mlsanityData to 14 Oct 2026

Positivity sets of hinge functions

arXiv 2503.13512 ↗First posted 14 Mar 2025stat.ML cs.DM cs.LGcited by 0

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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.

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.

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4 of 12 references.

References · 4

  1. 2021Towards Lower Bounds on the Depth of ReLU Neural Networkscited by 56
  2. 2020On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networkscited by 35
  3. 2022Piecewise Linear Neural Networks and Deep Learningcited by 7
  4. 2024Representing Piecewise-Linear Functions by Functions with Minimal Aritycited by 2

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