# Positivity sets of hinge functions

arXiv: https://arxiv.org/abs/2503.13512 · HTML: https://mlsanity.com/paper/2503.13512/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 4 of 4)

- [Towards Lower Bounds on the Depth of ReLU Neural Networks](https://mlsanity.com/paper/2105.14835/) (2021)
- [On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networks](https://mlsanity.com/paper/2008.09052/) (2020)
- [Piecewise Linear Neural Networks and Deep Learning](https://mlsanity.com/paper/2206.09149/) (2022)
- [Representing Piecewise-Linear Functions by Functions with Minimal Arity](https://mlsanity.com/paper/2406.02421/) (2024)

## Abstract (arXiv)

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 Rd. We give various examples of such one-layer neural networks.