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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
Convergence analysis of unsupervised Legendre-Galerkin neural networks
  for linear second-order elliptic PDEs
Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs
Seungchan Ko
S. Yun
Youngjoon Hong
195
6
0
16 Nov 2022
A Law of Data Separation in Deep Learning
A Law of Data Separation in Deep LearningProceedings of the National Academy of Sciences of the United States of America (PNAS), 2022
Hangfeng He
Weijie J. Su
OOD
344
49
0
31 Oct 2022
Ensemble Projection Pursuit for General Nonparametric Regression
Ensemble Projection Pursuit for General Nonparametric RegressionAnnals of Statistics (Ann. Stat.), 2022
Haoran Zhan
Mingke Zhang
Yingcun Xia
237
1
0
26 Oct 2022
Learning Ability of Interpolating Deep Convolutional Neural Networks
Learning Ability of Interpolating Deep Convolutional Neural NetworksSocial Science Research Network (SSRN), 2022
Tiancong Zhou
X. Huo
AI4CE
192
14
0
25 Oct 2022
Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis
Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis
Luca Galimberti
Anastasis Kratsios
Giulia Livieri
OOD
398
19
0
24 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A
  Representational Perspective
Neural Network Approximations of PDEs Beyond Linearity: A Representational PerspectiveInternational Conference on Machine Learning (ICML), 2022
Tanya Marwah
Zachary Chase Lipton
Jianfeng Lu
Andrej Risteski
309
15
0
21 Oct 2022
Towards Global Neural Network Abstractions with Locally-Exact
  Reconstruction
Towards Global Neural Network Abstractions with Locally-Exact ReconstructionNeural Networks (NN), 2022
Edoardo Manino
I. Bessa
Lucas C. Cordeiro
232
3
0
21 Oct 2022
Deep neural network expressivity for optimal stopping problems
Deep neural network expressivity for optimal stopping problemsFinance and Stochastics (Fin. Stoch.), 2022
Lukas Gonon
230
10
0
19 Oct 2022
SignReLU neural network and its approximation ability
SignReLU neural network and its approximation abilityJournal of Computational and Applied Mathematics (JCAM), 2022
Jianfei Li
Han Feng
Ding-Xuan Zhou
328
8
0
19 Oct 2022
Signal Processing for Implicit Neural Representations
Signal Processing for Implicit Neural RepresentationsNeural Information Processing Systems (NeurIPS), 2022
Dejia Xu
Peihao Wang
Lezhi Li
Zhiwen Fan
Zinan Lin
294
51
0
17 Oct 2022
Active Learning with Neural Networks: Insights from Nonparametric Statistics
Active Learning with Neural Networks: Insights from Nonparametric StatisticsNeural Information Processing Systems (NeurIPS), 2022
Yinglun Zhu
Robert D. Nowak
316
12
0
15 Oct 2022
Approximation analysis of CNNs from a feature extraction view
Approximation analysis of CNNs from a feature extraction viewSocial Science Research Network (SSRN), 2022
Jianfei Li
Han Feng
Ding-Xuan Zhou
292
5
0
14 Oct 2022
LieGG: Studying Learned Lie Group Generators
LieGG: Studying Learned Lie Group GeneratorsNeural Information Processing Systems (NeurIPS), 2022
A. Moskalev
A. Sepliarskaia
Ivan Sosnovik
A. Smeulders
336
33
0
09 Oct 2022
Probabilistic partition of unity networks for high-dimensional
  regression problems
Probabilistic partition of unity networks for high-dimensional regression problemsInternational Journal for Numerical Methods in Engineering (IJNME), 2022
Tiffany Fan
N. Trask
M. DÉlia
Eric F. Darve
212
1
0
06 Oct 2022
Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High
  Dimensional Regression
Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional RegressionJournal of the American Statistical Association (JASA), 2022
Jianqing Fan
Yihong Gu
462
38
0
05 Oct 2022
Analysis of the rate of convergence of an over-parametrized deep neural
  network estimate learned by gradient descent
Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descentIEEE Transactions on Information Theory (IEEE Trans. Inf. Theory), 2022
Michael Kohler
A. Krzyżak
178
12
0
04 Oct 2022
Nonlinear Reconstruction for Operator Learning of PDEs with
  Discontinuities
Nonlinear Reconstruction for Operator Learning of PDEs with DiscontinuitiesInternational Conference on Learning Representations (ICLR), 2022
