  Network initialization is the first and critical step for training neural
networks. In this paper, we propose a novel network initialization scheme based
on the celebrated Stein's identity. By viewing multi-layer feedforward neural
networks as cascades of multi-index models, the projection weights to the first
hidden layer are initialized using eigenvectors of the cross-moment matrix
between the input's second-order score function and the response. The input
data is then forward propagated to the next layer and such a procedure can be
repeated until all the hidden layers are initialized. Finally, the weights for
the output layer are initialized by generalized linear modeling. Such a
proposed SteinGLM method is shown through extensive numerical results to be
much faster and more accurate than other popular methods commonly used for
training neural networks.
