基于大模型使用方程双重验证提示的数学问题求解  

Double validation and rectification progressive prompt for equations in math word problem based on large language model

作　　者：张颖霖 刘昌辉[1] 黄淑芬 Zhang Yinglin;Liu Changhui;Huang Shufen(School of Computer Science&Engineering,Wuhan Institute of Technology,Wuhan 430205,China)

机构地区：[1]武汉工程大学计算机科学与工程学院,武汉430205

出　　处：《计算机应用研究》2024年第12期3729-3734,共6页Application Research of Computers

摘　　要：尽管使用思维链(chain of thought,CoT)的大模型(large language model,LLM)在单未知数的数学问题求解(math word problem,MWP)任务上取得了显著成果。但是,目前的研究缺乏适用于方程数学问题的方法。由于数学问题求解对推理步骤具有很高的敏感性,列方程出错会导致后续步骤连环出错,所以提出一种渐近式验证纠正的方法2ERP,一边验证一边纠正步骤错误,输出最有可能的正确答案。在验证环节使用等式和答案的双重验证,回代答案到等式确保计算的正确,从数学表达式获取数值关系来验证等式的正确性。在纠正流程中,根据回代的结果和双重验证的一致性排除错误的推理路径,逼近正确结果。与其他CoT方法相比,2ERP方法在6个数据集上均取得了性能上的提升,平均准确率达到了66.2%,尤其是方程问题的数据集上,平均提高了6.9百分点。2ERP方法是一种设计提示的零样本方法,通过多次迭代提高数学问题的准确率,并输出具有详细步骤的求解过程,该方法在方程问题上的提升更加明显。Although large language model using CoT method has achieved remarkable results in solving math word problem(MWP)with one unknown,there is currently a lack of methodology that is applicable to MWP involving equations.Equation problems are highly sensitive to the reasoning step,and an error in the equation-laying step can lead to a cascade of errors in subsequent steps.Therefore,this paper proposed a progressive prompt method called 2ERP,which rectified incorrect reasoning paths after validation and output the most likely answer.During the validation module,it substituted the answer back into the equation to ensure the accuracy of the calculation.Then,the method obtained numerical relationships from the mathematical expression to verify the equation.The rectification process approximated the correct result by eliminating incorrect reasoning paths based on the consistency of the double validation.2ERP method outperformed other CoT methods,achieving an ave-rage accuracy of 66.2%on six datasets.Notably,it achieved an average improvement of 6.9%on equation problems.In conclusion,2ERP method is a prompt-based zero-shot method,which improves the accuracy of MWP through multiple iterations and outputs a solving process with detailed steps.This method has a more significant improvement in equation problems.

关 键 词：数学问题求解 思维链 大语言模型 零样本 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]