5 papers
Approximation Rates for Metaplectic Neural Networks
Ahmed Abdeljawad, Marcello Carioni, Elena Cordero
In this paper we develop quantitative approximation results for shallow neural networks constructed using a dictionary based on metaplectic operators. First, we extend the concept…
Time-Frequency Analysis for Neural Networks
Ahmed Abdeljawad, Elena Cordero
We develop a quantitative approximation theory for shallow neural networks using tools from time-frequency analysis. Working in weighted modulation spaces $M^{p,q}_m(\mathbf{R}^{d}…
Approximation Rates in Fréchet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers
Ahmed Abdeljawad, Thomas Dittrich
Operator learning is a recent development in the simulation of Partial Differential Equations (PDEs) by means of neural networks. The idea behind this approach is to learn the beha…
Uniform Approximation with Quadratic Neural Networks
Ahmed Abdeljawad
In this work, we examine the approximation capabilities of deep neural networks utilizing the Rectified Quadratic Unit (ReQU) activation function, defined as \(\max(0,x)^2\), for a…
Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains
Ahmed Abdeljawad, Thomas Dittrich
In this work, we consider the approximation capabilities of shallow neural networks in weighted Sobolev spaces for functions in the spectral Barron space. The existing literature a…