical reasoning problems. However, many current open-source LLMs often still make calculation and semantic understanding errors in their intermediate reasoning steps. In this work, we propose PROVE, a simple yet effective framework that uses program-based verification as a heuristic to filter out potentially incorrect reasoning paths before aggregating the final answers. Instead of relying on vanilla majority voting, our approach rejects solutions whose corresponding program outputs are inconsistent with the generated solution, aggregating only those validated by Python programs. We conducted extensive experiments on 13 open-source LLMs from various model families and sizes, ranging from 0.5B to 13B parameters, across seven math benchmarks. We demonstrate that PROVE consistently outperforms vanilla majority voting as a heuristic for solving mathematical reasoning tasks across all datasets and model sizes. Notably, PROVE increases accuracy on the GSM8K benchmark from 48.85% to 53.83% for Qwen2-0.5B-Instruct, from 65.66% to 73.01% for Llama-3.2-1B-Instruct, from 73.39% to 79.61% for Gemma-2-2b-it, and from 41.32% to 59.51% for Llama-2-7B-chat. Our codes are available at https://github.com/declare-lab/prove.

本研究针对当前大语言模型在数学推理过程中常见的计算和语义理解错误问题，提出了PROVE框架，通过程序为基础的验证方法过滤潜在的不正确推理路径。实验结果表明，PROVE在多项数学基准测试中显著提高了模型的准确性，体现了其作为数学推理任务有效启发式工具的潜力。

并非所有投票都有效！程序验证提升语言模型在数学推理中的自一致性