Large-scale pre-trained language models (PLMs) bring new opportunities to
challenge 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 9.8% increase over best
baselines.

本文提出了合作推理的预训练语言模型 (CoRe)，以类人的推理框架，即系统 1 为生成器，系统 2 为验证器的方式解决数学单词问题，通过几个数学推理数据集的评估，相比于最佳基线方法，取得了相当的改进。