[论文] Long-Horizon AI Research for Grothendieck Constant: A Case Study in Hu...

论文概要

研究领域: ML 作者: Alan Li, Rahul Saha, Anton Xue, Swarat Chaudhuri, Adam Klivans, Pravesh K Kothari, Raghu Meka 发布时间: 2026-08-11 arXiv: 2608.11195

中文摘要

AI智能体越来越多地用于数学研究，但如何有效使用它们往往不清楚。为此，我们呈现了一个广泛的案例研究，展示如何利用AI改进Grothendieck常数KG的界限，该常数捕捉了组合问题与其连续松弛之间的难度。具体而言，虽然KG的精确值未知，但我们最近将最佳已知界限收紧为 [6π/11 ≤ KG ≤ π/(2log(1+√2)) - 10^-4]。关键的是，这些改进是通过一个能够得出被领域专家视为新颖的洞察的AI研究系统实现的。我们详细讨论了使用AI进行数学研究的经验，特别涉及其优势和劣势，以及我们为AI创造突破性洞察理想条件的经验。

原文摘要

AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant KG, which captures the hardness between combinatorial problems and their continuous relaxations. Specifically, while the precise value of KG is not known, we recently tightened the best known bounds to [ 6π/11 ≤ KG ≤ π/(2log(1+√2)) - 10^-4 ]. Crucially, these improvements were achieved using an AI research system that could arrive at insights deemed novel by领域专家. We give a detailed discussion of our experience using AI for mathematics research, particularly touching upon its strengths and weaknesses, as well as our experience with creating ideal conditions for AI to ar...

--- *自动采集于 2026-08-13*

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