S. Lanthaler
Roberto Molinaro
Patrik Hadorn
Siddhartha Mishra
356
29
0
03 Oct 2022
Limitations of neural network training due to numerical instability of
  backpropagation
Limitations of neural network training due to numerical instability of backpropagationAdvances in Computational Mathematics (ACM), 2022
Clemens Karner
V. Kazeev
P. Petersen
264
5
0
03 Oct 2022
Parameter-varying neural ordinary differential equations with
  partition-of-unity networks
Parameter-varying neural ordinary differential equations with partition-of-unity networks
Kookjin Lee
N. Trask
246
2
0
01 Oct 2022
Mega: Moving Average Equipped Gated Attention
Mega: Moving Average Equipped Gated AttentionInternational Conference on Learning Representations (ICLR), 2022
Xuezhe Ma
Chunting Zhou
Xiang Kong
Junxian He
Liangke Gui
Graham Neubig
Jonathan May
Luke Zettlemoyer
339
219
0
21 Sep 2022
Approximation results for Gradient Descent trained Shallow Neural
  Networks in $1d$
Approximation results for Gradient Descent trained Shallow Neural Networks in 1d1d1d
R. Gentile
G. Welper
ODL
276
9
0
17 Sep 2022
Small Transformers Compute Universal Metric Embeddings
Small Transformers Compute Universal Metric EmbeddingsJournal of machine learning research (JMLR), 2022
Anastasis Kratsios
Valentin Debarnot
Ivan Dokmanić
319
14
0
14 Sep 2022
Seeking Interpretability and Explainability in Binary Activated Neural
  Networks
Seeking Interpretability and Explainability in Binary Activated Neural Networks
Benjamin Leblanc
Pascal Germain
FAtt
460
1
0
07 Sep 2022
Solving Elliptic Problems with Singular Sources using Singularity
  Splitting Deep Ritz Method
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz MethodSIAM Journal on Scientific Computing (SISC), 2022
Tianhao Hu
Bangti Jin
Zhi Zhou
339
8
0
07 Sep 2022
A variational neural network approach for glacier modelling with
  nonlinear rheology
A variational neural network approach for glacier modelling with nonlinear rheologyCommunications in Computational Physics (Commun. Comput. Phys.), 2022
Tiangang Cui
Zhongjian Wang
Zhiwen Zhang
257
4
0
05 Sep 2022
From Monte Carlo to neural networks approximations of boundary value
  problems
From Monte Carlo to neural networks approximations of boundary value problems
L. Beznea
Iulian Cîmpean
Oana Lupascu-Stamate
Ionel Popescu
A. Zarnescu
126
5
0
03 Sep 2022
On the universal consistency of an over-parametrized deep neural network
  estimate learned by gradient descent
On the universal consistency of an over-parametrized deep neural network estimate learned by gradient descentAnnals of the Institute of Statistical Mathematics (AISM), 2022
Selina Drews
Michael Kohler
164
19
0
30 Aug 2022
CAS4DL: Christoffel Adaptive Sampling for function approximation via
  Deep Learning
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep LearningSampling Theory, Signal Processing, and Data Analysis (TSPDA), 2022
Ben Adcock
Juan M. Cardenas
N. Dexter
200
13
0
25 Aug 2022
Strategic Decision-Making in the Presence of Information Asymmetry:
  Provably Efficient RL with Algorithmic Instruments
Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments
Mengxin Yu
Zhuoran Yang
Jianqing Fan
OffRL
336
9
0
23 Aug 2022
Semi-Supervised Manifold Learning with Complexity Decoupled Chart
  Autoencoders
Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders
Stefan C. Schonsheck
Scott Mahan
T. Klock
A. Cloninger
Rongjie Lai
DRL
214
7
0
22 Aug 2022
Shallow neural network representation of polynomials
Shallow neural network representation of polynomials
A. Beknazaryan
373
0
0
17 Aug 2022
Universal Solutions of Feedforward ReLU Networks for Interpolations
Universal Solutions of Feedforward ReLU Networks for Interpolations
Changcun Huang
316
2
0
16 Aug 2022
K-UNN: k-Space Interpolation With Untrained Neural Network
K-UNN: k-Space Interpolation With Untrained Neural Network
Zhuoxu Cui
Seng Jia
Qingyong Zhu
Congcong Liu
Zhilang Qiu
Yuanyuan Liu
Jing Cheng
Haifeng Wang
Yanjie Zhu
Dong Liang
143
1
0
11 Aug 2022
Optimal Convergence Rates of Deep Neural Networks in a Classification
  Setting
