Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$ -widths of Shallow Neural Networks

29 January 2021

Papers citing "Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks"

49 / 49 papers shown

Title
Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Yuling Jiao Yanming Lai Yang Wang Bokai Yan 62 0 0 18 Apr 2025
Nonlocal techniques for the analysis of deep ReLU neural network approximations Cornelia Schneider Mario Ullrich Jan Vybiral 117 0 0 07 Apr 2025
Finite Samples for Shallow Neural Networks Yu Xia Zhiqiang Xu 63 0 0 17 Mar 2025
Curse of Dimensionality in Neural Network Optimization Sanghoon Na Haizhao Yang 87 0 0 07 Feb 2025
Orthogonal greedy algorithm for linear operator learning with shallow neural network Ye Lin Jiwei Jia Young Ju Lee Ran Zhang 78 1 0 06 Jan 2025
Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains Ahmed Abdeljawad Thomas Dittrich 50 0 0 06 Nov 2024
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains Ariel Neufeld Philipp Schmocker 72 3 0 18 Oct 2024
Nonuniform random feature models using derivative information Konstantin Pieper Zezhong Zhang Guannan Zhang 61 2 0 03 Oct 2024
On the expressiveness and spectral bias of KANs Yixuan Wang Jonathan W. Siegel Ziming Liu Thomas Y. Hou 119 13 0 02 Oct 2024
Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Method Yuling Jiao Yanming Lai Yang Wang AI4CE 32 1 0 19 May 2024
Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks Fanghui Liu L. Dadi Volkan Cevher 133 2 0 29 Apr 2024
On the rates of convergence for learning with convolutional neural networks Yunfei Yang Han Feng Ding-Xuan Zhou 122 3 0 25 Mar 2024
Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions Frank Cole Yulong Lu DiffM 63 5 0 12 Feb 2024
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss Yahong Yang Juncai He AI4CE 216 7 0 31 Jan 2024
Expressivity and Approximation Properties of Deep Neural Networks with ReLU $^k$ Activation Juncai He Tong Mao Jinchao Xu 77 4 0 27 Dec 2023
Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces Ahmed Abdeljawad Thomas Dittrich 58 2 0 13 Dec 2023
Minimum norm interpolation by perceptra: Explicit regularization and implicit bias Jiyoung Park Ian Pelakh Stephan Wojtowytsch 82 1 0 10 Nov 2023
Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications Yifan Zhang Joe Kileel 110 5 0 09 Nov 2023
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms Yahong Yang Yulong Lu 66 3 0 08 Nov 2023
Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities Rahul Parhi Michael Unser 134 5 0 05 Oct 2023
On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem Juncai He 96 11 0 10 Aug 2023
Tractability of approximation by general shallow networks H. Mhaskar Tong Mao 36 2 0 07 Aug 2023
Weighted variation spaces and approximation by shallow ReLU networks Ronald A. DeVore Robert D. Nowak Rahul Parhi Jonathan W. Siegel 133 5 0 28 Jul 2023
Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks Jonathan W. Siegel 315 7 0 28 Jul 2023
Sharp Convergence Rates for Matching Pursuit Jason M. Klusowski Jonathan W. Siegel 55 1 0 15 Jul 2023
Nonparametric regression using over-parameterized shallow ReLU neural networks Yunfei Yang Ding-Xuan Zhou 151 6 0 14 Jun 2023
Embedding Inequalities for Barron-type Spaces Lei Wu 76 0 0 30 May 2023
Embeddings between Barron spaces with higher order activation functions T. J. Heeringa L. Spek Felix L. Schwenninger C. Brune 77 3 0 25 May 2023
Approximation by non-symmetric networks for cross-domain learning H. Mhaskar 79 1 0 06 May 2023
Optimal rates of approximation by shallow ReLU $^k$ neural networks and applications to nonparametric regression Yunfei Yang Ding-Xuan Zhou 191 22 0 04 Apr 2023
Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data Jonathan W. Siegel 81 2 0 02 Feb 2023
Deep Learning Meets Sparse Regularization: A Signal Processing Perspective Rahul Parhi Robert D. Nowak 89 25 0 23 Jan 2023
Optimal transport map estimation in general function spaces Vincent Divol Jonathan Niles-Weed Aram-Alexandre Pooladian OT 90 24 0 07 Dec 2022
Limitations on approximation by deep and shallow neural networks G. Petrova P. Wojtaszczyk 115 9 0 30 Nov 2022
Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces Jonathan W. Siegel 187 30 0 25 Nov 2022
Consistency of Oblique Decision Tree and its Boosting and Random Forest Haoran Zhan Yu Liu Yingcun Xia 21 3 0 23 Nov 2022
Ensemble Projection Pursuit for General Nonparametric Regression Haoran Zhan Mingke Zhang Yingcun Xia 100 1 0 26 Oct 2022
DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning Siqi Xu Lin Liu Zhong Liu CML MedIm 67 9 0 10 Oct 2022
Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality Stephan Wojtowytsch 55 1 0 02 Sep 2022
$L^p$ sampling numbers for the Fourier-analytic Barron space F. Voigtlaender 22 7 0 16 Aug 2022
A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks El Mehdi Achour Armand Foucault Sébastien Gerchinovitz Franccois Malgouyres 74 7 0 09 Jun 2022
Optimal Learning P. Binev A. Bonito Ronald A. DeVore G. Petrova FedML 70 0 0 30 Mar 2022
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space Juncai He R. Tsai Rachel A. Ward 95 9 0 01 Mar 2022
$A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces$ A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu Sheng-Wei Zhou 46 0 0 25 Jan 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 216 39 0 01 Jan 2022
Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks Rahul Parhi Robert D. Nowak 113 39 0 18 Sep 2021
Characterization of the Variation Spaces Corresponding to Shallow Neural Networks Jonathan W. Siegel Jinchao Xu 137 44 0 28 Jun 2021
Optimal Convergence Rates for the Orthogonal Greedy Algorithm Jonathan W. Siegel Jinchao Xu 117 18 0 28 Jun 2021
Nonasymptotic theory for two-layer neural networks: Beyond the bias-variance trade-off Huiyuan Wang Wei Lin MLT 41 4 0 09 Jun 2021

Sharp Bounds on the Approximation Rates, Metric Entropy, and nnn-widths of Shallow Neural Networks

Papers citing "Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks"

Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$ -widths of Shallow Neural Networks