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In this work, we present some applications of random matrix theory for the
training of deep neural networks. Recently, random matrix theory (RMT) has been
applied to the overfitting problem in deep learning. Specifically, it has been
shown that the spectrum of the weight layers of a deep neural network (DNN) can
be studied and understood using techniques from RMT. In this work, these RMT
techniques will be used to determine which and how many singular values should
be removed from the weight layers of a DNN during training, via singular value
decomposition (SVD), so as to reduce overfitting and increase accuracy. We show
the results on a simple DNN model trained on MNIST. In general, these
techniques may be applied to any fully connected layer of a pretrained DNN to
reduce the number of parameters in the layer while preserving and sometimes
increasing the accuracy of the DNN.
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