Mathematics, Computation and Geometry of Data
Volume 2 (2022)
Machine-learning number fields
Pages: 49 – 66
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 $\gt 0.97$.
Y.H.H. is indebted to STFC UK, for grant ST/J00037X/1.
K.H.L. is partially supported by a grant from the Simons Foundation (#712100).
T.O. acknowledges support from the EPSRC through research grant EP/S032460/1.
Received 7 March 2021
Published 21 October 2022