Expressivity of Deep Neural Networks

9 July 2020

Papers citing "Expressivity of Deep Neural Networks"

50 / 59 papers shown

Title
From Alexnet to Transformers: Measuring the Non-linearity of Deep Neural Networks with Affine Optimal Transport Quentin Bouniot I. Redko Anton Mallasto Charlotte Laclau Karol Arndt Oliver Struckmeier Markus Heinonen Ville Kyrki Samuel Kaski 146 2 0 17 Oct 2023
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 99 1,544 0 10 Jul 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 64 126 0 08 Jul 2019
The phase diagram of approximation rates for deep neural networks Dmitry Yarotsky Anton Zhevnerchuk 65 122 0 22 Jun 2019
Approximation spaces of deep neural networks Rémi Gribonval Gitta Kutyniok M. Nielsen Felix Voigtländer 89 125 0 03 May 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 87 198 0 31 Mar 2019
Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks Kenta Oono Taiji Suzuki 96 58 0 24 Mar 2019
Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems C. Reisinger Yufei Zhang 42 70 0 15 Mar 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 89 200 0 21 Feb 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 68 210 0 08 Jan 2019
Physics-informed deep generative models Yibo Yang P. Perdikaris AI4CE PINN 79 59 0 09 Dec 2018
Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality Taiji Suzuki 182 246 0 18 Oct 2018
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 49 119 0 19 Sep 2018
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations Julius Berner Philipp Grohs Arnulf Jentzen 66 183 0 09 Sep 2018
Equivalence of approximation by convolutional neural networks and fully-connected networks P. Petersen Felix Voigtländer 60 80 0 04 Sep 2018
ResNet with one-neuron hidden layers is a Universal Approximator Hongzhou Lin Stefanie Jegelka 105 229 0 28 Jun 2018
Universality of Deep Convolutional Neural Networks Ding-Xuan Zhou HAI PINN 412 517 0 28 May 2018
Universal approximations of invariant maps by neural networks Dmitry Yarotsky 124 214 0 26 Apr 2018
Deep Neural Networks Learn Non-Smooth Functions Effectively Masaaki Imaizumi Kenji Fukumizu 150 124 0 13 Feb 2018
Optimal approximation of continuous functions by very deep ReLU networks Dmitry Yarotsky 196 294 0 10 Feb 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 120 757 0 20 Jan 2018
Expressive power of recurrent neural networks Valentin Khrulkov Alexander Novikov Ivan Oseledets 89 114 0 02 Nov 2017
Approximating Continuous Functions by ReLU Nets of Minimal Width Boris Hanin Mark Sellke 107 239 0 31 Oct 2017
Optimization Landscape and Expressivity of Deep CNNs Quynh N. Nguyen Matthias Hein 74 29 0 30 Oct 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 125 1,390 0 30 Sep 2017
Optimal approximation of piecewise smooth functions using deep ReLU neural networks P. Petersen Felix Voigtländer 223 475 0 15 Sep 2017
The Expressive Power of Neural Networks: A View from the Width Zhou Lu Hongming Pu Feicheng Wang Zhiqiang Hu Liwei Wang 99 899 0 08 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 93 2,067 0 24 Aug 2017
Nonparametric regression using deep neural networks with ReLU activation function Johannes Schmidt-Hieber 238 816 0 22 Aug 2017
Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations Boris Hanin 64 356 0 09 Aug 2017
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations Weinan E Jiequn Han Arnulf Jentzen 125 797 0 15 Jun 2017
Neural networks and rational functions Matus Telgarsky 66 82 0 11 Jun 2017
The power of deeper networks for expressing natural functions David Rolnick Max Tegmark 158 174 0 16 May 2017
Optimal Approximation with Sparsely Connected Deep Neural Networks Helmut Bölcskei Philipp Grohs Gitta Kutyniok P. Petersen 197 256 0 04 May 2017
Identity Matters in Deep Learning Moritz Hardt Tengyu Ma OOD 94 399 0 14 Nov 2016
Understanding Deep Neural Networks with Rectified Linear Units R. Arora A. Basu Poorya Mianjy Anirbit Mukherjee PINN 164 643 0 04 Nov 2016
Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review T. Poggio H. Mhaskar Lorenzo Rosasco Brando Miranda Q. Liao 143 576 0 02 Nov 2016
Deep Learning Approximation for Stochastic Control Problems Jiequn Han E. Weinan BDL 61 197 0 02 Nov 2016
Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks Itay Safran Ohad Shamir 87 175 0 31 Oct 2016
Why Deep Neural Networks for Function Approximation? Shiyu Liang R. Srikant 138 385 0 13 Oct 2016
Error bounds for approximations with deep ReLU networks Dmitry Yarotsky 198 1,233 0 03 Oct 2016
Deep vs. shallow networks : An approximation theory perspective H. Mhaskar T. Poggio 165 341 0 10 Aug 2016
On the Expressive Power of Deep Neural Networks M. Raghu Ben Poole Jon M. Kleinberg Surya Ganguli Jascha Narain Sohl-Dickstein 66 790 0 16 Jun 2016
Learning Functions: When Is Deep Better Than Shallow H. Mhaskar Q. Liao T. Poggio 72 144 0 03 Mar 2016
Benefits of depth in neural networks Matus Telgarsky 380 609 0 14 Feb 2016
The Power of Depth for Feedforward Neural Networks Ronen Eldan Ohad Shamir 221 732 0 12 Dec 2015
Deep Residual Learning for Image Recognition Kaiming He Xinming Zhang Shaoqing Ren Jian Sun MedIm 2.2K 194,510 0 10 Dec 2015
Provable approximation properties for deep neural networks Uri Shaham A. Cloninger Ronald R. Coifman 181 231 0 24 Sep 2015
On the Expressive Power of Deep Learning: A Tensor Analysis Nadav Cohen Or Sharir Amnon Shashua 81 472 0 16 Sep 2015
Highway Networks R. Srivastava Klaus Greff Jürgen Schmidhuber 183 1,773 0 03 May 2015