Machine learning invariants of arithmetic curves : WestminsterResearch

Publication dates
Title	Machine learning invariants of arithmetic curves
Type	Journal article
Authors	He, Y.-H., Lee, K.-H. and Oliver, T.
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 105, 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.
Keywords	Machine-learning
	Arithmetic geometry
	Elliptic curves
	Hyper-elliptic curves
	Birch-Swinnerton-Dyer conjecture
Journal	Journal of Symbolic Computation
Journal citation	115, pp. 478-491
ISSN	1095-855X
	0747-7171
Year	2023
Publisher	Elsevier
Publisher's version	published-arithmetic-curves.pdf License CC BY 4.0 File Access Level Open (open metadata and files)
Digital Object Identifier (DOI)	https://doi.org/10.1016/j.jsc.2022.08.017
Web address (URL)	https://www.sciencedirect.com/science/article/pii/S0747717122000839
Published	Mar 2023
Published online	22 Aug 2022

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Machine learning invariants of arithmetic curves

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