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A Comparative Analysis of the Optimization and Generalization Property
  of Two-layer Neural Network and Random Feature Models Under Gradient Descent
  Dynamics
v1v2 (latest)

A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics

8 April 2019
E. Weinan
Chao Ma
Lei Wu
    MLT
ArXiv (abs)PDFHTML

Papers citing "A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics"

41 / 91 papers shown
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
172
54
0
30 Jul 2020
The Interpolation Phase Transition in Neural Networks: Memorization and
  Generalization under Lazy Training
The Interpolation Phase Transition in Neural Networks: Memorization and Generalization under Lazy TrainingAnnals of Statistics (Ann. Stat.), 2020
Andrea Montanari
Yiqiao Zhong
394
103
0
25 Jul 2020
Understanding Implicit Regularization in Over-Parameterized Single Index
  Model
Understanding Implicit Regularization in Over-Parameterized Single Index ModelJournal of the American Statistical Association (JASA), 2020
Jianqing Fan
Zhuoran Yang
Mengxin Yu
315
22
0
16 Jul 2020
Phase diagram for two-layer ReLU neural networks at infinite-width limit
Phase diagram for two-layer ReLU neural networks at infinite-width limitJournal of machine learning research (JMLR), 2020
Yaoyu Zhang
Zhi-Qin John Xu
Zheng Ma
Yaoyu Zhang
210
71
0
15 Jul 2020
Generalization bound of globally optimal non-convex neural network
  training: Transportation map estimation by infinite dimensional Langevin
  dynamics
Generalization bound of globally optimal non-convex neural network training: Transportation map estimation by infinite dimensional Langevin dynamicsNeural Information Processing Systems (NeurIPS), 2020
Taiji Suzuki
225
23
0
11 Jul 2020
Towards an Understanding of Residual Networks Using Neural Tangent
  Hierarchy (NTH)
Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)CSIAM Transactions on Applied Mathematics (CSIAM Trans. Appl. Math.), 2020
Yuqing Li
Yaoyu Zhang
N. Yip
221
5
0
07 Jul 2020
A Revision of Neural Tangent Kernel-based Approaches for Neural Networks
Kyungsu Kim
A. Lozano
Eunho Yang
AAML
237
0
0
02 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
398
83
0
28 Jun 2020
The Quenching-Activation Behavior of the Gradient Descent Dynamics for
  Two-layer Neural Network Models
The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models
Chao Ma
Lei Wu
E. Weinan
MLT
190
11
0
25 Jun 2020
Optimal Rates for Averaged Stochastic Gradient Descent under Neural
  Tangent Kernel Regime
Optimal Rates for Averaged Stochastic Gradient Descent under Neural Tangent Kernel Regime
Atsushi Nitanda
Taiji Suzuki
283
45
0
22 Jun 2020
Global Convergence of Sobolev Training for Overparameterized Neural
  Networks
Global Convergence of Sobolev Training for Overparameterized Neural NetworksInternational Conference on Machine Learning, Optimization, and Data Science (MOD), 2020
Jorio Cocola
Paul Hand
124
8
0
14 Jun 2020
Non-convergence of stochastic gradient descent in the training of deep
  neural networks
Non-convergence of stochastic gradient descent in the training of deep neural networksJournal of Complexity (J. Complexity), 2020
Patrick Cheridito
Arnulf Jentzen
Florian Rossmannek
207
39
0
12 Jun 2020
Hardness of Learning Neural Networks with Natural Weights
Hardness of Learning Neural Networks with Natural Weights
Amit Daniely
Gal Vardi
220
21
0
05 Jun 2020
On the Convergence of Gradient Descent Training for Two-layer
  ReLU-networks in the Mean Field Regime
On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime
Stephan Wojtowytsch
MLT
191
53
0
27 May 2020
Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean
  field training perspective
Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective
Stephan Wojtowytsch
E. Weinan
MLT
178
59
0
21 May 2020
Kolmogorov Width Decay and Poor Approximators in Machine Learning:
  Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
E. Weinan
Stephan Wojtowytsch
249
32
0
21 May 2020
Memorizing Gaussians with no over-parameterizaion via gradient decent on
  neural networks
Memorizing Gaussians with no over-parameterizaion via gradient decent on neural networks
Amit Daniely
VLMMLT
115
15
0
28 Mar 2020
Dimension Independent Generalization Error by Stochastic Gradient
  Descent
Dimension Independent Generalization Error by Stochastic Gradient Descent
Xi Chen
Qiang Liu
Xin T. Tong
168
1
0
25 Mar 2020
Overall error analysis for the training of deep neural networks via
