Positivity sets of hinge functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912279541317632 |
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| author | Schicho, Josef Tewari, Ayush Kumar Warren, Audie |
| author_facet | Schicho, Josef Tewari, Ayush Kumar Warren, Audie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positivity sets of hinge functions Schicho, Josef Tewari, Ayush Kumar Warren, Audie Machine Learning Discrete Mathematics Symbolic Computation Combinatorics Functional Analysis 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. |
| title | Positivity sets of hinge functions |
| topic | Machine Learning Discrete Mathematics Symbolic Computation Combinatorics Functional Analysis |
| url | https://arxiv.org/abs/2503.13512 |