Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization of the transitions through intermediate solution steps to the goal state. We find that models that are supplied with such sequences as prompts can solve tasks with a significantly higher accuracy, and models that are trained to produce such sequences solve problems better than those that are trained with previously used human-generated sequences and other baselines. Our work thus takes several steps toward elucidating and improving how language models perform on tasks requiring multi-step mathematical reasoning.

翻译：大型语言模型最近显示,在数学推理方面,在与人类产生的序列进行微调时,在数学推理方面出现了有希望的进展。然而,解决方案序列没有正式结构,因此产生的模型序列可能无法反映我们期望专家人类能够产生的系统推理。在本文中,我们研究如何利用关系抽象概念在语言模型中建立更强的推理能力。我们引入了新型序列,更明确地通过向目标状态过渡的中间解决方案步骤提供抽象特征描述。我们发现,提供诸如提示等序列的模型能够以远为更精确的方式解决任务,而经过培训能够产生这些序列的模型则能够解决比以前使用人类生成序列和其他基线所培训的问题更好的问题。因此,我们的工作采取若干步骤,以阐明和改进语言模型如何执行需要多步数学推理的任务。