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Error bounds for approximations with deep ReLU networks
v1v2v3 (latest)

Error bounds for approximations with deep ReLU networks

3 October 2016
Dmitry Yarotsky
ArXiv (abs)PDFHTML

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

50 / 633 papers shown
Estimation error analysis of deep learning on the regression problem on
  the variable exponent Besov space
Estimation error analysis of deep learning on the regression problem on the variable exponent Besov spaceElectronic Journal of Statistics (EJS), 2020
Kazuma Tsuji
Taiji Suzuki
323
17
0
23 Sep 2020
Causal Inference of General Treatment Effects using Neural Networks with
  A Diverging Number of Confounders
Causal Inference of General Treatment Effects using Neural Networks with A Diverging Number of ConfoundersJournal of Econometrics (J. Econometrics), 2020
Xiaohong Chen
Wenshu Fan
Shujie Ma
Zheng-Zhong Zhang
CML
520
16
0
15 Sep 2020
The Seven-League Scheme: Deep learning for large time step Monte Carlo
  simulations of stochastic differential equations
The Seven-League Scheme: Deep learning for large time step Monte Carlo simulations of stochastic differential equationsRisks (Risks), 2020
Shuaiqiang Liu
L. Grzelak
C. Oosterlee
300
12
0
07 Sep 2020
Error estimate for a universal function approximator of ReLU network
  with a local connection
Error estimate for a universal function approximator of ReLU network with a local connection
Jaeyeon Kang
Sunghwan Moon
74
0
0
03 Sep 2020
Universal Approximation Property of Quantum Machine Learning Models in
  Quantum-Enhanced Feature Spaces
Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature SpacesPhysical Review Letters (PRL), 2020
Takahiro Goto
Quoc Hoan Tran
Kohei Nakajima
252
88
0
01 Sep 2020
How Powerful are Shallow Neural Networks with Bandlimited Random
  Weights?
How Powerful are Shallow Neural Networks with Bandlimited Random Weights?
Ming Li
Sho Sonoda
Feilong Cao
Yu Wang
Jiye Liang
236
10
0
19 Aug 2020
A deep network construction that adapts to intrinsic dimensionality
  beyond the domain
A deep network construction that adapts to intrinsic dimensionality beyond the domain
A. Cloninger
T. Klock
AI4CE
361
14
0
06 Aug 2020
Approximation of Smoothness Classes by Deep Rectifier Networks
Approximation of Smoothness Classes by Deep Rectifier NetworksSIAM Journal on Numerical Analysis (SINUM), 2020
Mazen Ali
A. Nouy
151
9
0
30 Jul 2020
On Representing (Anti)Symmetric Functions
On Representing (Anti)Symmetric Functions
Marcus Hutter
128
25
0
30 Jul 2020
Theory of Deep Convolutional Neural Networks II: Spherical Analysis
Theory of Deep Convolutional Neural Networks II: Spherical AnalysisNeural Networks (NN), 2020
Zhiying Fang
Han Feng
Shuo Huang
Ding-Xuan Zhou
223
40
0
28 Jul 2020
Depth separation for reduced deep networks in nonlinear model reduction:
  Distilling shock waves in nonlinear hyperbolic problems
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
170
10
0
28 Jul 2020
Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
Yunmei Chen
Hongcheng Liu
X. Ye
Qingchao Zhang
476
25
0
22 Jul 2020
Deep Learning Based Brain Tumor Segmentation: A Survey
Deep Learning Based Brain Tumor Segmentation: A SurveyComplex & Intelligent Systems (CIS), 2020
Zhihua Liu
Lei Tong
Zheheng Jiang
Long Chen
Feixiang Zhou
Qianni Zhang
Xiangrong Zhang
Ling Li
Huiyu Zhou
3DV
279
289
0
18 Jul 2020
Plateau Phenomenon in Gradient Descent Training of ReLU networks:
  Explanation, Quantification and Avoidance
Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification and AvoidanceSIAM Journal on Scientific Computing (SIAM J. Sci. Comput.), 2020
M. Ainsworth
Yeonjong Shin
ODL
112
29
0
14 Jul 2020
An Adversarial Approach to Structural Estimation
An Adversarial Approach to Structural EstimationSocial Science Research Network (SSRN), 2020
Tetsuya Kaji
