ResearchTrend.AI
  • Communities
  • Connect sessions
  • AI calendar
  • Organizations
  • Join Slack
  • Contact Sales
Papers
Communities
Social Events
Terms and Conditions
Pricing
Contact Sales
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2026 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2006.05982
  4. Cited By
Representation formulas and pointwise properties for Barron functions
v1v2 (latest)

Representation formulas and pointwise properties for Barron functions

Calculus of Variations and Partial Differential Equations (Calc. Var. PDEs), 2020
10 June 2020
E. Weinan
Stephan Wojtowytsch
ArXiv (abs)PDFHTML

Papers citing "Representation formulas and pointwise properties for Barron functions"

50 / 52 papers shown
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
Sven Dummer
Tjeerd Jan Heeringa
José A. Iglesias
222
3
0
30 Sep 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
263
1
0
11 Aug 2025
Scalable Complexity Control Facilitates Reasoning Ability of LLMs
Scalable Complexity Control Facilitates Reasoning Ability of LLMs
Liangkai Hang
Junjie Yao
Zhiwei Bai
Jiahao Huo
Yang Chen
...
Feiyu Xiong
Y. Zhang
Weinan E
Hongkang Yang
Zhi-hai Xu
LRM
240
3
0
29 May 2025
Nonlocal techniques for the analysis of deep ReLU neural network approximations
Nonlocal techniques for the analysis of deep ReLU neural network approximations
Cornelia Schneider
Mario Ullrich
Jan Vybiral
352
3
0
07 Apr 2025
Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon
Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon
Hao Yu
ODLAI4CE
265
0
0
03 Mar 2025
Curse of Dimensionality in Neural Network Optimization
Curse of Dimensionality in Neural Network Optimization
Sanghoon Na
Haizhao Yang
426
0
0
07 Feb 2025
High-dimensional classification problems with Barron regular boundaries under margin conditions
High-dimensional classification problems with Barron regular boundaries under margin conditionsNeural Networks (NN), 2024
Jonathan García
Philipp Petersen
365
1
0
10 Dec 2024
Dimension-independent learning rates for high-dimensional classification
  problems
Dimension-independent learning rates for high-dimensional classification problems
Andrés Felipe Lerma Pineda
P. Petersen
Simon Frieder
Thomas Lukasiewicz
213
1
0
26 Sep 2024
Approximation Bounds for Recurrent Neural Networks with Application to Regression
Approximation Bounds for Recurrent Neural Networks with Application to Regression
Yuling Jiao
Yang Wang
Bokai Yan
294
1
0
09 Sep 2024
Learning with Norm Constrained, Over-parameterized, Two-layer Neural
  Networks
Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks
Fanghui Liu
L. Dadi
Volkan Cevher
491
10
0
29 Apr 2024
Understanding the training of infinitely deep and wide ResNets with Conditional Optimal Transport
Understanding the training of infinitely deep and wide ResNets with Conditional Optimal TransportCommunications on Pure and Applied Mathematics (CPAM), 2024
Raphael Barboni
Gabriel Peyré
Franccois-Xavier Vialard
464
3
0
19 Mar 2024
Operator Learning: Algorithms and Analysis
Operator Learning: Algorithms and Analysis
Nikola B. Kovachki
S. Lanthaler
Andrew M. Stuart
563
82
0
24 Feb 2024
Score-based generative models break the curse of dimensionality in
  learning a family of sub-Gaussian probability distributions
Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
Frank Cole
Yuxuan Zhao
DiffM
448
8
0
12 Feb 2024
Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field
  Dynamics on the Attention Landscape
Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape
Juno Kim
Taiji Suzuki
441
42
0
02 Feb 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
219
4
0
13 Dec 2023
Learning a Sparse Representation of Barron Functions with the Inverse
  Scale Space Flow
Learning a Sparse Representation of Barron Functions with the Inverse Scale Space FlowJournal of Machine Learning (JML), 2023
T. J. Heeringa
Tim Roith
Christoph Brune
Martin Burger
280
1
0
05 Dec 2023
Minimum norm interpolation by perceptra: Explicit regularization and
  implicit bias
Minimum norm interpolation by perceptra: Explicit regularization and implicit biasNeural Information Processing Systems (NeurIPS), 2023
Jiyoung Park
Ian Pelakh
Stephan Wojtowytsch
251
2
0
10 Nov 2023
Barron Space for Graph Convolution Neural Networks
Barron Space for Graph Convolution Neural Networks
Seok-Young Chung
Qiyu Sun
GNN
265
2
0
06 Nov 2023
Piecewise Linear Functions Representable with Infinite Width Shallow
  ReLU Neural Networks
Piecewise Linear Functions Representable with Infinite Width Shallow ReLU Neural NetworksProceedings of the American Mathematical Society, Series B (Proc. Amer. Math. Soc.), 2023
Sarah McCarty
159
1
0
25 Jul 2023
Neural Hilbert Ladders: Multi-Layer Neural Networks in Function Space
Neural Hilbert Ladders: Multi-Layer Neural Networks in Function SpaceJournal of machine learning research (JMLR), 2023
Zhengdao Chen
523
4
0
03 Jul 2023
Sampling weights of deep neural networks
Sampling weights of deep neural networksNeural Information Processing Systems (NeurIPS), 2023
Iryna Burak
Erik Lien Bolager
Chinmay Datar
Q. Sun
Felix Dietrich
BDLUQCV
299
32
0
29 Jun 2023
Central Limit Theorems and Approximation Theory: Part II
Central Limit Theorems and Approximation Theory: Part II
Arun K. Kuchibhotla
153
0
0
26 Jun 2023
Embedding Inequalities for Barron-type Spaces
Embedding Inequalities for Barron-type SpacesJournal of Machine Learning (JML), 2023
Lei Wu
345
0
0
30 May 2023
Embeddings between Barron spaces with higher order activation functions
