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Optimal approximation of continuous functions by very deep ReLU networks

10 February 2018

Papers citing "Optimal approximation of continuous functions by very deep ReLU networks"

50 / 188 papers shown

Title
Approximation Results for Gradient Descent trained Neural Networks G. Welper 68 1 0 09 Sep 2023
Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Models Changyu Liu Yuling Jiao Junhui Wang Jian Huang AAML 43 2 0 02 Sep 2023
On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem Juncai He 96 11 0 10 Aug 2023
Tractability of approximation by general shallow networks H. Mhaskar Tong Mao 51 2 0 07 Aug 2023
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions Shijun Zhang Jianfeng Lu Hongkai Zhao 58 21 0 13 Jul 2023
Why Shallow Networks Struggle to Approximate and Learn High Frequencies Shijun Zhang Hongkai Zhao Yimin Zhong Haomin Zhou 79 6 0 29 Jun 2023
Universal approximation with complex-valued deep narrow neural networks Paul Geuchen Thomas Jahn Hannes Matt 52 4 0 26 May 2023
Exploring the Complexity of Deep Neural Networks through Functional Equivalence Guohao Shen 103 4 0 19 May 2023
Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regression Guohao Shen Yuling Jiao Yuanyuan Lin Jian Huang 123 3 0 01 May 2023
Deep neural network approximation of composite functions without the curse of dimensionality Adrian Riekert 55 0 0 12 Apr 2023
Approximation of Nonlinear Functionals Using Deep ReLU Networks Linhao Song Jun Fan Dirong Chen Ding-Xuan Zhou 178 16 0 10 Apr 2023
Optimal rates of approximation by shallow ReLU $^k$ neural networks and applications to nonparametric regression Yunfei Yang Ding-Xuan Zhou 194 22 0 04 Apr 2023
Operator learning with PCA-Net: upper and lower complexity bounds S. Lanthaler 95 26 0 28 Mar 2023
Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance Panos Pantidis Habiba Eldababy Christopher Miguel Tagle M. Mobasher 73 22 0 03 Mar 2023
Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data Jonathan W. Siegel 81 2 0 02 Feb 2023
On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network Shijun Zhang Jianfeng Lu Hongkai Zhao CoGe 108 4 0 29 Jan 2023
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs Ke Chen Chunmei Wang Haizhao Yang AI4CE 80 14 0 28 Jan 2023
Selected aspects of complex, hypercomplex and fuzzy neural networks A. Niemczynowicz Radosław Antoni Kycia Maciej Jaworski A. Siemaszko J. Calabuig ... Baruch Schneider Diana Berseghyan Irina Perfiljeva V. Novák Piotr Artiemjew 61 0 0 29 Dec 2022
On Solution Functions of Optimization: Universal Approximation and Covering Number Bounds Ming Jin Vanshaj Khattar Harshal D. Kaushik Bilgehan Sel R. Jia 61 8 0 02 Dec 2022
Limitations on approximation by deep and shallow neural networks G. Petrova P. Wojtaszczyk 115 9 0 30 Nov 2022
Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces Jonathan W. Siegel 195 30 0 25 Nov 2022
On the Universal Approximation Property of Deep Fully Convolutional Neural Networks Ting-Wei Lin Zuowei Shen Qianxiao Li 80 4 0 25 Nov 2022
Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs Seungchan Ko S. Yun Youngjoon Hong 78 5 0 16 Nov 2022
Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks A. Bishop 85 1 0 15 Nov 2022
Active Learning with Neural Networks: Insights from Nonparametric Statistics Yinglun Zhu Robert D. Nowak 102 7 0 15 Oct 2022
Probabilistic partition of unity networks for high-dimensional regression problems Tiffany Fan N. Trask M. DÉlia Eric F. Darve 60 1 0 06 Oct 2022
Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression Jianqing Fan Yihong Gu 93 23 0 05 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 78 3 0 03 Oct 2022
Parameter-varying neural ordinary differential equations with partition-of-unity networks Kookjin Lee N. Trask 82 2 0 01 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 104 7 0 17 Sep 2022
Seeking Interpretability and Explainability in Binary Activated Neural Networks Benjamin Leblanc Pascal Germain FAtt 107 1 0 07 Sep 2022
Neural Network Approximation of Continuous Functions in High Dimensions with Applications to Inverse Problems Santhosh Karnik Rongrong Wang M. Iwen 55 2 0 28 Aug 2022
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning Ben Adcock Juan M. Cardenas N. Dexter 88 10 0 25 Aug 2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems Qianxiao Li T. Lin Zuowei Shen 73 6 0 18 Aug 2022
The BUTTER Zone: An Empirical Study of Training Dynamics in Fully Connected Neural Networks Charles Edison Tripp J. Perr-Sauer L. Hayne M. Lunacek Jamil Gafur AI4CE 97 1 0 25 Jul 2022
Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networks Guohao Shen Yuling Jiao Yuanyuan Lin J. Horowitz Jian Huang 48 4 0 21 Jul 2022
Consistency of Neural Networks with Regularization Xiaoxi Shen Jinghang Lin 39 0 0 22 Jun 2022
A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks El Mehdi Achour Armand Foucault Sébastien Gerchinovitz Franccois Malgouyres 74 7 0 09 Jun 2022
Neural Network Architecture Beyond Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 3DV MDE 114 13 0 19 May 2022
On the inability of Gaussian process regression to optimally learn compositional functions M. Giordano Kolyan Ray Johannes Schmidt-Hieber 118 13 0 16 May 2022
Convolutional and Residual Networks Provably Contain Lottery Tickets R. Burkholz UQCV MLT 77 13 0 04 May 2022
Most Activation Functions Can Win the Lottery Without Excessive Depth R. Burkholz MLT 115 18 0 04 May 2022
ExSpliNet: An interpretable and expressive spline-based neural network Daniele Fakhoury Emanuele Fakhoury H. Speleers 69 41 0 03 May 2022
Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions? Anastasis Kratsios Behnoosh Zamanlooy MLT 117 3 0 24 Apr 2022
How do noise tails impact on deep ReLU networks? Jianqing Fan Yihong Gu Wen-Xin Zhou ODL 126 13 0 20 Mar 2022
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning Yong Zheng Ong Zuowei Shen Haizhao Yang 89 16 0 10 Mar 2022
Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer Beatrice Acciaio Anastasis Kratsios G. Pammer OOD 136 23 0 31 Jan 2022
Approximation bounds for norm constrained neural networks with applications to regression and GANs Yuling Jiao Yang Wang Yunfei Yang 85 20 0 24 Jan 2022
Learning Neural Ranking Models Online from Implicit User Feedback Yiling Jia Hongning Wang 94 6 0 17 Jan 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 216 39 0 01 Jan 2022