Hilbert Series, Machine Learning, and Applications to Physics

Autor: Yang-Hui He, Jiakang Bao, Johannes Hofscheier, Suvajit Majumder, Alexander Kasprzyk, Edward Hirst
Rok vydání: 2021
Předmět:
Zdroj: Physics Letters
ISSN: 0370-2693
DOI: 10.48550/arxiv.2103.13436
Popis: We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\sim}1$ mean absolute error, whilst classifiers predict dimension and Gorenstein index to $>90\%$ accuracy with ${\sim}0.5\%$ 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.
10 pages; v2: principle component analysis added; v3: minor corrections
Databáze: OpenAIRE
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