Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929762146975744 |
|---|---|
| author | Zanotti, Leo |
| author_facet | Zanotti, Leo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$ Zanotti, Leo Machine Learning Neural and Evolutionary Computing Metric Geometry 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. |
| title | Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$ |
| topic | Machine Learning Neural and Evolutionary Computing Metric Geometry |
| url | https://arxiv.org/abs/2503.13001 |