The Barron Space and the Flow-induced Function Spaces for Neural Network Models

18 June 2019

Chao Ma

Papers citing "The Barron Space and the Flow-induced Function Spaces for Neural Network Models"

29 / 29 papers shown

Title
How DNNs break the Curse of Dimensionality: Compositionality and Symmetry Learning Arthur Jacot Seok Hoan Choi Yuxiao Wen AI4CE 91 2 0 08 Jul 2024
Learning solution operators of PDEs defined on varying domains via MIONet Shanshan Xiao Pengzhan Jin Yifa Tang 42 3 0 23 Feb 2024
GIT-Net: Generalized Integral Transform for Operator Learning Chao Wang Alexandre H. Thiery AI4CE 31 0 0 05 Dec 2023
Reinforcement Learning with Function Approximation: From Linear to Nonlinear Jihao Long Jiequn Han 27 5 0 20 Feb 2023
A Mathematical Framework for Learning Probability Distributions Hongkang Yang 23 7 0 22 Dec 2022
Duality for Neural Networks through Reproducing Kernel Banach Spaces L. Spek T. J. Heeringa Felix L. Schwenninger C. Brune 13 13 0 09 Nov 2022
Importance Tempering: Group Robustness for Overparameterized Models Yiping Lu Wenlong Ji Zachary Izzo Lexing Ying 39 7 0 19 Sep 2022
The Deep Ritz Method for Parametric $p$ -Dirichlet Problems A. Kaltenbach Marius Zeinhofer 14 2 0 05 Jul 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 21 6 0 28 May 2022
Bayesian Deep Learning with Multilevel Trace-class Neural Networks Neil K. Chada Ajay Jasra K. Law Sumeetpal S. Singh BDL UQCV 83 3 0 24 Mar 2022
Perturbational Complexity by Distribution Mismatch: A Systematic Analysis of Reinforcement Learning in Reproducing Kernel Hilbert Space Jihao Long Jiequn Han 29 6 0 05 Nov 2021
Sobolev-type embeddings for neural network approximation spaces Philipp Grohs F. Voigtlaender 16 1 0 28 Oct 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 32 26 0 14 Jun 2021
Two-layer neural networks with values in a Banach space Yury Korolev 23 23 0 05 May 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems Jianfeng Lu Yulong Lu 34 29 0 04 May 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 30 37 0 05 Jan 2021
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 20 30 0 15 Dec 2020
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 34 29 0 11 Dec 2020
Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs Thomas O'Leary-Roseberry Umberto Villa Peng Chen Omar Ghattas 36 68 0 30 Nov 2020
Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime Andrea Agazzi Jianfeng Lu 13 15 0 22 Oct 2020
Machine Learning and Computational Mathematics Weinan E PINN AI4CE 24 61 0 23 Sep 2020
Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms Zhong Li Chao Ma Lei Wu 18 24 0 14 Sep 2020
Representation formulas and pointwise properties for Barron functions E. Weinan Stephan Wojtowytsch 23 79 0 10 Jun 2020
Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective Stephan Wojtowytsch E. Weinan MLT 26 48 0 21 May 2020
Machine Learning from a Continuous Viewpoint E. Weinan Chao Ma Lei Wu 23 102 0 30 Dec 2019
Deep Learning via Dynamical Systems: An Approximation Perspective Qianxiao Li Ting Lin Zuowei Shen AI4TS AI4CE 14 107 0 22 Dec 2019
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations E. Kharazmi Z. Zhang George Karniadakis 16 236 0 27 Nov 2019
The Local Elasticity of Neural Networks Hangfeng He Weijie J. Su 23 44 0 15 Oct 2019
A Priori Estimates of the Population Risk for Two-layer Neural Networks Weinan E Chao Ma Lei Wu 29 130 0 15 Oct 2018