Positivity sets of hinge functions
arXiv:2503.13512v1h-index: 1
Originality Synthesis-oriented
AI Analysis
This addresses a theoretical problem in understanding the expressivity of neural networks for researchers in machine learning theory.
The paper investigates which subsets of the real plane can be realized as positivity sets of one-layer ReLU neural networks, providing a full characterization for cones and a necessary condition for general subsets in higher dimensions.
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.