科学领域的大型语言模型：P vs. NP 研究

Large Language Model for Science: A Study on P vs. NP

September 11, 2023

作者: Qingxiu Dong, Li Dong, Ke Xu, Guangyan Zhou, Yaru Hao, Zhifang Sui, Furu Wei

cs.AI

摘要

在这项工作中，我们使用大型语言模型（LLMs）来增强和加速对P与NP问题的研究，这是理论计算机科学和数学中最重要的悬而未决问题之一。具体而言，我们提出了苏格拉底推理，这是一个促进LLMs深入思考复杂问题解决的通用框架。苏格拉底推理鼓励LLMs递归地发现、解决和整合问题，同时促进自我评估和完善。我们在P与NP问题上的试点研究表明，GPT-4成功地生成了证明框架，并在97个对话轮中进行了严谨推理，得出了“P不等于NP”的结论，与（Xu和Zhou，2023）一致。这项研究揭示了LLMs广泛解空间中的新见解，为科学中的LLMs投下了光芒。

English

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.