Quantified advantage of discontinuous weight selection in approximations with deep neural networks
Neural and Evolutionary Computing
2017-05-04 v1
Abstract
We consider approximations of 1D Lipschitz functions by deep ReLU networks of a fixed width. We prove that without the assumption of continuous weight selection the uniform approximation error is lower than with this assumption at least by a factor logarithmic in the size of the network.
Keywords
Cite
@article{arxiv.1705.01365,
title = {Quantified advantage of discontinuous weight selection in approximations with deep neural networks},
author = {Dmitry Yarotsky},
journal= {arXiv preprint arXiv:1705.01365},
year = {2017}
}
Comments
12 pages, submitted to J. Approx. Theory