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Optimal Approximation with Sparsely Connected Deep Neural Networks

Optimal Approximation with Sparsely Connected Deep Neural Networks

4 May 2017
Helmut Bölcskei
Philipp Grohs
Gitta Kutyniok
P. Petersen
ArXivPDFHTML

Papers citing "Optimal Approximation with Sparsely Connected Deep Neural Networks"

50 / 54 papers shown
Title
Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks
Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks
Sehwan Kim
F. Liang
FedML
57
0
0
04 May 2025
A Metric Topology of Deep Learning for Data Classification
A Metric Topology of Deep Learning for Data Classification
Jwo-Yuh Wu
L. Huang
Wen-Hsuan Li
Chun-Hung Liu
83
0
0
20 Jan 2025
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
Ariel Neufeld
Philipp Schmocker
21
2
0
18 Oct 2024
Blessing of Dimensionality for Approximating Sobolev Classes on Manifolds
Blessing of Dimensionality for Approximating Sobolev Classes on Manifolds
Hong Ye Tan
Subhadip Mukherjee
Junqi Tang
Carola-Bibiane Schönlieb
57
0
0
13 Aug 2024
Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of
  Experts
Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts
Anastasis Kratsios
Haitz Sáez de Ocáriz Borde
Takashi Furuya
Marc T. Law
MoE
41
1
0
05 Feb 2024
Mathematical Algorithm Design for Deep Learning under Societal and
  Judicial Constraints: The Algorithmic Transparency Requirement
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement
Holger Boche
Adalbert Fono
Gitta Kutyniok
FaML
31
4
0
18 Jan 2024
Sparse Deep Learning for Time Series Data: Theory and Applications
Sparse Deep Learning for Time Series Data: Theory and Applications
Mingxuan Zhang
Y. Sun
Faming Liang
AI4TS
OOD
BDL
39
2
0
05 Oct 2023
Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss
Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss
T. Getu
Georges Kaddoum
M. Bennis
40
1
0
13 Sep 2023
Rates of Approximation by ReLU Shallow Neural Networks
Rates of Approximation by ReLU Shallow Neural Networks
Tong Mao
Ding-Xuan Zhou
29
19
0
24 Jul 2023
Approximation analysis of CNNs from a feature extraction view
Approximation analysis of CNNs from a feature extraction view
Jianfei Li
Han Feng
Ding-Xuan Zhou
24
3
0
14 Oct 2022
Limitations of neural network training due to numerical instability of
  backpropagation
Limitations of neural network training due to numerical instability of backpropagation
Clemens Karner
V. Kazeev
P. Petersen
32
3
0
03 Oct 2022
Chaotic Hedging with Iterated Integrals and Neural Networks
Chaotic Hedging with Iterated Integrals and Neural Networks
Ariel Neufeld
Philipp Schmocker
36
10
0
21 Sep 2022
Deep Neural Network Approximation of Invariant Functions through
  Dynamical Systems
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems
Qianxiao Li
T. Lin
Zuowei Shen
21
6
0
18 Aug 2022
Sparse Deep Neural Network for Nonlinear Partial Differential Equations
Sparse Deep Neural Network for Nonlinear Partial Differential Equations
Yuesheng Xu
T. Zeng
33
5
0
27 Jul 2022
Neural and spectral operator surrogates: unified construction and
  expression rate bounds
Neural and spectral operator surrogates: unified construction and expression rate bounds
L. Herrmann
Christoph Schwab
Jakob Zech
51
9
0
11 Jul 2022
A PAC-Bayes oracle inequality for sparse neural networks
A PAC-Bayes oracle inequality for sparse neural networks
Maximilian F. Steffen
Mathias Trabs
UQCV
19
2
0
26 Apr 2022
The Mathematics of Artificial Intelligence
The Mathematics of Artificial Intelligence
Gitta Kutyniok
14
0
0
16 Mar 2022
Bayesian neural network priors for edge-preserving inversion
Bayesian neural network priors for edge-preserving inversion
Chen Li
Matthew M. Dunlop
G. Stadler
20
12
0
20 Dec 2021
Approximation of functions with one-bit neural networks
Approximation of functions with one-bit neural networks
C. S. Güntürk
Weilin Li
19
8
0
16 Dec 2021
Wasserstein Generative Adversarial Uncertainty Quantification in
  Physics-Informed Neural Networks
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
Yihang Gao
Michael K. Ng
38
28
0
30 Aug 2021
Optimal Approximation with Sparse Neural Networks and Applications
Optimal Approximation with Sparse Neural Networks and Applications
Khay Boon Hong
12
0
0
14 Aug 2021
High-Dimensional Distribution Generation Through Deep Neural Networks
High-Dimensional Distribution Generation Through Deep Neural Networks
Dmytro Perekrestenko
Léandre Eberhard
Helmut Bölcskei
OOD
32
6
0
26 Jul 2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed
  Number of Neurons
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons
Zuowei Shen
Haizhao Yang
Shijun Zhang
56
36
0
06 Jul 2021
Theory of Deep Convolutional Neural Networks III: Approximating Radial
  Functions
