Machine-Learning Number Fields

Thomas Oliver, Yang-Hui He, Kyu-Hwan Lee

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
JournalMathematics, Computation and Geometry of Data
Publication statusAccepted/In press - 2 Mar 2022

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