Error bounds for approximations with deep ReLU networks

3 October 2016

Papers citing "Error bounds for approximations with deep ReLU networks"

50 / 202 papers shown

Title
Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets Subhayan De Matthew J. Reynolds M. Hassanaly Ryan N. King Alireza Doostan AI4CE 26 37 0 03 Apr 2022
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation Josiah Park Stephan Wojtowytsch 26 1 0 25 Mar 2022
How do noise tails impact on deep ReLU networks? Jianqing Fan Yihong Gu Wen-Xin Zhou ODL 38 13 0 20 Mar 2022
The Mathematics of Artificial Intelligence Gitta Kutyniok 16 0 0 16 Mar 2022
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space Juncai He R. Tsai Rachel A. Ward 36 8 0 01 Mar 2022
Rates of convergence for nonparametric estimation of singular distributions using generative adversarial networks Minwoo Chae GAN 32 4 0 07 Feb 2022
Interplay between depth of neural networks and locality of target functions Takashi Mori Masakuni Ueda 25 0 0 28 Jan 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 26 1,180 0 14 Jan 2022
De Rham compatible Deep Neural Network FEM M. Longo J. Opschoor Nico Disch Christoph Schwab Jakob Zech 22 8 0 14 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
Approximation of functions with one-bit neural networks C. S. Güntürk Weilin Li 19 8 0 16 Dec 2021
ModelPred: A Framework for Predicting Trained Model from Training Data Yingyan Zeng Jiachen T. Wang Si-An Chen H. Just Ran Jin R. Jia TDI MU 33 2 0 24 Nov 2021
$Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,γ_d)$$ Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,γ_d)$ Christoph Schwab Jakob Zech 14 3 0 13 Nov 2021
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method Zhongjian Wang Jack Xin Zhiwen Zhang 39 15 0 02 Nov 2021
Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark S. Dubey S. Singh B. B. Chaudhuri 41 641 0 29 Sep 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 38 28 0 30 Aug 2021
Convergence rates of deep ReLU networks for multiclass classification Thijs Bos Johannes Schmidt-Hieber 19 22 0 02 Aug 2021
Neural Network Approximation of Refinable Functions Ingrid Daubechies Ronald A. DeVore Nadav Dym Shira Faigenbaum-Golovin S. Kovalsky Kung-Chin Lin Josiah Park G. Petrova B. Sober 23 14 0 28 Jul 2021
Convergence of Deep ReLU Networks Yuesheng Xu Haizhang Zhang 37 26 0 27 Jul 2021
Robust Nonparametric Regression with Deep Neural Networks Guohao Shen Yuling Jiao Yuanyuan Lin Jian Huang OOD 33 13 0 21 Jul 2021
Random Neural Networks in the Infinite Width Limit as Gaussian Processes Boris Hanin BDL 32 43 0 04 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
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 38 26 0 14 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
Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums Guido Montúfar Yue Ren Leon Zhang 13 39 0 16 Apr 2021
$Function approximation by deep neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$$ Function approximation by deep neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$ A. Beknazaryan 15 5 0 15 Mar 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
Parametric Complexity Bounds for Approximating PDEs with Neural Networks Tanya Marwah Zachary Chase Lipton Andrej Risteski 28 19 0 03 Mar 2021
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 101 115 0 28 Feb 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
Size and Depth Separation in Approximating Benign Functions with Neural Networks Gal Vardi Daniel Reichman T. Pitassi Ohad Shamir 26 7 0 30 Jan 2021
Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training Cong Fang Hangfeng He Qi Long Weijie J. Su FAtt 130 165 0 29 Jan 2021
Partition of unity networks: deep hp-approximation Kookjin Lee N. Trask Ravi G. Patel Mamikon A. Gulian E. Cyr 22 30 0 27 Jan 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 36 21 0 13 Jan 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 36 37 0 05 Jan 2021
Machine Learning Advances for Time Series Forecasting Ricardo P. Masini M. C. Medeiros Eduardo F. Mendes AI4TS 21 270 0 23 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
Estimation of the Mean Function of Functional Data via Deep Neural Networks Shuoyang Wang Guanqun Cao Zuofeng Shang 30 20 0 08 Dec 2020
The universal approximation theorem for complex-valued neural networks F. Voigtlaender 27 62 0 06 Dec 2020
Learning Barrier Functions with Memory for Robust Safe Navigation Kehan Long Cheng Qian Jorge Cortés Nikolay Atanasov 25 52 0 03 Nov 2020
Neural Network Approximation: Three Hidden Layers Are Enough Zuowei Shen Haizhao Yang Shijun Zhang 30 115 0 25 Oct 2020
On the Number of Linear Functions Composing Deep Neural Network: Towards a Refined Definition of Neural Networks Complexity Yuuki Takai Akiyoshi Sannai Matthieu Cordonnier 71 4 0 23 Oct 2020
Deep Equals Shallow for ReLU Networks in Kernel Regimes A. Bietti Francis R. Bach 28 86 0 30 Sep 2020
Causal Inference of General Treatment Effects using Neural Networks with A Diverging Number of Confounders Xiaohong Chen Yong Liu Shujie Ma Zheng-Zhong Zhang CML 22 11 0 15 Sep 2020
Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces Takahiro Goto Quoc Hoan Tran Kohei Nakajima 25 64 0 01 Sep 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
Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction Yunmei Chen Hongcheng Liu X. Ye Qingchao Zhang 56 23 0 22 Jul 2020