Solving Math Word Problems via Cooperative Reasoning induced Language Models

Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics Volume 1: Long Papers, pages 4471–4485 July 9-14, 2023 ©2023 Association for Computational Linguistics Solving Math Word Problems via Cooperative Reasoning induced Language Models Xinyu Zhu♢∗ Junjie Wang♠∗ Lin Zhang♡ Yuxiang Zhang♠ Yongfeng Huang♣ Ruyi Gan♡ Jiaxing Zhang♡ Yujiu Yang♢† ♢Tsinghua University ♠Waseda University ♡IDEA ♣The Chinese University of Hong Kong zhuxy21@mails.tsinghua.edu.cn yang.yujiu@sz.tsinghua.edu.cn wjj1020181822@toki.waseda.jp joel0495@asagi.waseda.jp {zhanglin, ganruyi, zhangjiaxing}@idea.edu.cn Abstract Large-scale pre-trained language models (PLMs) bring new opportunities to challeng- ing 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 re- liable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent im- provement over state-of-the-art methods, up to 9.6% increase over best baselines.1 1 Introduction Addressing math problems is a hallmark of human intelligence, which allows reasoning and adapting from limited data. We want neural models to be able to do the same, however, quick and flexible reasoning is challenging to current neural models as they must possess a certain level of prior expe- rience from a limited amount of new data while avoiding overfitting. The rapid growth of large- scale Pre-trained Language Models (PLMs) offers *Equal contribution. †Corresponding Author. 1Our codes are available at https://github.com/ TianHongZXY/CoRe (a) Prompt-based Methods (zero-shot/few-shot) Prompt Large-scale PLMs Reasoning Path Reasoning Path … Answer (b) Dual Process Theory (System 1&2) (few-shot/finetuning) Chain-of-Thought: 1 path; Self-consistency: multiple paths. Large-scale PLMs Prompt If few-shot: Reasoning Path Reasoning Path … Rules / Verifiers Answer (c) CoRe (ours) (zero-shot) Generators Verifiers Data Cooperative Training Cooperative Inference Self-Thinking Unseen datasets Figure 1: Comparing our CoRe with popular methods in mathematical logic reasoning tasks. unprecedented potential for this issue, often rely- ing on well-designed trigger prompts (Wei et al., 2022c; Li et al., 2022; Brown et al., 2020). Al- though appealing in terms of efficiency, its success relies on memorizing patterns with a sufficiently large number of parameters (≥ 100 billion) (Wei et al., 2022b), differentiating it from the fast adap- tivity in the human reasoning process. Active disciplines like neuroscience and cogni- tive science attempt to uncover the mechanism of human reasoning, and agree that our learning pro- cess is governed by an interaction mechanism, of- ten referred to as System 1 and System 2 (Evans, 2003; Kahneman, 2011). …

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