论文标题
机器学习编号字段
Machine-Learning Number Fields
论文作者
论文摘要
我们表明，可以对标准的机器学习算法进行训练，以预测某些代数数字字段的某些不变性。在有限的许多Dedekind Zeta系数上接受训练的随机索具分类器能够将具有数字1和2类的真实二次字段区分为0.96精度。此外，分类器能够在训练数据范围内推断出具有判别功能的字段。当对定义多项式的系数的GALOIS扩展范围2、6和8的训练时，Logistic回归分类器可以区分Galois组，并预测精度> 0.97的单位组的等级。
We show that standard machine-learning algorithms may be trained to predict certain invariants of algebraic number fields to high accuracy. A random-forest classifier that is trained on finitely many Dedekind zeta coefficients is able to distinguish between real quadratic fields with class number 1 and 2, to 0.96 precision. Furthermore, the classifier is able to extrapolate to fields with discriminant outside the range of the training data. When trained on the coefficients of defining polynomials for Galois extensions of degrees 2, 6, and 8, a logistic regression classifier can distinguish between Galois groups and predict the ranks of unit groups with precision >0.97.
