  A very popular model in machine learning is the feedforward neural network
(FFN). The FFN can approximate general functions and mitigate the curse of
dimensionality. Here we introduce FFNs which represent sections of holomorphic
line bundles on complex manifolds, and ask some questions about their
approximating power. We also explain formal similarities between the standard
approach to supervised learning and the problem of finding numerical Ricci flat
K\"ahler metrics, which allow carrying some ideas between the two problems.
