Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks
Machine Learning
2020-05-14 v3 Neural and Evolutionary Computing
Machine Learning
Abstract
We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower networks are much larger. This includes indicators of balls and ellipses; non-linear functions which are radial with respect to the norm; and smooth non-linear functions. We also show that these gaps can be observed experimentally: Increasing the depth indeed allows better learning than increasing width, when training neural networks to learn an indicator of a unit ball.
Cite
@article{arxiv.1610.09887,
title = {Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks},
author = {Itay Safran and Ohad Shamir},
journal= {arXiv preprint arXiv:1610.09887},
year = {2020}
}