Abstract

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.

Publication Type:	Article
Additional Information:	© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology > Mathematics

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