Hilbert series, machine learning, and applications to physics

Bao, Jiakang; He, Yang-Hui; Hirst, Edward; Hofscheier, Johannes; Kasprzyk, Alexander; Majumder, Suvajit

Abstract

We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenstein index to > 90% accuracy with ∼0.5% standard error. Binary random forest classifiers managed to distinguish whether the underlying HS describes a complete intersection with high accuracies exceeding 95%. Neural networks (NNs) exhibited success identifying HS from a Gorenstein ring to the same order of accuracy, whilst generation of "fake" HS proved trivial for NNs to distinguish from those associated to the three-dimensional Fano varieties considered.

Citation

Bao, J., He, Y.-H., Hirst, E., Hofscheier, J., Kasprzyk, A., & Majumder, S. (2022). Hilbert series, machine learning, and applications to physics. Physics Letters B, 827, Article 136966. https://doi.org/10.1016/j.physletb.2022.136966

• Journal Article Type: Article
• Acceptance Date: Feb 14, 2022
• Online Publication Date: Feb 18, 2022
• Publication Date: Apr 10, 2022
• Deposit Date: Feb 15, 2022
• Publicly Available Date: Feb 21, 2022
• Journal: Physics Letters B
• Print ISSN: 0370-2693
• Electronic ISSN: 1873-2445
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 827
• Article Number: 136966
• DOI: https://doi.org/10.1016/j.physletb.2022.136966
• Keywords: Nuclear and High Energy Physics
• Public URL: https://nottingham-repository.worktribe.com/output/7468356
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0370269322001009