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01/13/2023
Solving PDEs with Incomplete Information
We consider the problem of numerically approximating the solutions to a ...
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11/30/2022
Limitations on approximation by deep and shallow neural networks
We prove Carl's type inequalities for the error of approximation of comp...
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03/30/2022
Optimal Learning
This paper studies the problem of learning an unknown function f from gi...
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02/15/2022
On the entropy numbers and the Kolmogorov widths
Direct estimates between linear or nonlinear Kolmogorov widths and entro...
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11/02/2021
Lipschitz widths
This paper introduces a measure, called Lipschitz widths, of the optimal...
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07/28/2021
Neural Network Approximation of Refinable Functions
In the desire to quantify the success of neural networks in deep learnin...
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12/28/2020
Neural Network Approximation
Neural Networks (NNs) are the method of choice for building learning alg...
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09/21/2020
Optimal Stable Nonlinear Approximation
While it is well known that nonlinear methods of approximation can often...
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05/06/2020
