鸣群：人工智能辅助数学的案例研究
Murmurations: a case study in AI-assisted mathematics
AI总结：
本文通过人工智能技术发现并研究了算术中一种新的现象——鸣群，揭示其与数论和随机矩阵理论的联系。
摘要：
我们报告了在算术中出现的一种引人注目的新现象，我们称之为鸣群。首次通过在大规模算术数据集上取平均数实验性地观察到鸣群，可以使用机器学习中的标准可解释性工具进行检测和分析，包括主成分权重、显著性曲线和卷积滤波器。尽管是通过计算发现的，但鸣群构成了算术中真正新的且引人入胜的现象，可以使用数论的已建立工具进行表征和研究。特别是，鸣群编码了关于弗罗贝尼乌斯迹的细微信息，并自然地属于算术统计的框架中。更具体地说，鸣群与围绕 Birch 和 Swinnerton-Dyer 猜想的核心主题以及随机矩阵理论的观点相关。在本文中，我们概述了鸣群，并将其置于数论和人工智能的背景下。
英文摘要：
We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmurations can be detected and analyzed using standard interpretability tools from machine learning, including principal component weightings, saliency curves, and convolutional filters. Although discovered computationally, they constitute a genuinely new and intriguing phenomenon in arithmetic that can be formulated and investigated using established tools of number theory. In particular, murmurations encode subtle information about Frobenius traces and naturally belong to the framework of arithmetic statistics. More precisely, murmurations connect to central themes surrounding the conjecture of Birch and Swinnerton-Dyer and perspectives from random matrix theory. In this paper, we present an overview of murmurations, contextualizing them within number theory and AI.
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。
