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A Rigorous Framework for the Mean Field Limit of Multilayer Neural
  Networks
v1v2v3 (latest)

A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks

Mathematical Statistics and Learning (MSL), 2020
30 January 2020
Phan-Minh Nguyen
H. Pham
    AI4CE
ArXiv (abs)PDFHTML

Papers citing "A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks"

50 / 54 papers shown
Mean-Field Limits for Two-Layer Neural Networks Trained with Consensus-Based Optimization
Mean-Field Limits for Two-Layer Neural Networks Trained with Consensus-Based Optimization
William De Deyn
Michael Herty
Giovanni Samaey
212
0
0
26 Nov 2025
Block Coordinate Descent for Neural Networks Provably Finds Global Minima
Block Coordinate Descent for Neural Networks Provably Finds Global Minima
Shunta Akiyama
177
2
0
26 Oct 2025
Global Convergence and Rich Feature Learning in $L$-Layer Infinite-Width Neural Networks under $μ$P Parametrization
Global Convergence and Rich Feature Learning in LLL-Layer Infinite-Width Neural Networks under μμμP Parametrization
Zixiang Chen
Greg Yang
Qingyue Zhao
Q. Gu
MLT
307
3
0
12 Mar 2025
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
466
3
0
19 Mar 2024
A Survey on Statistical Theory of Deep Learning: Approximation, Training
  Dynamics, and Generative Models
A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative ModelsAnnual Review of Statistics and Its Application (ARSIA), 2024
Namjoon Suh
Guang Cheng
MedIm
492
23
0
14 Jan 2024
Wide Deep Neural Networks with Gaussian Weights are Very Close to
  Gaussian Processes
Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processes
Dario Trevisan
UQCVBDL
378
12
0
18 Dec 2023
How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing:
  The Curses of Symmetry and Initialization
How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing: The Curses of Symmetry and InitializationInternational Conference on Learning Representations (ICLR), 2023
Nuoya Xiong
Lijun Ding
Simon S. Du
549
21
0
03 Oct 2023
JoMA: Demystifying Multilayer Transformers via JOint Dynamics of MLP and
  Attention
JoMA: Demystifying Multilayer Transformers via JOint Dynamics of MLP and AttentionInternational Conference on Learning Representations (ICLR), 2023
Yuandong Tian
Yiping Wang
Zhenyu Zhang
Beidi Chen
Simon Shaolei Du
461
48
0
01 Oct 2023
Mode Connectivity and Data Heterogeneity of Federated Learning
Mode Connectivity and Data Heterogeneity of Federated Learning
Tailin Zhou
Jun Zhang
Danny H. K. Tsang
FedML
325
5
0
29 Sep 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
431
1
0
13 Sep 2023
Six Lectures on Linearized Neural Networks
Six Lectures on Linearized Neural NetworksJournal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech.), 2023
Theodor Misiakiewicz
Andrea Montanari
398
18
0
25 Aug 2023
Fundamental limits of overparametrized shallow neural networks for
  supervised learning
Fundamental limits of overparametrized shallow neural networks for supervised learning
Francesco Camilli
D. Tieplova
Jean Barbier
269
11
0
11 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
525
4
0
03 Jul 2023
Feature-Learning Networks Are Consistent Across Widths At Realistic
  Scales
Feature-Learning Networks Are Consistent Across Widths At Realistic ScalesNeural Information Processing Systems (NeurIPS), 2023
Nikhil Vyas
Alexander B. Atanasov
Blake Bordelon
Depen Morwani
Sabarish Sainathan
Cengiz Pehlevan
506
43
0
28 May 2023
Scan and Snap: Understanding Training Dynamics and Token Composition in
  1-layer Transformer
Scan and Snap: Understanding Training Dynamics and Token Composition in 1-layer TransformerNeural Information Processing Systems (NeurIPS), 2023
Yuandong Tian
Yiping Wang
Beidi Chen
S. Du
MLT
602
112
0
25 May 2023
