English

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 L1L_1-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 L1L_1-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}
}
R2 v1 2026-06-23T11:36:16.507Z