Optimal Approximation with Sparsely Connected Deep Neural Networks

4 May 2017

Papers citing "Optimal Approximation with Sparsely Connected Deep Neural Networks"

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Title
Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks Sehwan Kim F. Liang FedML 57 0 0 04 May 2025
A Metric Topology of Deep Learning for Data Classification Jwo-Yuh Wu L. Huang Wen-Hsuan Li Chun-Hung Liu 83 0 0 20 Jan 2025
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains Ariel Neufeld Philipp Schmocker 23 2 0 18 Oct 2024
Blessing of Dimensionality for Approximating Sobolev Classes on Manifolds Hong Ye Tan Subhadip Mukherjee Junqi Tang Carola-Bibiane Schönlieb 57 0 0 13 Aug 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
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement Holger Boche Adalbert Fono Gitta Kutyniok FaML 31 4 0 18 Jan 2024
Sparse Deep Learning for Time Series Data: Theory and Applications Mingxuan Zhang Y. Sun Faming Liang AI4TS OOD BDL 39 2 0 05 Oct 2023
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
Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs Lukas Gonon A. Jacquier 17 13 0 24 Jul 2023
Approximation analysis of CNNs from a feature extraction view Jianfei Li Han Feng Ding-Xuan Zhou 24 3 0 14 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 32 3 0 03 Oct 2022
Chaotic Hedging with Iterated Integrals and Neural Networks Ariel Neufeld Philipp Schmocker 39 10 0 21 Sep 2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems Qianxiao Li T. Lin Zuowei Shen 24 6 0 18 Aug 2022
Sparse Deep Neural Network for Nonlinear Partial Differential Equations Yuesheng Xu T. Zeng 33 5 0 27 Jul 2022
Neural and spectral operator surrogates: unified construction and expression rate bounds L. Herrmann Christoph Schwab Jakob Zech 51 9 0 11 Jul 2022
A PAC-Bayes oracle inequality for sparse neural networks Maximilian F. Steffen Mathias Trabs UQCV 19 2 0 26 Apr 2022
The Mathematics of Artificial Intelligence Gitta Kutyniok 16 0 0 16 Mar 2022
Bayesian neural network priors for edge-preserving inversion Chen Li Matthew M. Dunlop G. Stadler 20 12 0 20 Dec 2021
Approximation of functions with one-bit neural networks C. S. Güntürk Weilin Li 19 8 0 16 Dec 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 38 28 0 30 Aug 2021
Optimal Approximation with Sparse Neural Networks and Applications Khay Boon Hong 14 0 0 14 Aug 2021
High-Dimensional Distribution Generation Through Deep Neural Networks Dmytro Perekrestenko Léandre Eberhard Helmut Bölcskei OOD 35 6 0 26 Jul 2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 56 36 0 06 Jul 2021
Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions Tong Mao Zhongjie Shi Ding-Xuan Zhou 16 33 0 02 Jul 2021
Layer Folding: Neural Network Depth Reduction using Activation Linearization Amir Ben Dror Niv Zehngut Avraham Raviv E. Artyomov Ran Vitek R. Jevnisek 29 20 0 17 Jun 2021
Metric Entropy Limits on Recurrent Neural Network Learning of Linear Dynamical Systems Clemens Hutter R. Gül Helmut Bölcskei 18 9 0 06 May 2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces Philipp Grohs F. Voigtlaender 16 34 0 06 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
Quantitative approximation results for complex-valued neural networks A. Caragea D. Lee J. Maly G. Pfander F. Voigtlaender 13 5 0 25 Feb 2021
Estimating Vector Fields from Noisy Time Series Harish S. Bhat Majerle Reeves Ramin Raziperchikolaei AI4TS 25 1 0 06 Dec 2020
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks M. Longo Suman Mishra T. Konstantin Rusch Christoph Schwab 35 20 0 06 Sep 2020
Phase Transitions in Rate Distortion Theory and Deep Learning Philipp Grohs Andreas Klotz F. Voigtlaender 14 7 0 03 Aug 2020
Approximation of Smoothness Classes by Deep Rectifier Networks Mazen Ali A. Nouy 11 9 0 30 Jul 2020
Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems Donsub Rim Luca Venturi Joan Bruna Benjamin Peherstorfer 28 9 0 28 Jul 2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions Philipp Grohs L. Herrmann 30 52 0 10 Jul 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 2020
Approximation in shift-invariant spaces with deep ReLU neural networks Yunfei Yang Zhen Li Yang Wang 34 14 0 25 May 2020
Learning on dynamic statistical manifolds F. Boso D. Tartakovsky 24 10 0 07 May 2020
Deep Network Approximation for Smooth Functions Jianfeng Lu Zuowei Shen Haizhao Yang Shijun Zhang 67 247 0 09 Jan 2020
Stochastic Feedforward Neural Networks: Universal Approximation Thomas Merkh Guido Montúfar 17 8 0 22 Oct 2019
Nonlinear Approximation and (Deep) ReLU Networks Ingrid Daubechies Ronald A. DeVore S. Foucart Boris Hanin G. Petrova 22 138 0 05 May 2019
Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks N. D. Santo S. Deparis Luca Pegolotti 19 66 0 02 Apr 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 15 158 0 07 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 17 199 0 21 Feb 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 14 207 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 11 167 0 07 Sep 2018
NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation Anastasis Kratsios Cody B. Hyndman OOD 28 17 0 31 Aug 2018