A general approximation lower bound in $L^p$ norm, with applications to
feed-forward neural networks

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A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks

9 June 2022

El Mehdi Achour

Armand Foucault

Sébastien Gerchinovitz

Franccois Malgouyres

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Papers citing "A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks"

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Title
Optimal learning of high-dimensional classification problems using deep neural networks P. Petersen F. Voigtlaender 60 10 0 23 Dec 2021
VC dimension of partially quantized neural networks in the overparametrized regime Yutong Wang Clayton D. Scott 76 1 0 06 Oct 2021
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 157 118 0 28 Feb 2021
Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$ -widths of Shallow Neural Networks Jonathan W. Siegel Jinchao Xu 123 87 0 29 Jan 2021
The phase diagram of approximation rates for deep neural networks Dmitry Yarotsky Anton Zhevnerchuk 62 121 0 22 Jun 2019
Universal Approximation with Deep Narrow Networks Patrick Kidger Terry Lyons 130 333 0 21 May 2019
Optimal approximation of continuous functions by very deep ReLU networks Dmitry Yarotsky 192 293 0 10 Feb 2018
Approximation beats concentration? An approximation view on inference with smooth radial kernels M. Belkin 95 69 0 10 Jan 2018
Optimal approximation of piecewise smooth functions using deep ReLU neural networks P. Petersen Felix Voigtländer 223 475 0 15 Sep 2017
Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks Peter L. Bartlett Nick Harvey Christopher Liaw Abbas Mehrabian 208 432 0 08 Mar 2017
Error bounds for approximations with deep ReLU networks Dmitry Yarotsky 195 1,230 0 03 Oct 2016
L p -norm Sauer-Shelah Lemma for Margin Multi-category Classifiers Y. Guermeur 61 22 0 26 Sep 2016
Benefits of depth in neural networks Matus Telgarsky 367 609 0 14 Feb 2016
Covering Numbers for Convex Functions Adityanand Guntuboyina B. Sen 89 77 0 31 Mar 2012