探究大语言模型在数学推理中的组合性缺陷
Exploring the Compositional Deficiency of Large Language Models in Mathematical Reasoning
AI总结：
本研究构建含逻辑陷阱的MathTrap数据集，发现LLMs虽具备所需知识却无法自发组合以处理数学推理中的新案例，并验证了提示、微调及类人“慢思考”可部分缓解此组合性缺陷。
摘要：
人类认知展现出系统性的组合性，即从有限已学组件生成无限新组合的代数能力，这是理解与推理复杂逻辑的关键。在本研究中，我们探讨大语言模型（LLMs）在数学推理中的组合性。具体而言，我们通过在MATH和GSM8K的问题描述中引入精心设计的逻辑陷阱，构建了一个新数据集\ extsc{MathTrap}。由于现实世界中存在逻辑缺陷的问题相当罕见，这些对LLMs而言属于“未见过”的案例。解决这些问题需要模型系统性地组合（1）原始问题涉及的数学知识与（2）与引入陷阱相关的知识。我们的实验表明，尽管LLMs具备这两部分所需知识，但它们不会自发地将其结合起来以处理这些新案例。我们探索了多种缓解该缺陷的方法，如自然语言提示、少样本演示和微调。此外，我们测试了最近发布的OpenAI o1模型，发现类人的“慢思考”有助于提升LLMs的组合性。总体而言，系统性组合性对大语言模型仍是一个开放挑战。
英文摘要：
Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset \textsc{MathTrap} by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent "unseen" cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not \textbf{spontaneously} combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. Additionally, we test the recently released OpenAI o1 model and find that human-like `slow thinking' helps improve the compositionality of LLMs. Overall, systematic compositionality remains an open challenge for large language models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
