9 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…
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…
Sampling Complexity of Deep Approximation Spaces
Ahmed Abdeljawad, Philipp Grohs
While it is well-known that neural networks enjoy excellent approximation capabilities, it remains a big challenge to compute such approximations from point samples. Based on tools…
Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces
Ahmed Abdeljawad, Thomas Dittrich
Approximation capabilities of shallow neural networks (SNNs) form an integral part in understanding the properties of deep neural networks (DNNs). In the study of these approximati…
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…
Integral representations of shallow neural network with Rectified Power Unit activation function
Ahmed Abdeljawad, Philipp Grohs
In this effort, we derive a formula for the integral representation of a shallow neural network with the Rectified Power Unit activation function. Mainly, our first result deals wi…
Approximations with deep neural networks in Sobolev time-space
Ahmed Abdeljawad, Philipp Grohs
Solutions of evolution equation generally lies in certain Bochner-Sobolev spaces, in which the solution may has regularity and integrability properties for the time variable that c…