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12/23/2021
Optimal learning of high-dimensional classification problems using deep neural networks
We study the problem of learning classification functions from noiseless...
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08/12/2021
Deep Microlocal Reconstruction for Limited-Angle Tomography
We present a deep learning-based algorithm to jointly solve a reconstruc...
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05/09/2021
The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning. Thi...
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11/18/2020
Neural network approximation and estimation of classifiers with classification boundary in a Barron class
We prove bounds for the approximation and estimation of certain classifi...
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04/25/2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
We perform a comprehensive numerical study of the effect of approximatio...
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01/30/2020
Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs
We demonstrate that deep neural networks with the ReLU activation functi...
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04/09/2019
Approximation in L^p(μ) with deep ReLU neural networks
We discuss the expressive power of neural networks which use the non-smo...
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03/31/2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
We derive upper bounds on the complexity of ReLU neural networks approxi...
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02/21/2019
Error bounds for approximations with deep ReLU neural networks in W^s,p norms
We analyze approximation rates of deep ReLU neural networks for Sobolev-...
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01/05/2019
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
Microlocal analysis provides deep insight into singularity structures an...
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09/04/2018
Equivalence of approximation by convolutional neural networks and fully-connected networks
Convolutional neural networks are the most widely used type of neural ne...
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09/15/2017