$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

21 February 2019

Papers citing "Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms"

28 / 28 papers shown

Title
Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks A. Celaya Yimo Wang David T. Fuentes Beatrice Riviere 41 0 0 12 Feb 2025
On the optimal approximation of Sobolev and Besov functions using deep ReLU neural networks Yunfei Yang 62 2 0 02 Sep 2024
Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning Tyler Chang Andrew Gillette R. Maulik 49 2 0 04 Apr 2024
Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts Anastasis Kratsios Haitz Sáez de Ocáriz Borde Takashi Furuya Marc T. Law MoE 41 1 0 05 Feb 2024
Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss T. Getu Georges Kaddoum M. Bennis 40 1 0 13 Sep 2023
Rates of Approximation by ReLU Shallow Neural Networks Tong Mao Ding-Xuan Zhou 29 19 0 24 Jul 2023
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives Yahong Yang Haizhao Yang Yang Xiang 31 19 0 15 May 2023
Deep neural network approximation of composite functions without the curse of dimensionality Adrian Riekert 24 0 0 12 Apr 2023
Operator theory, kernels, and Feedforward Neural Networks P. Jorgensen Myung-Sin Song James Tian 35 0 0 03 Jan 2023
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 32 3 0 03 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 52 6 0 17 Sep 2022
Variational Physics Informed Neural Networks: the role of quadratures and test functions S. Berrone C. Canuto Moreno Pintore 23 40 0 05 Sep 2021
Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks S. Maddu D. Sturm Christian L. Müller I. Sbalzarini AI4CE 26 81 0 02 Jul 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 21 100 0 28 Jun 2021
ReLU Deep Neural Networks from the Hierarchical Basis Perspective Juncai He Lin Li Jinchao Xu AI4CE 28 30 0 10 May 2021
On the approximation of functions by tanh neural networks Tim De Ryck S. Lanthaler Siddhartha Mishra 21 137 0 18 Apr 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 26 45 0 10 Mar 2021
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 28 30 0 15 Dec 2020
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 36 29 0 11 Dec 2020
Neural Network Approximation: Three Hidden Layers Are Enough Zuowei Shen Haizhao Yang Shijun Zhang 30 115 0 25 Oct 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 2020
Deep Network Approximation for Smooth Functions Jianfeng Lu Zuowei Shen Haizhao Yang Shijun Zhang 67 247 0 09 Jan 2020
Deep Learning via Dynamical Systems: An Approximation Perspective Qianxiao Li Ting Lin Zuowei Shen AI4TS AI4CE 19 107 0 22 Dec 2019
Growing axons: greedy learning of neural networks with application to function approximation Daria Fokina Ivan V. Oseledets 21 18 0 28 Oct 2019
Universal Approximation with Deep Narrow Networks Patrick Kidger Terry Lyons 31 324 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 Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 14 207 0 08 Jan 2019
On the stable recovery of deep structured linear networks under sparsity constraints F. Malgouyres 22 7 0 31 May 2017