Machine-learning number fields

He, Y.-H., Lee, K.-H. and Oliver, T. 2022. Machine-learning number fields. Mathematics, Computation and Geometry of Data. 2 (1), pp. 49-66. https://doi.org/10.4310/MCGD.2022.v2.n1.a2

TitleMachine-learning number fields
TypeJournal article
AuthorsHe, Y.-H., Lee, K.-H. and Oliver, T.
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 precision 0.96. 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 , , and , a logistic regression classifier can distinguish between Galois groups and predict the ranks of unit groups with precision >0.97.

JournalMathematics, Computation and Geometry of Data
Journal citation2 (1), pp. 49-66
ISSN2642-1909
2642-1917
Year2022
PublisherInternational Press
Digital Object Identifier (DOI)https://doi.org/10.4310/MCGD.2022.v2.n1.a2
Web address (URL)https://www.intlpress.com/site/pub/pages/journals/items/mcgd/content/vols/0002/0001/a002/index.php?mode=ns
Publication dates
Published21 Oct 2022

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