Neural network integral representations with the ReLU activation function
Machine Learning
2020-06-12 v3 Machine Learning
Abstract
In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite -norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all possible representations. Additionally, in this case our formula allows one to explicitly solve the least -norm neural network representation for a given function.
Keywords
Cite
@article{arxiv.1910.02743,
title = {Neural network integral representations with the ReLU activation function},
author = {Armenak Petrosyan and Anton Dereventsov and Clayton Webster},
journal= {arXiv preprint arXiv:1910.02743},
year = {2020}
}