  stochastic gradient descent with random initialisation
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisationApplied Mathematics and Computation (Appl. Math. Comput.), 2020
Arnulf Jentzen
Timo Welti
160
20
0
03 Mar 2020
Learning Parities with Neural Networks
Learning Parities with Neural NetworksNeural Information Processing Systems (NeurIPS), 2020
Amit Daniely
Eran Malach
280
89
0
18 Feb 2020
Stochasticity of Deterministic Gradient Descent: Large Learning Rate for
  Multiscale Objective Function
Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective FunctionNeural Information Processing Systems (NeurIPS), 2020
Lingkai Kong
Molei Tao
126
30
0
14 Feb 2020
Machine Learning from a Continuous Viewpoint
Machine Learning from a Continuous ViewpointScience China Mathematics (Sci. China Math.), 2019
E. Weinan
Chao Ma
Lei Wu
298
110
0
30 Dec 2019
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
167
1
0
06 Dec 2019
Neural Networks Learning and Memorization with (almost) no
  Over-Parameterization
Neural Networks Learning and Memorization with (almost) no Over-ParameterizationNeural Information Processing Systems (NeurIPS), 2019
Amit Daniely
160
36
0
22 Nov 2019
Learning Boolean Circuits with Neural Networks
Learning Boolean Circuits with Neural Networks
Eran Malach
Shai Shalev-Shwartz
172
4
0
25 Oct 2019
Over Parameterized Two-level Neural Networks Can Learn Near Optimal
  Feature Representations
Over Parameterized Two-level Neural Networks Can Learn Near Optimal Feature Representations
Cong Fang
Hanze Dong
Tong Zhang
123
18
0
25 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
316
51
0
15 Oct 2019
On the convergence of gradient descent for two layer neural networks
Lei Li
MLT
147
0
0
30 Sep 2019
ID3 Learns Juntas for Smoothed Product Distributions
ID3 Learns Juntas for Smoothed Product DistributionsAnnual Conference Computational Learning Theory (COLT), 2019
Alon Brutzkus
Amit Daniely
Eran Malach
148
20
0
20 Jun 2019
Gradient Dynamics of Shallow Univariate ReLU Networks
Gradient Dynamics of Shallow Univariate ReLU NetworksNeural Information Processing Systems (NeurIPS), 2019
Francis Williams
Matthew Trager
Claudio Silva
Daniele Panozzo
Denis Zorin
Joan Bruna
172
84
0
18 Jun 2019
Generalization Guarantees for Neural Networks via Harnessing the
  Low-rank Structure of the Jacobian
Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian
Samet Oymak
Zalan Fabian
Mingchen Li
Mahdi Soltanolkotabi
MLT
238
100
0
12 Jun 2019
Decoupling Gating from Linearity
Decoupling Gating from Linearity
Jonathan Fiat
Eran Malach
Shai Shalev-Shwartz
203
31
0
12 Jun 2019
Generalization Bounds of Stochastic Gradient Descent for Wide and Deep
  Neural Networks
Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural NetworksNeural Information Processing Systems (NeurIPS), 2019
Yuan Cao
Quanquan Gu
MLTAI4CE
347
416
0
30 May 2019
Explicitizing an Implicit Bias of the Frequency Principle in Two-layer
  Neural Networks
Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks
Yaoyu Zhang
Zhi-Qin John Xu
Yaoyu Zhang
Zheng Ma
MLTAI4CE
240
43
0
24 May 2019
A type of generalization error induced by initialization in deep neural
  networks
A type of generalization error induced by initialization in deep neural networksMathematical and Scientific Machine Learning (MSML), 2019
Yaoyu Zhang
Zhi-Qin John Xu
Yaoyu Zhang
Zheng Ma
259
52
0
19 May 2019
Analysis of the Gradient Descent Algorithm for a Deep Neural Network
  Model with Skip-connections
Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections
E. Weinan
Chao Ma
Qingcan Wang
Lei Wu
MLT
267
22
0
10 Apr 2019
Gradient Descent with Early Stopping is Provably Robust to Label Noise
  for Overparameterized Neural Networks
Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks
Mingchen Li
Mahdi Soltanolkotabi
Samet Oymak
NoLa
455
379
0
27 Mar 2019
A Theoretical Analysis of Deep Q-Learning
A Theoretical Analysis of Deep Q-Learning
Jianqing Fan
Zhuoran Yang
Yuchen Xie
Zhaoran Wang
583
704
0
01 Jan 2019
On Lazy Training in Differentiable Programming
On Lazy Training in Differentiable Programming
Lénaïc Chizat
Edouard Oyallon
Francis R. Bach
538
909
0
19 Dec 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
169
141
0
15 Oct 2018
Spurious Valleys in Two-layer Neural Network Optimization Landscapes
Spurious Valleys in Two-layer Neural Network Optimization Landscapes
Luca Venturi
Afonso S. Bandeira
Joan Bruna
321
75
0
18 Feb 2018
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