NeurIPS 2018spotlight317 citations
ResNet with one-neuron hidden layers is a Universal Approximator
Hongzhou Lin, Stefanie Jegelka
Abstract
We demonstrate that a very deep ResNet with stacked modules that have one neuron per hidden layer and ReLU activation functions can uniformly approximate any Lebesgue integrable function in d dimensions, i.e. \ell_1(R^d). Due to the identity mapping inherent to ResNets, our network has alternating layers of dimension one and d. This stands in sharp contrast to fully connected networks, which are not universal approximators if their width is the input dimension d [21,11]. Hence, our result implies an increase in representational power for narrow deep networks by the ResNet architecture.
BibTeX
@inproceedings{NEURIPS2018_03bfc1d4,
author = {Lin, Hongzhou and Jegelka, Stefanie},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {ResNet with one-neuron hidden layers is a Universal Approximator},
url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/03bfc1d4783966c69cc6aef8247e0103-Paper.pdf},
volume = {31},
year = {2018}
}