  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 h^1,1 and h^3,1 for these manifolds. We find that
h^1,1 can be successfully learned (to 96% precision) by fully connected
classifier and regressor networks. While both types of networks fail for h^3,1,
we show that a more complicated two-branch network, combined with feature
enhancement, can act as an efficient regressor (to 98% precision) for h^3,1, at
least for a subset of the data. This hints at the existence of an, as yet
unknown, formula for Hodge numbers.
