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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
Learning the mapping $\mathbf{x}\mapsto \sum_{i=1}^d x_i^2$: the cost of
  finding the needle in a haystack
Learning the mapping x↦∑i=1dxi2\mathbf{x}\mapsto \sum_{i=1}^d x_i^2x↦∑i=1d​xi2​: the cost of finding the needle in a haystack
Jiefu Zhang
Leonardo Zepeda-Núnez
Xingtai Lv
Lin Lin
100
0
0
24 Feb 2020
A closer look at the approximation capabilities of neural networks
A closer look at the approximation capabilities of neural networksInternational Conference on Learning Representations (ICLR), 2020
Kai Fong Ernest Chong
72
18
0
16 Feb 2020
Learning CHARME models with neural networks
Learning CHARME models with neural networks
José G. Gómez-García
M. Fadili
C. Chesneau
113
1
0
08 Feb 2020
A Corrective View of Neural Networks: Representation, Memorization and
  Learning
A Corrective View of Neural Networks: Representation, Memorization and LearningAnnual Conference Computational Learning Theory (COLT), 2020
Guy Bresler
Dheeraj M. Nagaraj
MLT
231
21
0
01 Feb 2020
The gap between theory and practice in function approximation with deep
  neural networks
The gap between theory and practice in function approximation with deep neural networksSIAM Journal on Mathematics of Data Science (SIMODS), 2020
Ben Adcock
N. Dexter
291
113
0
16 Jan 2020
Approximation smooth and sparse functions by deep neural networks
  without saturation
Approximation smooth and sparse functions by deep neural networks without saturation
Xia Liu
90
1
0
13 Jan 2020
Deep Network Approximation for Smooth Functions
Deep Network Approximation for Smooth FunctionsSIAM Journal on Mathematical Analysis (SIAM J. Math. Anal.), 2020
Jianfeng Lu
Zuowei Shen
Haizhao Yang
Shijun Zhang
842
279
0
09 Jan 2020
Deep learning architectures for nonlinear operator functions and
  nonlinear inverse problems
Deep learning architectures for nonlinear operator functions and nonlinear inverse problemsMathematical Statistics and Learning (MSL), 2019
Maarten V. de Hoop
Matti Lassas
C. Wong
251
31
0
23 Dec 2019
Deep Learning via Dynamical Systems: An Approximation Perspective
Deep Learning via Dynamical Systems: An Approximation Perspective
Qianxiao Li
Ting Lin
Zuowei Shen
AI4TSAI4CE
257
122
0
22 Dec 2019
iPromoter-BnCNN: a Novel Branched CNN Based Predictor for Identifying
  and Classifying Sigma Promoters
iPromoter-BnCNN: a Novel Branched CNN Based Predictor for Identifying and Classifying Sigma PromotersbioRxiv (bioRxiv), 2019
Ruhul Amin
C. R. Rahman
Md. Habibur Rahman Sifat
Md Nazmul Khan Liton
Md. Moshiur Rahman
Swakkhar Shatabda
Sajid Ahmed
173
51
0
21 Dec 2019
Chart Auto-Encoders for Manifold Structured Data
Chart Auto-Encoders for Manifold Structured Data
Stefan C. Schonsheck
Jie Chen
Rongjie Lai
DRLGNN
204
32
0
20 Dec 2019
Realization of spatial sparseness by deep ReLU nets with massive data
Realization of spatial sparseness by deep ReLU nets with massive dataIEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2019
C. Chui
Shao-Bo Lin
Bo Zhang
Ding-Xuan Zhou
118
24
0
16 Dec 2019
On the approximation of rough functions with deep neural networks
On the approximation of rough functions with deep neural networksSeMA Journal (SeMA), 2019
Tim De Ryck
Siddhartha Mishra
Deep Ray
97
9
0
13 Dec 2019
Robust Training and Initialization of Deep Neural Networks: An Adaptive
  Basis Viewpoint
Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis ViewpointMathematical and Scientific Machine Learning (MSML), 2019
E. Cyr
Mamikon A. Gulian
Ravi G. Patel
M. Perego
N. Trask
193
82
0
10 Dec 2019
Analysis of Deep Neural Networks with Quasi-optimal polynomial
  approximation rates
Analysis of Deep Neural Networks with Quasi-optimal polynomial approximation rates
Joseph Daws
Clayton Webster
99
10
0
04 Dec 2019
Variable Selection with Rigorous Uncertainty Quantification using Deep
  Bayesian Neural Networks: Posterior Concentration and Bernstein-von Mises
  Phenomenon
Variable Selection with Rigorous Uncertainty Quantification using Deep Bayesian Neural Networks: Posterior Concentration and Bernstein-von Mises PhenomenonInternational Conference on Artificial Intelligence and Statistics (AISTATS), 2019
Jeremiah Zhe Liu
BDL
253
10
0
03 Dec 2019
Neural Contextual Bandits with UCB-based Exploration
