Jonathan W. Siegel | DeepAI

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Featured Co-authors

Jinchao Xu
31 publications
Wenrui Hao
15 publications
Qingguo Hong
13 publications
Xianlin Jin
3 publications
Qinyang Tan
2 publications
Jianhong Chen
2 publications

∙ 02/02/2023

Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data

We study the interpolation, or memorization, power of deep ReLU neural n...

0 Jonathan W. Siegel, et al. ∙

∙ 11/25/2022

Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev Spaces

We study the problem of how efficiently, in terms of the number of param...

0 Jonathan W. Siegel, et al. ∙

∙ 08/09/2022

On the Activation Function Dependence of the Spectral Bias of Neural Networks

Neural networks are universal function approximators which are known to ...

12 Qingguo Hong, et al. ∙

∙ 07/09/2021

An efficient greedy training algorithm for neural networks and applications in PDEs

Recently, neural networks have been widely applied for solving partial d...

0 Wenrui Hao, et al. ∙

∙ 06/28/2021

Characterization of the Variation Spaces Corresponding to Shallow Neural Networks

We consider the variation space corresponding to a dictionary of functio...

8 Jonathan W. Siegel, et al. ∙

∙ 06/28/2021

Improved Convergence Rates for the Orthogonal Greedy Algorithm

We analyze the orthogonal greedy algorithm when applied to dictionaries ...

0 Jonathan W. Siegel, et al. ∙

∙ 06/28/2021

Sharp Lower Bounds on the Approximation Rate of Shallow Neural Networks

We consider the approximation rates of shallow neural networks with resp...

11 Jonathan W. Siegel, et al. ∙

∙ 04/07/2021

Rademacher Complexity and Numerical Quadrature Analysis of Stable Neural Networks with Applications to Numerical PDEs

Methods for solving PDEs using neural networks have recently become a ve...

0 Qingguo Hong, et al. ∙

∙ 01/29/2021

Optimal Approximation Rates and Metric Entropy of ReLU^k and Cosine Networks

This article addresses several fundamental issues associated with the ap...

1 Jonathan W. Siegel, et al. ∙

∙ 12/14/2020

High-Order Approximation Rates for Neural Networks with ReLU^k Activation Functions

We study the approximation properties of shallow neural networks (NN) wi...

0 Jonathan W. Siegel, et al. ∙

∙ 08/21/2020

Training Sparse Neural Networks using Compressed Sensing

Pruning the weights of neural networks is an effective and widely-used t...

14 Jonathan W. Siegel, et al. ∙

∙ 04/04/2019

On the Approximation Properties of Neural Networks

We prove two new results concerning the approximation properties of neur...

0 Jonathan W. Siegel, et al. ∙