Rational neural networks
Neural and Evolutionary Computing
2020-10-01 v2 Machine Learning
Numerical Analysis
Numerical Analysis
Machine Learning
Abstract
We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks with exponentially smaller depth. The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU, as we demonstrate with numerical experiments.
Cite
@article{arxiv.2004.01902,
title = {Rational neural networks},
author = {Nicolas Boullé and Yuji Nakatsukasa and Alex Townsend},
journal= {arXiv preprint arXiv:2004.01902},
year = {2020}
}
Comments
21 pages, 7 figures