An effective SteinGLM initialization scheme for training multi-layer feedforward sigmoidal neural networks

Abstract

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 sigmoidal 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.

Keywords: Generalized linear model; Initialization scheme; Multi-index model; Multi-layer feedforward neural network; Stein’s identity.