Positivity sets of hinge functions
arXiv:2503.13512v1 Announce Type: new
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 $mathbb R^d$. We give various examples of such one-layer neural networks.
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 $mathbb R^d$. We give various examples of such one-layer neural networks.
Josef Schicho, Ayush Kumar Tewari, Audie Warren
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