Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem
Numerical Analysis
2020-05-20 v2 Machine Learning
Numerical Analysis
Abstract
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov--Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.
Cite
@article{arxiv.1906.11945,
title = {Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem},
author = {Hadrien Montanelli and Haizhao Yang},
journal= {arXiv preprint arXiv:1906.11945},
year = {2020}
}