Representation formulas and pointwise properties for Barron functions

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Representation formulas and pointwise properties for Barron functions

10 June 2020

Stephan Wojtowytsch

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Papers citing "Representation formulas and pointwise properties for Barron functions"

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Title
High-dimensional classification problems with Barron regular boundaries under margin conditions Jonathan García Philipp Petersen 112 1 0 10 Dec 2024
Penalising the biases in norm regularisation enforces sparsity Etienne Boursier Nicolas Flammarion 92 17 0 02 Mar 2023
A Note on the Representation Power of GHHs Zhou Lu 58 5 0 27 Jan 2021
Neural network approximation and estimation of classifiers with classification boundary in a Barron class A. Caragea P. Petersen F. Voigtlaender 48 36 0 18 Nov 2020
On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime Stephan Wojtowytsch MLT 102 50 0 27 May 2020
Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective Stephan Wojtowytsch E. Weinan MLT 66 50 0 21 May 2020
Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels E. Weinan Stephan Wojtowytsch 129 31 0 21 May 2020
A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks Phan-Minh Nguyen H. Pham AI4CE 79 81 0 30 Jan 2020
Machine Learning from a Continuous Viewpoint E. Weinan Chao Ma Lei Wu 109 104 0 30 Dec 2019
The Barron Space and the Flow-induced Function Spaces for Neural Network Models E. Weinan Chao Ma Lei Wu 71 110 0 18 Jun 2019
A Priori Estimates of the Population Risk for Two-layer Neural Networks Weinan E Chao Ma Lei Wu 62 131 0 15 Oct 2018
On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport Lénaïc Chizat Francis R. Bach OT 204 735 0 24 May 2018
A Mean Field View of the Landscape of Two-Layers Neural Networks Song Mei Andrea Montanari Phan-Minh Nguyen MLT 93 858 0 18 Apr 2018
$Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $ \ell^1 $ and $ \ell^0 $ Controls$ Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $\ell^1$ and $\ell^0$ Controls Jason M. Klusowski Andrew R. Barron 264 143 0 26 Jul 2016
Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networks Jason M. Klusowski Andrew R. Barron 73 70 0 05 Jul 2016
Breaking the Curse of Dimensionality with Convex Neural Networks Francis R. Bach 184 706 0 30 Dec 2014