Optimal approximation of piecewise smooth functions using deep ReLU neural networks

15 September 2017

Papers citing "Optimal approximation of piecewise smooth functions using deep ReLU neural networks"

29 / 79 papers shown

Title
Approximation of Smoothness Classes by Deep Rectifier Networks Mazen Ali A. Nouy 14 9 0 30 Jul 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 2020
Hierarchically Compositional Tasks and Deep Convolutional Networks Arturo Deza Q. Liao Andrzej Banburski T. Poggio BDL OOD 25 2 0 24 Jun 2020
Approximation in shift-invariant spaces with deep ReLU neural networks Yunfei Yang Zhen Li Yang Wang 34 14 0 25 May 2020
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space Nikolas Nusken Lorenz Richter AI4CE 19 104 0 11 May 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 22 15 0 03 Mar 2020
Deep Network Approximation for Smooth Functions Jianfeng Lu Zuowei Shen Haizhao Yang Shijun Zhang 67 247 0 09 Jan 2020
Uniform error estimates for artificial neural network approximations for heat equations Lukas Gonon Philipp Grohs Arnulf Jentzen David Kofler David Siska 29 34 0 20 Nov 2019
Deep Learning for space-variant deconvolution in galaxy surveys F. Sureau Alexis Lechat Jean-Luc Starck 3DPC 22 21 0 01 Nov 2019
Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization T. Poggio Andrzej Banburski Q. Liao ODL 31 161 0 25 Aug 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 29 33 0 11 Aug 2019
The phase diagram of approximation rates for deep neural networks Dmitry Yarotsky Anton Zhevnerchuk 22 121 0 22 Jun 2019
Deep Network Approximation Characterized by Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 23 182 0 13 Jun 2019
Universal Approximation with Deep Narrow Networks Patrick Kidger Terry Lyons 40 327 0 21 May 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 20 197 0 31 Mar 2019
Deep learning observables in computational fluid dynamics K. Lye Siddhartha Mishra Deep Ray OOD AI4CE 18 158 0 07 Mar 2019
A lattice-based approach to the expressivity of deep ReLU neural networks V. Corlay J. Boutros P. Ciblat L. Brunel 13 4 0 28 Feb 2019
Nonlinear Approximation via Compositions Zuowei Shen Haizhao Yang Shijun Zhang 26 92 0 26 Feb 2019
$Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms$ Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms Ingo Gühring Gitta Kutyniok P. Petersen 22 199 0 21 Feb 2019
The Oracle of DLphi Dominik Alfke W. Baines J. Blechschmidt Mauricio J. del Razo Sarmina Amnon Drory ... L. Thesing Philipp Trunschke Johannes von Lindheim David Weber Melanie Weber 39 0 0 17 Jan 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 16 207 0 08 Jan 2019
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients Arnulf Jentzen Diyora Salimova Timo Welti AI4CE 16 116 0 19 Sep 2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philippe von Wurstemberger 16 167 0 07 Sep 2018
On Tighter Generalization Bound for Deep Neural Networks: CNNs, ResNets, and Beyond Xingguo Li Junwei Lu Zhaoran Wang Jarvis Haupt T. Zhao 27 78 0 13 Jun 2018
Posterior Concentration for Sparse Deep Learning Nicholas G. Polson Veronika Rockova UQCV BDL 30 88 0 24 Mar 2018
Deep Neural Networks Learn Non-Smooth Functions Effectively Masaaki Imaizumi Kenji Fukumizu 20 123 0 13 Feb 2018
Optimal approximation of continuous functions by very deep ReLU networks Dmitry Yarotsky 27 294 0 10 Feb 2018
Optimal Approximation with Sparsely Connected Deep Neural Networks Helmut Bölcskei Philipp Grohs Gitta Kutyniok P. Petersen 30 255 0 04 May 2017
Benefits of depth in neural networks Matus Telgarsky 151 602 0 14 Feb 2016