اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHilbert Series, Machine Learning, and Applications to Physics
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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.
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