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

• URL: http://arxiv.org/abs/2002.07867v3
• Date: Thu, 17 Dec 2020 19:45:04 GMT
• Title: Global Convergence of Deep Networks with One Wide Layer Followed by Pyramidal Topology
• Authors: Quynh Nguyen and Marco Mondelli
• Abstract summary: We prove that, for deep networks, a single layer of width $N$ following the input layer suffices to ensure a similar guarantee. All the remaining layers are allowed to have constant widths, and form a pyramidal topology.
• Score: 28.49901662584467
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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