Hilbert series, machine learning, and applications to physics
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Volume
827
DOI
10.1016/j.physletb.2022.136966
Journal
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
ISSN
0370-2693
Metadata
Show full item recordAbstract
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.
Authors
Bao, J; He, YH; Hirst, E; Hofscheier, J; Kasprzyk, A; Majumder, SCollections
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