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Global Convergence of Deep Networks with One Wide Layer Followed by Pyramidal Topology

Quynh Nguyen · Marco Mondelli

Poster Session 1 #461

Keywords: [ Generative Models ] [ Deep Learning ] [ Adversarial Networks ]


Recent works have shown that gradient descent can find a global minimum for over-parameterized neural networks where the widths of all the hidden layers scale polynomially with N (N being the number of training samples). In this paper, we prove that, for deep networks, a single layer of width N following the input layer suffices to ensure a similar guarantee. In particular, all the remaining layers are allowed to have constant widths, and form a pyramidal topology. We show an application of our result to the widely used LeCun's initialization and obtain an over-parameterization requirement for the single wide layer of order N^2.

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