Deep linear neural networks with arbitrary loss: All local minima are global
Machine Learning
2018-07-25 v2 Machine Learning
Abstract
We consider deep linear networks with arbitrary convex differentiable loss. We provide a short and elementary proof of the fact that all local minima are global minima if the hidden layers are either 1) at least as wide as the input layer, or 2) at least as wide as the output layer. This result is the strongest possible in the following sense: If the loss is convex and Lipschitz but not differentiable then deep linear networks can have sub-optimal local minima.
Cite
@article{arxiv.1712.01473,
title = {Deep linear neural networks with arbitrary loss: All local minima are global},
author = {Thomas Laurent and James von Brecht},
journal= {arXiv preprint arXiv:1712.01473},
year = {2018}
}