On decision regions of narrow deep neural networks
Machine Learning
2021-03-04 v4 Artificial Intelligence
Neural and Evolutionary Computing
Machine Learning
Abstract
We show that for neural network functions that have width less or equal to the input dimension all connected components of decision regions are unbounded. The result holds for continuous and strictly monotonic activation functions as well as for the ReLU activation function. This complements recent results on approximation capabilities by [Hanin 2017 Approximating] and connectivity of decision regions by [Nguyen 2018 Neural] for such narrow neural networks. Our results are illustrated by means of numerical experiments.
Keywords
Cite
@article{arxiv.1807.01194,
title = {On decision regions of narrow deep neural networks},
author = {Hans-Peter Beise and Steve Dias Da Cruz and Udo Schröder},
journal= {arXiv preprint arXiv:1807.01194},
year = {2021}
}
Comments
This paper is accepted for publication in Neural Networks (Elsevier Journal)