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

29 January 2021

Jonathan W. Siegel

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

17 / 17 papers shown

Title
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains Ariel Neufeld Philipp Schmocker 21 2 0 18 Oct 2024
On the expressiveness and spectral bias of KANs Yixuan Wang Jonathan W. Siegel Ziming Liu Thomas Y. Hou 37 10 0 02 Oct 2024
Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks Fanghui Liu L. Dadi V. Cevher 82 2 0 29 Apr 2024
Expressivity and Approximation Properties of Deep Neural Networks with ReLU $^k$ Activation Juncai He Tong Mao Jinchao Xu 37 3 0 27 Dec 2023
Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities Rahul Parhi Michael Unser 41 5 0 05 Oct 2023
Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks Jonathan W. Siegel 45 7 0 28 Jul 2023
Embeddings between Barron spaces with higher order activation functions T. J. Heeringa L. Spek Felix L. Schwenninger C. Brune 34 3 0 25 May 2023
Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data Jonathan W. Siegel 11 2 0 02 Feb 2023
Deep Learning Meets Sparse Regularization: A Signal Processing Perspective Rahul Parhi Robert D. Nowak 40 25 0 23 Jan 2023
Optimal transport map estimation in general function spaces Vincent Divol Jonathan Niles-Weed Aram-Alexandre Pooladian OT 38 22 0 07 Dec 2022
Limitations on approximation by deep and shallow neural networks G. Petrova P. Wojtaszczyk 19 7 0 30 Nov 2022
A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks E. M. Achour Armand Foucault Sébastien Gerchinovitz Franccois Malgouyres 32 7 0 09 Jun 2022
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space Juncai He R. Tsai Rachel A. Ward 36 8 0 01 Mar 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 32 36 0 01 Jan 2022
Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks Rahul Parhi Robert D. Nowak 56 38 0 18 Sep 2021
Optimal Convergence Rates for the Orthogonal Greedy Algorithm Jonathan W. Siegel Jinchao Xu 21 18 0 28 Jun 2021
$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 130 142 0 26 Jul 2016