科學的大型語言模型：對P vs. NP的研究

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

在這項工作中，我們使用大型語言模型（LLMs）來擴充和加速對P與NP問題的研究，這是理論計算機科學和數學中最重要的未解問題之一。具體而言，我們提出了蘇格拉底推理，這是一個促進LLMs進行深入思考以解決複雜問題的通用框架。蘇格拉底推理鼓勵LLMs遞迴地發現、解決和整合問題，同時促進自我評估和改進。我們對P與NP問題的試驗性研究表明，GPT-4成功地生成了證明架構，並在97次對話中進行了嚴謹的推理，得出了“P不等於NP”的結論，這與（Xu和Zhou，2023）一致。這項研究揭示了LLMs廣泛解決空間中的新見解，為科學中的LLMs提供了新的視野。

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.