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
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
Metric Entropy Limits on Recurrent Neural Network Learning of Linear
  Dynamical Systems
Metric Entropy Limits on Recurrent Neural Network Learning of Linear Dynamical Systems
Clemens Hutter
R. Gül
Helmut Bölcskei
16
9
0
06 May 2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling
  Complexity bounds for Neural Network Approximation Spaces
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
Philipp Grohs
F. Voigtlaender
13
34
0
06 Apr 2021
A Deep Learning approach to Reduced Order Modelling of Parameter
  Dependent Partial Differential Equations
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
Quantitative approximation results for complex-valued neural networks
Quantitative approximation results for complex-valued neural networks
A. Caragea
D. Lee
J. Maly
G. Pfander
F. Voigtlaender
13
5
0
25 Feb 2021
Estimating Vector Fields from Noisy Time Series
Estimating Vector Fields from Noisy Time Series
Harish S. Bhat
Majerle Reeves
Ramin Raziperchikolaei
AI4TS
23
1
0
06 Dec 2020
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks
M. Longo
Suman Mishra
T. Konstantin Rusch
Christoph Schwab
30
20
0
06 Sep 2020
Phase Transitions in Rate Distortion Theory and Deep Learning
Phase Transitions in Rate Distortion Theory and Deep Learning
Philipp Grohs
Andreas Klotz
F. Voigtlaender
14
7
0
03 Aug 2020
Approximation of Smoothness Classes by Deep Rectifier Networks
Approximation of Smoothness Classes by Deep Rectifier Networks
Mazen Ali
A. Nouy
9
9
0
30 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
28
9
0
28 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 conditions
Philipp Grohs
L. Herrmann
27
52
0
10 Jul 2020
Expressivity of Deep Neural Networks
Expressivity of Deep Neural Networks
Ingo Gühring
Mones Raslan
Gitta Kutyniok
16
51
0
09 Jul 2020
Approximation in shift-invariant spaces with deep ReLU neural networks
Approximation in shift-invariant spaces with deep ReLU neural networks
Yunfei Yang
Zhen Li
Yang Wang
34
14
0
25 May 2020
Learning on dynamic statistical manifolds
Learning on dynamic statistical manifolds
F. Boso
D. Tartakovsky
21
10
0
07 May 2020
Deep Network Approximation for Smooth Functions
Deep Network Approximation for Smooth Functions
Jianfeng Lu
Zuowei Shen
Haizhao Yang
Shijun Zhang
67
247
0
09 Jan 2020
Stochastic Feedforward Neural Networks: Universal Approximation
Stochastic Feedforward Neural Networks: Universal Approximation
Thomas Merkh
Guido Montúfar
17
8
0
22 Oct 2019
Data driven approximation of parametrized PDEs by Reduced Basis and
  Neural Networks
Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks
N. D. Santo
S. Deparis
Luca Pegolotti
19
66
0
02 Apr 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
Gitta Kutyniok
P. Petersen
Mones Raslan
R. Schneider
20
197
0
31 Mar 2019
Deep learning observables in computational fluid dynamics
Deep learning observables in computational fluid dynamics
K. Lye
Siddhartha Mishra
Deep Ray
OOD
AI4CE
13
158
0
07 Mar 2019
Error bounds for approximations with deep ReLU neural networks in
  $W^{s,p}$ norms
Error bounds for approximations with deep ReLU neural networks in Ws,pW^{s,p}Ws,p norms
Ingo Gühring
Gitta Kutyniok
P. Petersen
14
199
0
21 Feb 2019
Deep Neural Network Approximation Theory
Deep Neural Network Approximation Theory
Dennis Elbrächter
Dmytro Perekrestenko
Philipp Grohs
Helmut Bölcskei
14
207
0
08 Jan 2019
A proof that deep artificial neural networks overcome the curse of
  dimensionality in the numerical approximation of Kolmogorov partial
  differential equations with constant diffusion and nonlinear drift
  coefficients
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients
Arnulf Jentzen
Diyora Salimova
Timo Welti
AI4CE
16
116
0
19 Sep 2018
A proof that artificial neural networks overcome the curse of
  dimensionality in the numerical approximation of Black-Scholes partial
  differential equations
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Philipp Grohs
F. Hornung
Arnulf Jentzen
Philippe von Wurstemberger
11
167
0
07 Sep 2018
NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation
NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation
Anastasis Kratsios
Cody B. Hyndman
OOD
25
17
0
31 Aug 2018
The universal approximation power of finite-width deep ReLU networks
The universal approximation power of finite-width deep ReLU networks
Dmytro Perekrestenko
Philipp Grohs
Dennis Elbrächter
Helmut Bölcskei
13
36
0
05 Jun 2018
Solving the Kolmogorov PDE by means of deep learning
Solving the Kolmogorov PDE by means of deep learning
C. Beck
S. Becker
Philipp Grohs
Nor Jaafari
Arnulf Jentzen
6
91
0
01 Jun 2018
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