English

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 Rd\mathbb R^d. 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}
}
R2 v1 2026-06-28T22:24:07.281Z