Positivity sets of hinge functions

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 $\mathbb R^d$. We give various examples of such one-layer neural networks.

@article{schicho2025_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 }
}