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07/28/2023
Weighted variation spaces and approximation by shallow ReLU networks
We investigate the approximation of functions f on a bounded domain Ω⊂ℝ^...
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07/28/2023
Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks
We study the following two related problems. The first is to determine t...
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07/15/2023
Sharp Convergence Rates for Matching Pursuit
We study the fundamental limits of matching pursuit, or the pure greedy ...
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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...
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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...
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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 ...
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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...
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06/28/2021
Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
We consider the variation space corresponding to a dictionary of functio...
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06/28/2021
Improved Convergence Rates for the Orthogonal Greedy Algorithm
We analyze the orthogonal greedy algorithm when applied to dictionaries ...
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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...
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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...
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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...
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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...
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08/21/2020
Training Sparse Neural Networks using Compressed Sensing
Pruning the weights of neural networks is an effective and widely-used t...
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04/04/2019