English

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.

Keywords

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

R2 v1 2026-06-23T14:39:11.450Z