Error bounds for approximations with deep ReLU networks
Machine Learning
2017-05-02 v3 Neural and Evolutionary Computing
Abstract
We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz functions we describe adaptive depth-6 network architectures more efficient than the standard shallow architecture.
Cite
@article{arxiv.1610.01145,
title = {Error bounds for approximations with deep ReLU networks},
author = {Dmitry Yarotsky},
journal= {arXiv preprint arXiv:1610.01145},
year = {2017}
}
Comments
31 pages; major revision in v3; submitted to Neural Networks