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Risk Bounds for High-dimensional Ridge Function Combinations Including
  Neural Networks
v1v2v3v4 (latest)

Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networks

5 July 2016
Jason M. Klusowski
Andrew R. Barron
ArXiv (abs)PDFHTML

Papers citing "Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networks"

42 / 42 papers shown
A Neural Network Algorithm for KL Divergence Estimation with Quantitative Error Bounds
A Neural Network Algorithm for KL Divergence Estimation with Quantitative Error Bounds
Mikil Foss
Andrew Lamperski
155
0
0
06 Oct 2025
Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions
Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions
Ziang Chen
Liqiang Huang
255
1
0
11 Aug 2025
FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling
FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling
Sifan Wang
Zehao Dou
Tong-Rui Liu
Lu Lu
Lu Lu
DiffM
378
16
0
09 Jun 2025
Kolmogorov GAM Networks are all you need!
Kolmogorov GAM Networks are all you need!Entropy (Entropy), 2025
Sarah Polson
Vadim Sokolov
271
2
0
03 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
521
10
0
18 Oct 2024
Space-Time Approximation with Shallow Neural Networks in Fourier
  Lebesgue spaces
Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces
Ahmed Abdeljawad
Thomas Dittrich
216
4
0
13 Dec 2023
Exploring the Approximation Capabilities of Multiplicative Neural
  Networks for Smooth Functions
Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions
Ido Ben-Shaul
Tomer Galanti
S. Dekel
344
4
0
11 Jan 2023
Shallow neural network representation of polynomials
Shallow neural network representation of polynomials
A. Beknazaryan
403
0
0
17 Aug 2022
$L^p$ sampling numbers for the Fourier-analytic Barron space
LpL^pLp sampling numbers for the Fourier-analytic Barron space
F. Voigtlaender
146
10
0
16 Aug 2022
Intrinsic dimensionality and generalization properties of the
  $\mathcal{R}$-norm inductive bias
Intrinsic dimensionality and generalization properties of the R\mathcal{R}R-norm inductive biasAnnual Conference Computational Learning Theory (COLT), 2022
Navid Ardeshir
Daniel J. Hsu
Clayton Sanford
CMLAI4CE
373
7
0
10 Jun 2022
Optimal Convergence Rates of Deep Convolutional Neural Networks:
  Additive Ridge Functions
Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functions
Zhiying Fang
Guang Cheng
MLT
315
6
0
24 Feb 2022
Understanding Value Decomposition Algorithms in Deep Cooperative
  Multi-Agent Reinforcement Learning
Understanding Value Decomposition Algorithms in Deep Cooperative Multi-Agent Reinforcement Learning
Zehao Dou
J. Kuba
Yaodong Yang
FAtt
156
8
0
10 Feb 2022
Optimal learning of high-dimensional classification problems using deep
  neural networks
Optimal learning of high-dimensional classification problems using deep neural networks
P. Petersen
F. Voigtlaender
345
10
0
23 Dec 2021
Risk bounds for aggregated shallow neural networks using Gaussian prior
Risk bounds for aggregated shallow neural networks using Gaussian priorAnnual Conference Computational Learning Theory (COLT), 2021
L. Tinsi
A. Dalalyan
BDL
367
8
0
21 Dec 2021
A spectral-based analysis of the separation between two-layer neural
  networks and linear methods
A spectral-based analysis of the separation between two-layer neural networks and linear methodsJournal of machine learning research (JMLR), 2021
Lei Wu
Jihao Long
285
9
0
10 Aug 2021
On Learnability via Gradient Method for Two-Layer ReLU Neural Networks
  in Teacher-Student Setting
On Learnability via Gradient Method for Two-Layer ReLU Neural Networks in Teacher-Student SettingInternational Conference on Machine Learning (ICML), 2021
Shunta Akiyama
Taiji Suzuki
MLT
335
16
0
11 Jun 2021
A Class of Dimension-free Metrics for the Convergence of Empirical
  Measures
A Class of Dimension-free Metrics for the Convergence of Empirical MeasuresStochastic Processes and their Applications (SPA), 2021
Jiequn Han
Ruimeng Hu
Jihao Long
449
4
0
24 Apr 2021
Benefit of deep learning with non-convex noisy gradient descent:
  Provable excess risk bound and superiority to kernel methods
Benefit of deep learning with non-convex noisy gradient descent: Provable excess risk bound and superiority to kernel methodsInternational Conference on Learning Representations (ICLR), 2020
Taiji Suzuki
Shunta Akiyama
MLT
303
12
0
06 Dec 2020
Neural network approximation and estimation of classifiers with
  classification boundary in a Barron class
Neural network approximation and estimation of classifiers with classification boundary in a Barron classThe Annals of Applied Probability (Ann. Appl. Probab.), 2020
A. Caragea
P. Petersen
F. Voigtlaender
267
41
0
18 Nov 2020
Machine Learning and Computational Mathematics
Machine Learning and Computational MathematicsCommunications in Computational Physics (Commun. Comput. Phys.), 2020
Weinan E