Neural Contextual Bandits with UCB-based Exploration
Dongruo Zhou
Lihong Li
Quanquan Gu
390
16
0
11 Nov 2019
ChebNet: Efficient and Stable Constructions of Deep Neural Networks with
  Rectified Power Units via Chebyshev Approximations
ChebNet: Efficient and Stable Constructions of Deep Neural Networks with Rectified Power Units via Chebyshev ApproximationsCommunications in Mathematics and Statistics (CMS), 2019
Shanshan Tang
Bo Li
Haijun Yu
93
18
0
07 Nov 2019
Deep least-squares methods: an unsupervised learning-based numerical
  method for solving elliptic PDEs
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEsJournal of Computational Physics (JCP), 2019
Z. Cai
Jingshuang Chen
Min Liu
Xinyu Liu
343
101
0
05 Nov 2019
Deep learning is adaptive to intrinsic dimensionality of model
  smoothness in anisotropic Besov space
Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov spaceNeural Information Processing Systems (NeurIPS), 2019
Taiji Suzuki
Atsushi Nitanda
288
71
0
28 Oct 2019
Growing axons: greedy learning of neural networks with application to
  function approximation
Growing axons: greedy learning of neural networks with application to function approximationRussian Journal of Numerical Analysis and Mathematical Modelling (JRNAMM), 2019
Daria Fokina
Ivan Oseledets
147
19
0
28 Oct 2019
Global Capacity Measures for Deep ReLU Networks via Path Sampling
Global Capacity Measures for Deep ReLU Networks via Path Sampling
Ryan Theisen
Jason M. Klusowski
Huan Wang
N. Keskar
Caiming Xiong
R. Socher
82
3
0
22 Oct 2019
Stochastic Feedforward Neural Networks: Universal Approximation
Stochastic Feedforward Neural Networks: Universal Approximation
Thomas Merkh
Guido Montúfar
153
8
0
22 Oct 2019
Neural tangent kernels, transportation mappings, and universal
  approximation
Neural tangent kernels, transportation mappings, and universal approximationInternational Conference on Learning Representations (ICLR), 2019
Ziwei Ji
Matus Telgarsky
Ruicheng Xian
126
43
0
15 Oct 2019
The Local Elasticity of Neural Networks
The Local Elasticity of Neural NetworksInternational Conference on Learning Representations (ICLR), 2019
Hangfeng He
Weijie J. Su
302
51
0
15 Oct 2019
Improved Generalization Bounds of Group Invariant / Equivariant Deep
  Networks via Quotient Feature Spaces
Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature SpacesConference on Uncertainty in Artificial Intelligence (UAI), 2019
Akiyoshi Sannai
Masaaki Imaizumi
M. Kawano
MLT
199
35
0
15 Oct 2019
Algorithm-Dependent Generalization Bounds for Overparameterized Deep
  Residual Networks
Algorithm-Dependent Generalization Bounds for Overparameterized Deep Residual NetworksNeural Information Processing Systems (NeurIPS), 2019
Spencer Frei
Yuan Cao
Quanquan Gu
ODL
162
32
0
07 Oct 2019
Bayesian Learning-Based Adaptive Control for Safety Critical Systems
Bayesian Learning-Based Adaptive Control for Safety Critical SystemsIEEE International Conference on Robotics and Automation (ICRA), 2019
David D. Fan
Jennifer Nguyen
Rohan Thakker
Nikhilesh Alatur
Ali-akbar Agha-mohammadi
Evangelos A. Theodorou
BDL
339
94
0
05 Oct 2019
A Function Space View of Bounded Norm Infinite Width ReLU Nets: The
  Multivariate Case
A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate CaseInternational Conference on Learning Representations (ICLR), 2019
Greg Ongie
Rebecca Willett
Daniel Soudry
Nathan Srebro
199
170
0
03 Oct 2019
Full error analysis for the training of deep neural networks
Full error analysis for the training of deep neural networksInfinite Dimensional Analysis Quantum Probability and Related Topics (IDAQP), 2019
C. Beck
Arnulf Jentzen
Benno Kuckuck
258
55
0
30 Sep 2019
Classification Logit Two-sample Testing by Neural Networks
Classification Logit Two-sample Testing by Neural NetworksIEEE Transactions on Information Theory (IEEE Trans. Inf. Theory), 2019
Xiuyuan Cheng
A. Cloninger
185
38
0
25 Sep 2019
A Multi-level procedure for enhancing accuracy of machine learning
  algorithms
A Multi-level procedure for enhancing accuracy of machine learning algorithmsEuropean journal of applied mathematics (EJAM), 2019
K. Lye
Siddhartha Mishra
Roberto Molinaro
185
34
0
20 Sep 2019
Optimal Function Approximation with Relu Neural Networks
Optimal Function Approximation with Relu Neural Networks
Bo Liu
Yi Liang
103
38
0
09 Sep 2019
