Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$

Leo Zanotti
3/17/2025
cs.LGcs.NEmath.MG

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Abstract

It is shown that any continuous piecewise affine (CPA) function $\mathbb{R}^2\to\mathbb{R}$ with $p$ pieces can be represented by a ReLU neural network with two hidden layers and $O(p)$ neurons. Unlike prior work, which focused on convex pieces, this analysis considers CPA functions with connected but potentially non-convex pieces.

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Cite this paper

@article{zanotti2025linearsize,
  title  = {Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$},
  author = {Leo Zanotti},
  year   = {2025},
  eprint = {2503.13001},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2503.13001v1}
}

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