Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often cannot generalize the reasoning pattern to out-of-distribution test cases. In this work, we propose a hybrid system capable of solving arithmetic problems that require compositional and systematic reasoning over sequences of symbols. The model acquires such a skill by learning appropriate substitution rules, which are applied iteratively to the input string until the expression is completely resolved. We show that the proposed system can accurately solve nested arithmetical expressions even when trained only on a subset including the simplest cases, significantly outperforming both a sequence-to-sequence model trained end-to-end and a state-of-the-art large language model.

翻译：解决需要组合性和系统性的符号推理问题被视为人类智能的关键要素之一。然而，符号推理对深度学习模型而言仍是一大挑战，这类模型往往无法将推理模式泛化至分布外的测试案例。本研究提出一种混合系统，能够解决需要对符号序列进行组合性与系统性推理的算术问题。该模型通过学习适当的替代规则来获得此类技能，这些规则被迭代应用于输入字符串，直至表达式完全解析。我们证明，即便仅在包含最简单情况的子集上训练，所提出的系统也能准确求解嵌套算术表达式，其表现显著优于端到端训练的序列到序列模型以及当前最先进的大型语言模型。