Positivity sets of hinge functions
Machine Learning
2025-03-19 v1 Discrete Mathematics
Machine Learning
Symbolic Computation
Combinatorics
Functional Analysis
Abstract
In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give a necessary condition for any subset of . We give various examples of such one-layer neural networks.
Cite
@article{arxiv.2503.13512,
title = {Positivity sets of hinge functions},
author = {Josef Schicho and Ayush Kumar Tewari and Audie Warren},
journal= {arXiv preprint arXiv:2503.13512},
year = {2025}
}