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Exact Solutions of a Deep Linear Network

Liu Ziyin · Botao Li · Xiangming Meng

Hall J (level 1) #515

Keywords: [ Exact Solution ] [ Collapse ] [ deep linear network ]

Abstract: This work finds the analytical expression of the global minima of a deep linear network with weight decay and stochastic neurons, a fundamental model for understanding the landscape of neural networks. Our result implies that zero is a special point in deep neural network architecture. We show that weight decay strongly interacts with the model architecture and can create bad minima at zero in a network with more than $1$ hidden layer, qualitatively different from a network with only $1$ hidden layer. Practically, our result implies that common deep learning initialization methods are insufficient to ease the optimization of neural networks in general.

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