Machine learning invariants of arithmetic curves

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

Research output: Contribution to journalArticlepeer-review

Abstract

We show that standard machine learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around 100,000, we demonstrate the utility of machine learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the recognition of integral points, the accuracies can reach 0.998.
Original languageEnglish
Pages (from-to)478-491
Number of pages14
JournalJournal of Symbolic Computation
Volume115
Publication statusPublished - 22 Aug 2022

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