Approximated Orthonormal Normalisation in Training Neural Networks

Abstract: Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to improve the generalisation capacity of a DNN model. Considering a weight matrix W from a particular neural layer in the model, our objective is to design a function h(W) such that its row vectors are approximately orthogonal to each other while allowing the DNN model to fit the training data sufficiently accurate. By doing so, it would avoid co-adaptation among neurons of the same layer to be able to improve network-generalisation capacity. Specifically, at each iteration, we first approximate (WW^T)^-1/2 using its Taylor expansion before multiplying the matrix W. After that, the matrix product is then normalised by applying the spectral normalisation (SN) technique to obtain h(W). Conceptually speaking, AON is designed to turn orthonormal regularisation into orthonormal normalisation to avoid manual balancing the original and penalty functions. Experimental results show that AON yields promising validation performance compared to orthonormal regularisation.