4 papers
The Information-Theoretic Benefit of Shared Representations under Orthogonality Constraints
Thomas Dittrich, Oliver Potocki, Philipp Grohs
Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models. Empirically, exp…
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…
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…