Linear-Size Neural Network Representation of Piecewise Affine Functions in ℝ2
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Abstract (arXiv)
It is shown that any continuous piecewise affine (CPA) function ℝ2→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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 12 of its 24 references that are in the map. First posted on arXiv 17 Mar 2025.
Builds on
12 of 24 references.
References · 12
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- 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 257
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- 2021Towards Lower Bounds on the Depth of ReLU Neural Networkscited by 56
- 2023Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopescited by 36
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- 2024Decomposition Polyhedra of Piecewise Linear Functionscited by 9
- 2023Representing Piecewise Linear Functions by Functions with Small Aritycited by 7
- 2025Bounds on the Number of Pieces in Continuous Piecewise Affine Functionscited by 2
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Citing papers per year: 2025: 1.
1 paper.