Approximation with Neural Networks in Variable Lebesgue Spaces
Functional Analysis
2020-07-09 v1 Machine Learning
Abstract
This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks with any desired accuracy. This result subsequently leads to determine the universality of the approximation depending on the boundedness of the exponent function. Furthermore, whenever the exponent is unbounded, we obtain some characterization results for the subspace of functions that can be approximated.
Cite
@article{arxiv.2007.04166,
title = {Approximation with Neural Networks in Variable Lebesgue Spaces},
author = {Ángela Capel and Jesús Ocáriz},
journal= {arXiv preprint arXiv:2007.04166},
year = {2020}
}
Comments
20 pages