Hilbert series, machine learning, and applications to physics

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