Group-Invariant Machine Learning on the Kreuzer-Skarke Dataset

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. In fact, we find that machine learning models that incorporate these symmetries outperform models that do not. We compare approaches incorporating different degrees of invariance and improve the state-of-the-art on the dataset.