@Article{JML-3-107,
author = {Welper , Gerrit},
title = {Approximation Results for Gradient Flow Trained Neural Networks},
journal = {Journal of Machine Learning},
year = {2024},
volume = {3},
number = {2},
pages = {107--175},
abstract = {<p style="text-align: justify;">The paper contains approximation guarantees for neural networks that are trained with gradient
flow, with error measured in the continuous $L_2(\mathbb{S}^{d−1
)}$-norm on the $d$-dimensional unit sphere and targets that
are Sobolev smooth. The networks are fully connected of constant depth and increasing width. We show
gradient flow convergence based on a neural tangent kernel (NTK) argument for the non-convex optimization
of the second but last layer. Unlike standard NTK analysis, the continuous error norm implies an under-parametrized regime, possible by the natural smoothness assumption required for approximation. The typical over-parametrization re-enters the results in form of a loss in approximation rate relative to established
approximation methods for Sobolev smooth functions.</p>},
issn = {2790-2048},
doi = {https://doi.org/10.4208/jml.230924},
url = {http://global-sci.org/intro/article_detail/jml/23210.html}
}