用机器学习分析数域伽罗瓦群，发现新判别准则
Machines Learn Number Fields, But How? The Case of Galois Groups
- 用决策树等可解释模型分析黎曼ζ系数
- 对4,6,8,9,10次扩张的伽罗瓦群实现高精度分类
- 为数学研究提供机器学习驱动的新范式
通过应用决策树等可解释机器学习方法，我们研究了简单模型如何利用戴德金ζ系数对Q上的4、6、8、9和10次伽罗瓦扩张的伽罗瓦群进行分类。对机器学习结果的解释使我们得以理解ζ系数分布与伽罗瓦群之间的关系，并推导出这些扩张伽罗瓦群的新判别准则。结合已有成果，本工作展示了由机器学习驱动的数学研究新范式。
原文摘要 · Abstract (English)
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.
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