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03/29/2023
Optimal approximation of C^k-functions using shallow complex-valued neural networks
We prove a quantitative result for the approximation of functions of reg...
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12/01/2022
Sampling numbers of smoothness classes via ℓ^1-minimization
Using techniques developed recently in the field of compressed sensing w...
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08/16/2022
L^p sampling numbers for the Fourier-analytic Barron space
In this paper, we consider Barron functions f : [0,1]^d →ℝ of smoothness...
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05/26/2022
Training ReLU networks to high uniform accuracy is intractable
Statistical learning theory provides bounds on the necessary number of t...
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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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10/28/2021
Sobolev-type embeddings for neural network approximation spaces
We consider neural network approximation spaces that classify functions ...
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04/06/2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
We study the computational complexity of (deterministic or randomized) a...
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12/06/2020
The universal approximation theorem for complex-valued neural networks
We generalize the classical universal approximation theorem for neural n...
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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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08/03/2020
Phase Transitions in Rate Distortion Theory and Deep Learning
Rate distortion theory is concerned with optimally encoding a given sign...
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05/03/2019
Approximation spaces of deep neural networks
We study the expressivity of deep neural networks. Measuring a network's...
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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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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