E. Manresa
G. Pouliot
314
36
0
13 Jul 2020
Deep neural network approximation for high-dimensional elliptic PDEs
  with boundary conditions
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditionsIMA Journal of Numerical Analysis (IMA J. Numer. Anal.), 2020
Philipp Grohs
L. Herrmann
240
57
0
10 Jul 2020
Expressivity of Deep Neural Networks
Expressivity of Deep Neural Networks
Ingo Gühring
Mones Raslan
Gitta Kutyniok
212
61
0
09 Jul 2020
Error Estimation and Correction from within Neural Network Differential
  Equation Solvers
Error Estimation and Correction from within Neural Network Differential Equation Solvers
Akshunna S. Dogra
162
1
0
09 Jul 2020
Maximum-and-Concatenation Networks
Maximum-and-Concatenation NetworksInternational Conference on Machine Learning (ICML), 2020
Xingyu Xie
Hao Kong
Yue Yu
Wayne Zhang
Guangcan Liu
Zhouchen Lin
270
2
0
09 Jul 2020
Approximation with Neural Networks in Variable Lebesgue Spaces
Approximation with Neural Networks in Variable Lebesgue Spaces
Á. Capel
J. Ocáriz
86
7
0
08 Jul 2020
Regularization Matters: A Nonparametric Perspective on Overparametrized
  Neural Network
Regularization Matters: A Nonparametric Perspective on Overparametrized Neural Network
Tianyang Hu
Wei Cao
Cong Lin
Guang Cheng
313
56
0
06 Jul 2020
Approximation Theory of Tree Tensor Networks: Tensorized Univariate
  Functions -- Part I
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
Mazen Ali
A. Nouy
261
16
0
30 Jun 2020
Estimates on the generalization error of Physics Informed Neural
  Networks (PINNs) for approximating a class of inverse problems for PDEs
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs
Siddhartha Mishra
Roberto Molinaro
PINN
327
315
0
29 Jun 2020
Estimates on the generalization error of Physics Informed Neural
  Networks (PINNs) for approximating PDEs
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs
Siddhartha Mishra
Roberto Molinaro
PINN
299
207
0
29 Jun 2020
Two-Layer Neural Networks for Partial Differential Equations:
  Optimization and Generalization Theory
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
Yaoyu Zhang
Haizhao Yang
398
83
0
28 Jun 2020
Layer Sparsity in Neural Networks
Layer Sparsity in Neural Networks
Mohamed Hebiri
Johannes Lederer
191
10
0
28 Jun 2020
Hierarchically Compositional Tasks and Deep Convolutional Networks
Hierarchically Compositional Tasks and Deep Convolutional NetworksJournal of Vision (J Vis), 2020
Arturo Deza
Q. Liao
Andrzej Banburski
T. Poggio
BDLOOD
184
2
0
24 Jun 2020
Towards Understanding Hierarchical Learning: Benefits of Neural
  Representations
Towards Understanding Hierarchical Learning: Benefits of Neural RepresentationsNeural Information Processing Systems (NeurIPS), 2020
Minshuo Chen
Yu Bai
Jason D. Lee
T. Zhao
Huan Wang
Caiming Xiong
R. Socher
SSL
303
53
0
24 Jun 2020
Deep Network with Approximation Error Being Reciprocal of Width to Power
  of Square Root of Depth
Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
Zuowei Shen
Haizhao Yang
Shijun Zhang
272
7
0
22 Jun 2020
A block coordinate descent optimizer for classification problems
  exploiting convexity
A block coordinate descent optimizer for classification problems exploiting convexity
Ravi G. Patel
N. Trask
Mamikon A. Gulian
E. Cyr
ODL
119
8
0
17 Jun 2020
Globally Injective ReLU Networks
Globally Injective ReLU Networks
Michael Puthawala
K. Kothari
Matti Lassas
Ivan Dokmanić
Maarten V. de Hoop
326
29
0
15 Jun 2020
Learning the geometry of wave-based imaging
Learning the geometry of wave-based imagingNeural Information Processing Systems (NeurIPS), 2020
K. Kothari
Maarten V. de Hoop
Ivan Dokmanić
AI4CE
193
10
0
10 Jun 2020
Approximating Lipschitz continuous functions with GroupSort neural
  networks
Approximating Lipschitz continuous functions with GroupSort neural networks
Ugo Tanielian
Maxime Sangnier
Gérard Biau
199
43
0
09 Jun 2020
