Solving Math Word Problems via Cooperative Reasoning induced Language Models
Xinyu Zhu♢♢\diamondsuit♢111Equal contribution. Junjie Wang♠♠\spadesuit♠111Equal contribution. Lin Zhang♡♡\heartsuit♡ Yuxiang Zhang♠♠\spadesuit♠ Ruyi Gan♡normal-♡\heartsuit♡ Jiaxing Zhang♡normal-♡\heartsuit♡ Yujiu Yang♢normal-♢\diamondsuit♢222Corresponding Author. ♢♢\diamondsuit♢Tsinghua University ♠♠\spadesuit♠Waseda University ♡♡\heartsuit♡International Digital Economy Academy {zhanglin, ganruyi,
Abstract
Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to $9.6\%$ increase over best baselines.111Our codes are available at https:
中文速览
数学应用题(Math Word Problems)对机器来说很难，因为模型在生成解题过程时缺乏有效的监督反馈，容易走偏。受认知科学中"双系统"理论启发——人类用系统1快速直觉反应、用系统2深思熟虑验证——研究者提出了协作推理框架CoRe，将语言模型拆分为"生成器（系统1）"和"验证器（系统2）"两个角色：生成器负责产生推理路径，两个验证器（分别在词级和句级）则通过蒙特卡洛树搜索（MCTS）在生成过程中实时打分反馈，引导生成器朝更可靠的推理路径收敛。此外，框架还引入"自我思考"机制，用高质量的自生成数据迭代微调模型，进一步提升泛化能力。在多个数学推理数据集上的实验表明，CoRe相比最优基线最高提升9.6%，且所用模型规模（约12B参数）远小于对比的百亿乃至千亿参数大模型，说明引入结构化验证反馈比单纯堆参数更为高效。
原文 arXiv:2210.16257;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2210.16257v5