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
Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Models Changyu Liu Yuling Jiao Junhui Wang Jian Huang AAML 17 2 0 02 Sep 2023
On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem Juncai He 21 10 0 10 Aug 2023
Tractability of approximation by general shallow networks H. Mhaskar Tong Mao 11 2 0 07 Aug 2023
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions Shijun Zhang Jianfeng Lu Hongkai Zhao 27 17 0 13 Jul 2023
Why Shallow Networks Struggle with Approximating and Learning High Frequency: A Numerical Study Shijun Zhang Hongkai Zhao Yimin Zhong Haomin Zhou 21 7 0 29 Jun 2023
Universal approximation with complex-valued deep narrow neural networks Paul Geuchen Thomas Jahn Hannes Matt 18 3 0 26 May 2023
Exploring the Complexity of Deep Neural Networks through Functional Equivalence Guohao Shen 30 2 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 50 3 0 01 May 2023
Deep neural network approximation of composite functions without the curse of dimensionality Adrian Riekert 24 0 0 12 Apr 2023
Approximation of Nonlinear Functionals Using Deep ReLU Networks Linhao Song Jun Fan Dirong Chen Ding-Xuan Zhou 15 14 0 10 Apr 2023
Optimal rates of approximation by shallow ReLU $^k$ neural networks and applications to nonparametric regression Yunfei Yang Ding-Xuan Zhou 39 19 0 04 Apr 2023
Operator learning with PCA-Net: upper and lower complexity bounds S. Lanthaler 26 25 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 35 20 0 03 Mar 2023
Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data Jonathan W. Siegel 14 2 0 02 Feb 2023
On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network Shijun Zhang Jianfeng Lu Hongkai Zhao CoGe 36 4 0 29 Jan 2023
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs Ke Chen Chunmei Wang Haizhao Yang AI4CE 24 13 0 28 Jan 2023
Selected aspects of complex, hypercomplex and fuzzy neural networks A. Niemczynowicz R. Kycia Maciej Jaworski A. Siemaszko J. Calabuig ... Baruch Schneider Diana Berseghyan Irina Perfiljeva V. Novák Piotr Artiemjew 27 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 24 8 0 02 Dec 2022
Limitations on approximation by deep and shallow neural networks G. Petrova P. Wojtaszczyk 19 7 0 30 Nov 2022
Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces Jonathan W. Siegel 25 28 0 25 Nov 2022
On the Universal Approximation Property of Deep Fully Convolutional Neural Networks Ting-Wei Lin Zuowei Shen Qianxiao Li 34 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 22 5 0 16 Nov 2022
Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks A. Bishop 42 1 0 15 Nov 2022
Active Learning with Neural Networks: Insights from Nonparametric Statistics Yinglun Zhu Robert D. Nowak 72 6 0 15 Oct 2022
Probabilistic partition of unity networks for high-dimensional regression problems Tiffany Fan N. Trask M. DÉlia Eric F. Darve 11 1 0 06 Oct 2022
Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression Jianqing Fan Yihong Gu 16 21 0 05 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
Parameter-varying neural ordinary differential equations with partition-of-unity networks Kookjin Lee N. Trask 22 2 0 01 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 52 6 0 17 Sep 2022
Seeking Interpretability and Explainability in Binary Activated Neural Networks Benjamin Leblanc Pascal Germain FAtt 40 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 16 2 0 28 Aug 2022
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning Ben Adcock Juan M. Cardenas N. Dexter 33 8 0 25 Aug 2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems Qianxiao Li T. Lin Zuowei Shen 24 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 21 0 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 27 4 0 21 Jul 2022
Consistency of Neural Networks with Regularization Xiaoxi Shen Jinghang Lin 25 0 0 22 Jun 2022
A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks E. M. Achour Armand Foucault Sébastien Gerchinovitz Franccois Malgouyres 32 7 0 09 Jun 2022
Neural Network Architecture Beyond Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 3DV MDE 33 13 0 19 May 2022
On the inability of Gaussian process regression to optimally learn compositional functions M. Giordano Kolyan Ray Johannes Schmidt-Hieber 39 12 0 16 May 2022
Convolutional and Residual Networks Provably Contain Lottery Tickets R. Burkholz UQCV MLT 40 13 0 04 May 2022
Most Activation Functions Can Win the Lottery Without Excessive Depth R. Burkholz MLT 74 18 0 04 May 2022
ExSpliNet: An interpretable and expressive spline-based neural network Daniele Fakhoury Emanuele Fakhoury H. Speleers 11 33 0 03 May 2022
Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions? Anastasis Kratsios Behnoosh Zamanlooy MLT 67 3 0 24 Apr 2022
How do noise tails impact on deep ReLU networks? Jianqing Fan Yihong Gu Wen-Xin Zhou ODL 38 13 0 20 Mar 2022
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning Yong Zheng Ong Zuowei Shen Haizhao Yang 18 15 0 10 Mar 2022
Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer Beatrice Acciaio Anastasis Kratsios G. Pammer OOD 52 20 0 31 Jan 2022
Approximation bounds for norm constrained neural networks with applications to regression and GANs Yuling Jiao Yang Wang Yunfei Yang 36 19 0 24 Jan 2022
Learning Neural Ranking Models Online from Implicit User Feedback Yiling Jia Hongning Wang 11 6 0 17 Jan 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 32 36 0 01 Jan 2022
Risk bounds for aggregated shallow neural networks using Gaussian prior L. Tinsi A. Dalalyan BDL 20 7 0 21 Dec 2021