Optimal Convergence Rates of Deep Neural Networks in a Classification SettingElectronic Journal of Statistics (EJS), 2022
Josephine T. Meyer
150
2
0
25 Jul 2022
Estimation of Non-Crossing Quantile Regression Process with Deep ReQU
  Neural Networks
Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networks
Guohao Shen
Yuling Jiao
Yuanyuan Lin
J. Horowitz
Jian Huang
162
4
0
21 Jul 2022
Approximation Power of Deep Neural Networks: an explanatory mathematical
  survey
Approximation Power of Deep Neural Networks: an explanatory mathematical survey
Mohammad Motamed
152
4
0
19 Jul 2022
Approximation Capabilities of Neural Networks using Morphological
  Perceptrons and Generalizations
Approximation Capabilities of Neural Networks using Morphological Perceptrons and GeneralizationsAsilomar Conference on Signals, Systems and Computers (ACSSC), 2022
William Chang
Hassan Hamad
K. Chugg
90
2
0
16 Jul 2022
Error analysis for deep neural network approximations of parametric
  hyperbolic conservation laws
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
Tim De Ryck
Siddhartha Mishra
PINN
181
15
0
15 Jul 2022
Size and depth of monotone neural networks: interpolation and
  approximation
Size and depth of monotone neural networks: interpolation and approximationIEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2022
Dan Mikulincer
Daniel Reichman
222
11
0
12 Jul 2022
Functional Generalized Empirical Likelihood Estimation for Conditional
  Moment Restrictions
Functional Generalized Empirical Likelihood Estimation for Conditional Moment RestrictionsInternational Conference on Machine Learning (ICML), 2022
Heiner Kremer
Jia-Jie Zhu
Krikamol Muandet
Bernhard Schölkopf
220
8
0
11 Jul 2022
Minimax Optimal Deep Neural Network Classifiers Under Smooth Decision
  Boundary
Minimax Optimal Deep Neural Network Classifiers Under Smooth Decision Boundary
Tianyang Hu
Ruiqi Liu
Zuofeng Shang
Guang Cheng
138
3
0
04 Jul 2022
Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks
  for PDEs
Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs
A. A. Ramabathiran
P. Ramachandran
AI4CE
202
0
0
01 Jul 2022
Expressive power of binary and ternary neural networks
Expressive power of binary and ternary neural networks
A. Beknazaryan
MQ
191
0
0
27 Jun 2022
Consistency of Neural Networks with Regularization
Consistency of Neural Networks with Regularization
Xiaoxi Shen
Jinghang Lin
174
0
0
22 Jun 2022
Simultaneous approximation of a smooth function and its derivatives by
  deep neural networks with piecewise-polynomial activations
Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activationsNeural Networks (NN), 2022
Denis Belomestny
A. Naumov
Nikita Puchkin
S. Samsonov
144
34
0
20 Jun 2022
Piecewise Linear Neural Networks and Deep Learning
Piecewise Linear Neural Networks and Deep LearningNature Reviews Methods Primers (NRMP), 2022
Qinghua Tao
Li Li
Xiaolin Huang
Xiangming Xi
Shuning Wang
Johan A. K. Suykens
152
39
0
18 Jun 2022
Density Regression and Uncertainty Quantification with Bayesian Deep
  Noise Neural Networks
Density Regression and Uncertainty Quantification with Bayesian Deep Noise Neural Networks
Daiwei Zhang
Tianci Liu
Jian Kang
BDLUQCV
191
3
0
12 Jun 2022
Benefits of Overparameterized Convolutional Residual Networks: Function
  Approximation under Smoothness Constraint
Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness ConstraintInternational Conference on Machine Learning (ICML), 2022
Hao Liu
Minshuo Chen
Siawpeng Er
Wenjing Liao
Tong Zhang
Tuo Zhao
185
15
0
09 Jun 2022
A general approximation lower bound in $L^p$ norm, with applications to
  feed-forward neural networks
A general approximation lower bound in LpL^pLp norm, with applications to feed-forward neural networksNeural Information Processing Systems (NeurIPS), 2022
El Mehdi Achour
Armand Foucault
Sébastien Gerchinovitz
Franccois Malgouyres
221
12
0
09 Jun 2022
Deep neural networks can stably solve high-dimensional, noisy,
  non-linear inverse problems
Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problemsAnalysis and Applications (Anal. Appl.), 2022
Andrés Felipe Lerma Pineda
P. Petersen
316
7
0
02 Jun 2022
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