Machine-Learning Number Fields
This work provides a new computational approach for number theorists to explore and classify algebraic number fields, potentially accelerating discoveries in an abstract mathematical domain.
This paper demonstrates that machine learning algorithms can accurately predict invariants of algebraic number fields. A random-forest classifier achieved 0.96 precision in distinguishing real quadratic fields with class numbers 1 and 2, even extrapolating beyond training data. A logistic regression classifier distinguished Galois groups and predicted unit group ranks with >0.97 precision for Galois extensions of degrees 2, 6, and 8.
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.