Integral representations of shallow neural network with Rectified Power Unit activation function
Neural and Evolutionary Computing
2021-12-22 v1 Machine Learning
Functional Analysis
Abstract
In this effort, we derive a formula for the integral representation of a shallow neural network with the Rectified Power Unit activation function. Mainly, our first result deals with the univariate case of representation capability of RePU shallow networks. The multidimensional result in this paper characterizes the set of functions that can be represented with bounded norm and possibly unbounded width.
Keywords
Cite
@article{arxiv.2112.11157,
title = {Integral representations of shallow neural network with Rectified Power Unit activation function},
author = {Ahmed Abdeljawad and Philipp Grohs},
journal= {arXiv preprint arXiv:2112.11157},
year = {2021}
}
Comments
22 pages, This is the first version. Some revisions in the near future is expected to be performed. arXiv admin note: text overlap with arXiv:1910.01635 by other authors