Group-invariant machine learning on the Kreuzer-Skarke dataset

Abstract

We use supervised machine learning to predict Hodge numbers for Calabi-Yau threefolds encoded by reflexive polyhedra. The Hodge number is invariant to the order of the vertices and the swapping of axes. Incorporating these properties, i.e. the invariance of column and row permutations for a matrix containing the polyhedron's vertices, promises better performance for Hodge number prediction. On a medium-sized subset of the Kreuzer-Skarke dataset, we train and evaluate approaches with different degrees of invariance. Our comparison shows that machine learning models incorporating symmetries actually outperform models that do not, with our best model achieving almost 97% accuracy.