RoeNets: Predicting Discontinuity of Hyperbolic Systems from Continuous
  Data
RoeNets: Predicting Discontinuity of Hyperbolic Systems from Continuous Data
S. Xiong
Xingzhe He
Yunjin Tong
Runze Liu
Bo Zhu
AI4CE
121
4
0
07 Jun 2020
Sharp Representation Theorems for ReLU Networks with Precise Dependence
  on Depth
Sharp Representation Theorems for ReLU Networks with Precise Dependence on Depth
Guy Bresler
Dheeraj M. Nagaraj
208
26
0
07 Jun 2020
Neural Networks with Small Weights and Depth-Separation Barriers
Neural Networks with Small Weights and Depth-Separation Barriers
Gal Vardi
Ohad Shamir
212
18
0
31 May 2020
Statistical Guarantees for Regularized Neural Networks
Statistical Guarantees for Regularized Neural NetworksNeural Networks (NN), 2020
Mahsa Taheri
Fang Xie
Johannes Lederer
268
41
0
30 May 2020
Provably Good Solutions to the Knapsack Problem via Neural Networks of
  Bounded Size
Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded SizeAAAI Conference on Artificial Intelligence (AAAI), 2020
Christoph Hertrich
M. Skutella
373
27
0
28 May 2020
Approximation in shift-invariant spaces with deep ReLU neural networks
Approximation in shift-invariant spaces with deep ReLU neural networksNeural Networks (NN), 2020
Yunfei Yang
Zhen Li
Yang Wang
235
14
0
25 May 2020
Model Reduction and Neural Networks for Parametric PDEs
Model Reduction and Neural Networks for Parametric PDEs
K. Bhattacharya
Bamdad Hosseini
Nikola B. Kovachki
Andrew M. Stuart
492
402
0
07 May 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural
  Networks
Numerical Solution of the Parametric Diffusion Equation by Deep Neural NetworksJournal of Scientific Computing (J. Sci. Comput.), 2020
Moritz Geist
P. Petersen
Mones Raslan
R. Schneider
Gitta Kutyniok
204
93
0
25 Apr 2020
Hedging with Linear Regressions and Neural Networks
Hedging with Linear Regressions and Neural NetworksJournal of business & economic statistics (JBES), 2020
Johannes Ruf
Weiguan Wang
122
29
0
19 Apr 2020
A Universal Approximation Theorem of Deep Neural Networks for Expressing
  Probability Distributions
A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributions
Yulong Lu
Jianfeng Lu
224
19
0
19 Apr 2020
Rational neural networks
Rational neural networksNeural Information Processing Systems (NeurIPS), 2020
Nicolas Boullé
Y. Nakatsukasa
Alex Townsend
177
100
0
04 Apr 2020
Depth Selection for Deep ReLU Nets in Feature Extraction and
  Generalization
Depth Selection for Deep ReLU Nets in Feature Extraction and GeneralizationIEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2020
Zhi Han
Siquan Yu
Shao-Bo Lin
Ding-Xuan Zhou
OOD
153
45
0
01 Apr 2020
Nonconvex sparse regularization for deep neural networks and its
  optimality
Nonconvex sparse regularization for deep neural networks and its optimalityNeural Computation (Neural Comput.), 2020
Ilsang Ohn
Yongdai Kim
161
21
0
26 Mar 2020
A Novel Learnable Gradient Descent Type Algorithm for Non-convex
  Non-smooth Inverse Problems
A Novel Learnable Gradient Descent Type Algorithm for Non-convex Non-smooth Inverse Problems
Qingchao Zhang
X. Ye
Hongcheng Liu
Yunmei Chen
148
3
0
15 Mar 2020
Error bounds for PDE-regularized learning
Error bounds for PDE-regularized learning
Carsten Gräser
P. A. Srinivasan
96
0
0
14 Mar 2020
Overall error analysis for the training of deep neural networks via
  stochastic gradient descent with random initialisation
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisationApplied Mathematics and Computation (Appl. Math. Comput.), 2020
Arnulf Jentzen
Timo Welti
160
20
0
03 Mar 2020
Uncertainty Quantification for Sparse Deep Learning
Uncertainty Quantification for Sparse Deep LearningInternational Conference on Artificial Intelligence and Statistics (AISTATS), 2020
Yuexi Wang
Veronika Rockova
BDLUQCV
277
34
0
26 Feb 2020
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