Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models

作者：Jiayu Liu, Zhenya Huang, Qi Liu, Zhiyuan Ma, ChengXiang Zhai, Enhong Chen · 发表于：IEEE Transactions on Knowledge and Data Engineering · 年份：2025 · DOI：10.1109/tkde.2025.3556367 · 被引用次数：7 · 研究领域：Intelligent Tutoring Systems and Adaptive Learning、AI-based Problem Solving and Planning、Natural Language Processing Techniques

Math word problem (MWP) serves as a critical milestone for assessing the text mining ability and knowledge mastery level of models. Recent advancements have witnessed large language models (LLMs) showcasing remarkable performance on MWP. However, current LLMs still frequently exhibit logical errors, which highlights their inability to fully grasp the knowledge required for genuine step-by-step mathematical reasoning. To this end, in this paper, we propose a novel Knowledge-guided Solver (KNOS) framework that empowers LLMs to simulate human mathematical reasoning, whose core idea is toInvoke-Verify-Injectnecessary knowledge to solve MWP. We draw inspiration from the dual-process theory to construct two cooperative systems: aKnowledge Systemand anInference System. Specifically, theKnowledge Systememploys LLMs as the knowledge base and develops a novelknowledge invokerthat can elicit their relevant knowledge to support the strict step-level mathematical reasoning. In theInference System, we propose aknowledge verifierand aknowledge injectorto evaluate the knowledge rationality and further guide the step-wise symbolic deduction in an interpretable manner based on human cognitive mechanism, respectively. Moreover, to tackle the potential scarcity issue of mathematics-specific knowledge in LLMs, we consider an open-book exam scenario and propose an improved version of KNOS called EKNOS. In EKNOS, we meticulously designknowledge selectorsto extract the most relevant commonsense and ...