PowerNet: Efficient Representations of Polynomials and Smooth Functions
  by Deep Neural Networks with Rectified Power Units
PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power UnitsJournal of Mathematical Study (JMS), 2019
Bo Li
Shanshan Tang
Haijun Yu
69
21
0
09 Sep 2019
On the rate of convergence of fully connected very deep neural network
  regression estimates
On the rate of convergence of fully connected very deep neural network regression estimates
Michael Kohler
S. Langer
206
40
0
29 Aug 2019
Theoretical Issues in Deep Networks: Approximation, Optimization and
  Generalization
Theoretical Issues in Deep Networks: Approximation, Optimization and GeneralizationProceedings of the National Academy of Sciences of the United States of America (PNAS), 2019
T. Poggio
Andrzej Banburski
Q. Liao
ODL
192
185
0
25 Aug 2019
Space-time error estimates for deep neural network approximations for
  differential equations
Space-time error estimates for deep neural network approximations for differential equationsAdvances in Computational Mathematics (Adv. Comput. Math.), 2019
Philipp Grohs
F. Hornung
Arnulf Jentzen
Philipp Zimmermann
152
39
0
11 Aug 2019
Convergence Rates of Variational Inference in Sparse Deep Learning
Convergence Rates of Variational Inference in Sparse Deep LearningInternational Conference on Machine Learning (ICML), 2019
Badr-Eddine Chérief-Abdellatif
BDL
308
41
0
09 Aug 2019
Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU
  Networks : Function Approximation and Statistical Recovery
Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery
Minshuo Chen
Haoming Jiang
Wenjing Liao
T. Zhao
630
101
0
05 Aug 2019
Fast generalization error bound of deep learning without scale
  invariance of activation functions
Fast generalization error bound of deep learning without scale invariance of activation functionsNeural Networks (NN), 2019
Y. Terada
Ryoma Hirose
MLT
147
8
0
25 Jul 2019
Adaptive Approximation and Generalization of Deep Neural Network with
  Intrinsic Dimensionality
Adaptive Approximation and Generalization of Deep Neural Network with Intrinsic Dimensionality
Ryumei Nakada
Masaaki Imaizumi
AI4CE
207
39
0
04 Jul 2019
Error bounds for deep ReLU networks using the Kolmogorov--Arnold
  superposition theorem
Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theoremNeural Networks (NN), 2019
Hadrien Montanelli
Haizhao Yang
205
106
0
27 Jun 2019
The phase diagram of approximation rates for deep neural networks
The phase diagram of approximation rates for deep neural networksNeural Information Processing Systems (NeurIPS), 2019
Dmitry Yarotsky
Anton Zhevnerchuk
192
139
0
22 Jun 2019
Smooth function approximation by deep neural networks with general
  activation functions
Smooth function approximation by deep neural networks with general activation functions
Ilsang Ohn
Yongdai Kim
104
87
0
17 Jun 2019
Interpretations of Deep Learning by Forests and Haar Wavelets
Interpretations of Deep Learning by Forests and Haar Wavelets
Changcun Huang
FAtt
187
0
0
16 Jun 2019
Deep Network Approximation Characterized by Number of Neurons
Deep Network Approximation Characterized by Number of NeuronsCommunications in Computational Physics (Commun. Comput. Phys.), 2019
Zuowei Shen
Haizhao Yang
Shijun Zhang
430
203
0
13 Jun 2019
A gradual, semi-discrete approach to generative network training via
  explicit Wasserstein minimization
A gradual, semi-discrete approach to generative network training via explicit Wasserstein minimizationInternational Conference on Machine Learning (ICML), 2019
Yucheng Chen
Matus Telgarsky
Chao Zhang
Bolton Bailey
Daniel J. Hsu
Jian-wei Peng
GANOT
133
22
0
08 Jun 2019
Function approximation by deep networks
Function approximation by deep networksCommunications on Pure and Applied Analysis (CPAA), 2019
H. Mhaskar
T. Poggio
188
25
0
30 May 2019
Implicit Rugosity Regularization via Data Augmentation
Implicit Rugosity Regularization via Data Augmentation
Daniel LeJeune
Randall Balestriero
Hamid Javadi
Richard G. Baraniuk
210
4
0
28 May 2019
Expression of Fractals Through Neural Network Functions
Expression of Fractals Through Neural Network FunctionsIEEE Journal on Selected Areas in Information Theory (JSAIT), 2019
Nadav Dym
B. Sober
Ingrid Daubechies
137
15
0
27 May 2019
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