Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains
A Abdeljawad, T Dittrich - arXiv preprint arXiv:2411.04108, 2024 - arxiv.org
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 …
weighted Sobolev spaces for functions in the spectral Barron space. The existing literature …
Sampling complexity of deep approximation spaces
A Abdeljawad, P Grohs - arXiv preprint arXiv:2312.13379, 2023 - arxiv.org
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 …
remains a big challenge to compute such approximations from point samples. Based on …
Uniform Approximation with Quadratic Neural Networks
A Abdeljawad - Available at SSRN 5020130 - papers.ssrn.com
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 …
Rectified Quadratic Unit (ReQU) activation function, defined as\(\max (0, x)^ 2\), for …