On the expressivity of deep Heaviside networks

Fuente: arXiv
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Autori principali: Kong, Insung, Chen, Juntong, Langer, Sophie, Schmidt-Hieber, Johannes
Natura: Preprint
Pubblicazione: 2025
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author Kong, Insung
Chen, Juntong
Langer, Sophie
Schmidt-Hieber, Johannes
author_facet Kong, Insung
Chen, Juntong
Langer, Sophie
Schmidt-Hieber, Johannes
contents We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC) dimensions and approximation rates of these network classes. As an application, we derive statistical convergence rates for DHN fits in the nonparametric regression model.
format Preprint
id arxiv_https___arxiv_org_abs_2505_00110
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the expressivity of deep Heaviside networks
Kong, Insung
Chen, Juntong
Langer, Sophie
Schmidt-Hieber, Johannes
Machine Learning
Numerical Analysis
We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC) dimensions and approximation rates of these network classes. As an application, we derive statistical convergence rates for DHN fits in the nonparametric regression model.
title On the expressivity of deep Heaviside networks
topic Machine Learning
Numerical Analysis
url https://arxiv.org/abs/2505.00110