标题： 机器学习数域，但如何实现？ 伽罗瓦群的情况 显示英文标题

标题： Machines Learn Number Fields, But How? The Case of Galois Groups

摘要： 通过应用可解释的机器学习方法，如决策树，我们研究了简单模型如何利用狄利克雷ζ系数对次数为4、6、8、9和10的$\mathbb{Q}$上的伽罗瓦扩张的伽罗瓦群进行分类。 我们对机器学习结果的解释使我们能够理解ζ系数的分布如何依赖于伽罗瓦群，并证明了这些扩张的伽罗瓦群分类的新准则。 结合之前的结果，这项工作提供了机器学习驱动的数学研究新范式的一个例子。 显示英文摘要

摘要： By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of Galois extensions over $\mathbb{Q}$ of degrees 4, 6, 8, 9, and 10, using Dedekind zeta coefficients. Our interpretation of the machine learning results allows us to understand how the distribution of zeta coefficients depends on the Galois group, and to prove new criteria for classifying the Galois groups of these extensions. Combined with previous results, this work provides another example of a new paradigm in mathematical research driven by machine learning.