Machine learning Calabi-Yau four-folds

Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we consider the data set of complete intersection Calabi-Yau four-folds, a set of about 900,000 topological types, and study supervised learning of the Hodge numbers h1,1 and h3,1 for these manifolds. We find that h1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.