PINNAI4CE
249
74
0
23 Sep 2020
Towards a Mathematical Understanding of Neural Network-Based Machine
  Learning: what we know and what we don't
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tCSIAM Transactions on Applied Mathematics (CSIAM Trans. Appl. Math.), 2020
E. Weinan
Chao Ma
Stephan Wojtowytsch
Lei Wu
AI4CE
432
148
0
22 Sep 2020
On the Banach spaces associated with multi-layer ReLU networks: Function
  representation, approximation theory and gradient descent dynamics
On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamicsCSIAM Transactions on Applied Mathematics (CSIAM Trans. Appl. Math.), 2020
E. Weinan
Stephan Wojtowytsch
MLT
226
56
0
30 Jul 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
463
84
0
28 Jun 2020
Representation formulas and pointwise properties for Barron functions
Representation formulas and pointwise properties for Barron functionsCalculus of Variations and Partial Differential Equations (Calc. Var. PDEs), 2020
E. Weinan
Stephan Wojtowytsch
356
99
0
10 Jun 2020
Banach Space Representer Theorems for Neural Networks and Ridge Splines
Banach Space Representer Theorems for Neural Networks and Ridge Splines
Rahul Parhi
Robert D. Nowak
286
7
0
10 Jun 2020
A priori generalization error for two-layer ReLU neural network through minimum norm solution
Zhi-Qin John Xu
Jiwei Zhang
Yaoyu Zhang
Chengchao Zhao
MLT
235
1
0
06 Dec 2019
Neural network integral representations with the ReLU activation
  function
Neural network integral representations with the ReLU activation functionMathematical and Scientific Machine Learning (MSML), 2019
Armenak Petrosyan
Anton Dereventsov
Clayton Webster
291
25
0
07 Oct 2019
Neural Policy Gradient Methods: Global Optimality and Rates of
  Convergence
Neural Policy Gradient Methods: Global Optimality and Rates of ConvergenceInternational Conference on Learning Representations (ICLR), 2019
Lingxiao Wang
Qi Cai
Zhuoran Yang
Zhaoran Wang
632
267
0
29 Aug 2019
The Barron Space and the Flow-induced Function Spaces for Neural Network
  Models
The Barron Space and the Flow-induced Function Spaces for Neural Network Models
E. Weinan
Chao Ma
Lei Wu
262
115
0
18 Jun 2019
A Selective Overview of Deep Learning
A Selective Overview of Deep Learning
Jianqing Fan
Cong Ma
Yiqiao Zhong
BDLVLM
552
148
0
10 Apr 2019
A Comparative Analysis of the Optimization and Generalization Property
  of Two-layer Neural Network and Random Feature Models Under Gradient Descent
  Dynamics
A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics
E. Weinan
Chao Ma
Lei Wu
MLT
269
129
0
08 Apr 2019
A Priori Estimates of the Population Risk for Residual Networks
A Priori Estimates of the Population Risk for Residual Networks
E. Weinan
Chao Ma
Qingcan Wang
UQCV
275
62
0
06 Mar 2019
Complexity, Statistical Risk, and Metric Entropy of Deep Nets Using
  Total Path Variation
Complexity, Statistical Risk, and Metric Entropy of Deep Nets Using Total Path Variation
Andrew R. Barron
Jason M. Klusowski
277
32
0
02 Feb 2019
A Theoretical Analysis of Deep Q-Learning
A Theoretical Analysis of Deep Q-Learning
Jianqing Fan
Zhuoran Yang
Yuchen Xie
Zhaoran Wang
852
733
0
01 Jan 2019
Adaptivity of deep ReLU network for learning in Besov and mixed smooth
  Besov spaces: optimal rate and curse of dimensionality
Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality
Taiji Suzuki
440
284
0
18 Oct 2018
A Priori Estimates of the Population Risk for Two-layer Neural Networks
A Priori Estimates of the Population Risk for Two-layer Neural Networks
Weinan E
Chao Ma
Lei Wu
215
142
0
15 Oct 2018
Approximation and Estimation for High-Dimensional Deep Learning Networks
Approximation and Estimation for High-Dimensional Deep Learning Networks
Andrew R. Barron
Jason M. Klusowski
311
61
0
10 Sep 2018
Posterior Concentration for Sparse Deep Learning
Posterior Concentration for Sparse Deep Learning
Nicholas G. Polson
Veronika Rockova
UQCVBDL
407
100
0
24 Mar 2018
Nonparametric regression using deep neural networks with ReLU activation
  function
Nonparametric regression using deep neural networks with ReLU activation function
Johannes Schmidt-Hieber
817
978
0
22 Aug 2017
Convergence Analysis of Two-layer Neural Networks with ReLU Activation
Convergence Analysis of Two-layer Neural Networks with ReLU Activation
Yuanzhi Li
Yang Yuan
MLT
424
676
0
28 May 2017
Minimax Lower Bounds for Ridge Combinations Including Neural Nets
Minimax Lower Bounds for Ridge Combinations Including Neural NetsInternational Symposium on Information Theory (ISIT), 2017
Jason M. Klusowski
Andrew R. Barron
215
22
0
09 Feb 2017
Approximation by Combinations of ReLU and Squared ReLU Ridge Functions
  with $ \ell^1 $ and $ \ell^0 $ Controls
Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $ \ell^1 $ and $ \ell^0 $ Controls
Jason M. Klusowski
Andrew R. Barron
626
171
0
26 Jul 2016
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