Expressivity of Deep Neural Networks
Machine Learning
2020-07-10 v1 Functional Analysis
Machine Learning
Abstract
In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks. Approximation rates for classical function spaces as well as benefits of deep neural networks over shallow ones for specifically structured function classes are discussed. While the mainbody of existing results is for general feedforward architectures, we also depict approximation results for convolutional, residual and recurrent neural networks.
Cite
@article{arxiv.2007.04759,
title = {Expressivity of Deep Neural Networks},
author = {Ingo Gühring and Mones Raslan and Gitta Kutyniok},
journal= {arXiv preprint arXiv:2007.04759},
year = {2020}
}
Comments
This review paper will appear as a book chapter in the book "Theory of Deep Learning" by Cambridge University Press