Embeddings between Barron spaces with higher order activation functionsApplied and Computational Harmonic Analysis (ACHA), 2023
T. J. Heeringa
L. Spek
Felix L. Schwenninger
C. Brune
255
5
0
25 May 2023
ReLU Neural Networks with Linear Layers are Biased Towards Single- and Multi-Index Models
ReLU Neural Networks with Linear Layers are Biased Towards Single- and Multi-Index ModelsSIAM Journal on Mathematics of Data Science (SIMODS), 2023
Suzanna Parkinson
Greg Ongie
Rebecca Willett
593
8
0
24 May 2023
Infinite-dimensional reservoir computing
Infinite-dimensional reservoir computingNeural Networks (Neural Netw.), 2023
Lukas Gonon
Lyudmila Grigoryeva
Juan-Pablo Ortega
320
12
0
02 Apr 2023
Delay-SDE-net: A deep learning approach for time series modelling with
  memory and uncertainty estimates
Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates
M. Eggen
A. Midtfjord
245
3
0
14 Mar 2023
Penalising the biases in norm regularisation enforces sparsity
Penalising the biases in norm regularisation enforces sparsityNeural Information Processing Systems (NeurIPS), 2023
Etienne Boursier
Nicolas Flammarion
617
20
0
02 Mar 2023
Duality for Neural Networks through Reproducing Kernel Banach Spaces
Duality for Neural Networks through Reproducing Kernel Banach SpacesSocial Science Research Network (SSRN), 2022
L. Spek
T. J. Heeringa
Felix L. Schwenninger
C. Brune
533
18
0
09 Nov 2022
Understanding Deep Neural Function Approximation in Reinforcement
  Learning via $ε$-Greedy Exploration
Understanding Deep Neural Function Approximation in Reinforcement Learning via εεε-Greedy ExplorationNeural Information Processing Systems (NeurIPS), 2022
Fanghui Liu
Luca Viano
Volkan Cevher
373
27
0
15 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
424
14
0
14 Sep 2022
Optimal bump functions for shallow ReLU networks: Weight decay, depth
  separation and the curse of dimensionality
Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality
Stephan Wojtowytsch
252
1
0
02 Sep 2022
$L^p$ sampling numbers for the Fourier-analytic Barron space
LpL^pLp sampling numbers for the Fourier-analytic Barron space
F. Voigtlaender
163
10
0
16 Aug 2022
Universality and approximation bounds for echo state networks with
  random weights
Universality and approximation bounds for echo state networks with random weightsIEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2022
Zhen Li
Yunfei Yang
328
8
0
12 Jun 2022
Qualitative neural network approximation over R and C: Elementary proofs
  for analytic and polynomial activation
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation
Josiah Park
Stephan Wojtowytsch
274
3
0
25 Mar 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
365
10
0
23 Dec 2021
Integral representations of shallow neural network with Rectified Power
  Unit activation function
Integral representations of shallow neural network with Rectified Power Unit activation functionNeural Networks (NN), 2021
Ahmed Abdeljawad
Philipp Grohs
204
13
0
20 Dec 2021
Tighter Sparse Approximation Bounds for ReLU Neural Networks
Tighter Sparse Approximation Bounds for ReLU Neural Networks
Carles Domingo-Enrich
Youssef Mroueh
340
4
0
07 Oct 2021
Wasserstein Generative Adversarial Uncertainty Quantification in
  Physics-Informed Neural Networks
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural NetworksJournal of Computational Physics (JCP), 2021
Yihang Gao
Michael K. Ng
290
40
0
30 Aug 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
914
58
0
06 Jul 2021
Characterization of the Variation Spaces Corresponding to Shallow Neural
  Networks
Characterization of the Variation Spaces Corresponding to Shallow Neural NetworksConstructive approximation (Constr. Approx.), 2021
Jonathan W. Siegel
Jinchao Xu
412
67
0
28 Jun 2021
Two-layer neural networks with values in a Banach space
Two-layer neural networks with values in a Banach spaceSIAM Journal on Mathematical Analysis (SIAM J. Math. Anal.), 2021
Yury Korolev
509
31
0
05 May 2021
Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for
  Neural Networks
Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural NetworksSIAM Journal on Mathematics of Data Science (SIMODS), 2021
Yuqing Li
Yaoyu Zhang
Chao Ma
CML
346
2
0
30 Mar 2021
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth
Optimal Approximation Rate of ReLU Networks in terms of Width and DepthJournal des Mathématiques Pures et Appliquées (JMPA), 2021
Zuowei Shen
Haizhao Yang
Shijun Zhang
709
155
0
28 Feb 2021
Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths
  of Shallow Neural Networks
Sharp Bounds on the Approximation Rates, Metric Entropy, and nnn-widths of Shallow Neural NetworksFoundations of Computational Mathematics (FoCM), 2021
Jonathan W. Siegel
Jinchao Xu
1.0K
120
0
29 Jan 2021
Some observations on high-dimensional partial differential equations
  with Barron data
Some observations on high-dimensional partial differential equations with Barron dataMathematical and Scientific Machine Learning (MSML), 2020
E. Weinan
Stephan Wojtowytsch
AI4CE
402
24
0
02 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
269
41
0
18 Nov 2020
A priori estimates for classification problems using neural networks
A priori estimates for classification problems using neural networks
E. Weinan
Stephan Wojtowytsch
167
8
0
28 Sep 2020
Machine Learning and Computational Mathematics
Machine Learning and Computational MathematicsCommunications in Computational Physics (Commun. Comput. Phys.), 2020
Weinan E
PINNAI4CE
263
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
435
148
0
22 Sep 2020
12
Next
Page 1 of 2