Depth Dependence of $μ$P Learning Rates in ReLU MLPs
Depth Dependence of μμμP Learning Rates in ReLU MLPs
Samy Jelassi
Boris Hanin
Ziwei Ji
Sashank J. Reddi
Srinadh Bhojanapalli
Surinder Kumar
214
9
0
13 May 2023
Depth Separation with Multilayer Mean-Field Networks
Depth Separation with Multilayer Mean-Field NetworksInternational Conference on Learning Representations (ICLR), 2023
Y. Ren
Mo Zhou
Rong Ge
OOD
327
5
0
03 Apr 2023
Global Optimality of Elman-type RNN in the Mean-Field Regime
Global Optimality of Elman-type RNN in the Mean-Field RegimeInternational Conference on Machine Learning (ICML), 2023
Andrea Agazzi
Jian-Xiong Lu
Sayan Mukherjee
MLT
183
2
0
12 Mar 2023
PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash
  Equilibrium
PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium
Shihong Ding
Hanze Dong
Cong Fang
Zhouchen Lin
Tong Zhang
265
1
0
02 Mar 2023
Over-Parameterization Exponentially Slows Down Gradient Descent for
  Learning a Single Neuron
Over-Parameterization Exponentially Slows Down Gradient Descent for Learning a Single NeuronAnnual Conference Computational Learning Theory (COLT), 2023
Weihang Xu
S. Du
436
22
0
20 Feb 2023
M22: A Communication-Efficient Algorithm for Federated Learning Inspired
  by Rate-Distortion
M22: A Communication-Efficient Algorithm for Federated Learning Inspired by Rate-DistortionIEEE Transactions on Communications (IEEE Trans. Commun.), 2023
Yangyi Liu
Stefano Rini
Sadaf Salehkalaibar
Jun Chen
FedML
260
4
0
23 Jan 2023
Uniform-in-time propagation of chaos for mean field Langevin dynamics
Uniform-in-time propagation of chaos for mean field Langevin dynamicsAnnales De L Institut Henri Poincare-probabilites Et Statistiques (Ann. Inst. Henri Poincaré Probab. Stat.), 2022
Fan Chen
Zhenjie Ren
Song-bo Wang
494
41
0
06 Dec 2022
On the symmetries in the dynamics of wide two-layer neural networks
On the symmetries in the dynamics of wide two-layer neural networksElectronic Research Archive (ERA), 2022
Karl Hajjar
Lénaïc Chizat
324
11
0
16 Nov 2022
A Functional-Space Mean-Field Theory of Partially-Trained Three-Layer
  Neural Networks
A Functional-Space Mean-Field Theory of Partially-Trained Three-Layer Neural Networks
Zhengdao Chen
Eric Vanden-Eijnden
Joan Bruna
MLT
418
5
0
28 Oct 2022
Mean-field analysis for heavy ball methods: Dropout-stability,
  connectivity, and global convergence
Mean-field analysis for heavy ball methods: Dropout-stability, connectivity, and global convergence
Diyuan Wu
Vyacheslav Kungurtsev
Marco Mondelli
240
3
0
13 Oct 2022
Analysis of the rate of convergence of an over-parametrized deep neural
  network estimate learned by gradient descent
Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descentIEEE Transactions on Information Theory (IEEE Trans. Inf. Theory), 2022
Michael Kohler
A. Krzyżak
294
12
0
04 Oct 2022
On the universal consistency of an over-parametrized deep neural network
  estimate learned by gradient descent
On the universal consistency of an over-parametrized deep neural network estimate learned by gradient descentAnnals of the Institute of Statistical Mathematics (AISM), 2022
Selina Drews
Michael Kohler
256
19
0
30 Aug 2022
Limitations of the NTK for Understanding Generalization in Deep Learning
Limitations of the NTK for Understanding Generalization in Deep Learning
Nikhil Vyas
Yamini Bansal
Preetum Nakkiran
359
39
0
20 Jun 2022
Mean-Field Analysis of Two-Layer Neural Networks: Global Optimality with
  Linear Convergence Rates
Mean-Field Analysis of Two-Layer Neural Networks: Global Optimality with Linear Convergence Rates
Jingwei Zhang
Xunpeng Huang
Jincheng Yu
MLT
313
1
0
19 May 2022
Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide
  Neural Networks
Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural NetworksNeural Information Processing Systems (NeurIPS), 2022
Blake Bordelon
Cengiz Pehlevan
MLT
458
123
0
19 May 2022
On Feature Learning in Neural Networks with Global Convergence
  Guarantees
On Feature Learning in Neural Networks with Global Convergence GuaranteesInternational Conference on Learning Representations (ICLR), 2022
Zhengdao Chen
Eric Vanden-Eijnden
Joan Bruna
MLT
337
15
0
22 Apr 2022
Quantitative Gaussian Approximation of Randomly Initialized Deep Neural
  Networks
Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks
Andrea Basteri
Dario Trevisan
BDL
310
39
0
14 Mar 2022
Complexity from Adaptive-Symmetries Breaking: Global Minima in the
  Statistical Mechanics of Deep Neural Networks
Complexity from Adaptive-Symmetries Breaking: Global Minima in the Statistical Mechanics of Deep Neural Networks
Shaun Li
AI4CE
261
1
0
03 Jan 2022
Gradient flows on graphons: existence, convergence, continuity equations
Gradient flows on graphons: existence, convergence, continuity equations
Sewoong Oh
Soumik Pal
Raghav Somani
Raghavendra Tripathi
293
5
0
18 Nov 2021
Mean-field Analysis of Piecewise Linear Solutions for Wide ReLU Networks
Mean-field Analysis of Piecewise Linear Solutions for Wide ReLU NetworksJournal of machine learning research (JMLR), 2021
Aleksandr Shevchenko
Vyacheslav Kungurtsev
Marco Mondelli
MLT
339
16
0
03 Nov 2021
Limiting fluctuation and trajectorial stability of multilayer neural
  networks with mean field training
Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field trainingNeural Information Processing Systems (NeurIPS), 2021
H. Pham
Phan-Minh Nguyen
162
6
0
29 Oct 2021
Gradient Descent on Infinitely Wide Neural Networks: Global Convergence
  and Generalization
Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization
Francis R. Bach
Lénaïc Chizat
MLT
183
28
0
15 Oct 2021
On the Global Convergence of Gradient Descent for multi-layer ResNets in
  the mean-field regime
On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime
Zhiyan Ding
Shi Chen
Qin Li
S. Wright
MLTAI4CE
277
10
0
06 Oct 2021
A theory of representation learning gives a deep generalisation of
  kernel methods
A theory of representation learning gives a deep generalisation of kernel methodsInternational Conference on Machine Learning (ICML), 2021
Adam X. Yang
Maxime Robeyns
Edward Milsom
Ben Anson
Nandi Schoots
Laurence Aitchison
BDL
683
15
0
30 Aug 2021
Understanding Deflation Process in Over-parametrized Tensor
  Decomposition
Understanding Deflation Process in Over-parametrized Tensor DecompositionNeural Information Processing Systems (NeurIPS), 2021
Rong Ge
Y. Ren
Xiang Wang
Mo Zhou
239
21
0
11 Jun 2021
Heavy Tails in SGD and Compressibility of Overparametrized Neural
  Networks
Heavy Tails in SGD and Compressibility of Overparametrized Neural NetworksNeural Information Processing Systems (NeurIPS), 2021
Melih Barsbey
Romain Chor
Murat A. Erdogdu
Gaël Richard
Umut Simsekli
326
51
0
07 Jun 2021
Overparameterization of deep ResNet: zero loss and mean-field analysis
Overparameterization of deep ResNet: zero loss and mean-field analysisJournal of machine learning research (JMLR), 2021
Zhiyan Ding
Shi Chen
Qin Li
S. Wright
ODL
345
28
0
30 May 2021
Global Convergence of Three-layer Neural Networks in the Mean Field
  Regime
Global Convergence of Three-layer Neural Networks in the Mean Field RegimeInternational Conference on Learning Representations (ICLR), 2021
H. Pham
Phan-Minh Nguyen
MLTAI4CE
376
23
0
11 May 2021
Deep Nonparametric Regression on Approximate Manifolds: Non-Asymptotic
  Error Bounds with Polynomial Prefactors
Deep Nonparametric Regression on Approximate Manifolds: Non-Asymptotic Error Bounds with Polynomial PrefactorsAnnals of Statistics (Ann. Stat.), 2021
Yuling Jiao
Guohao Shen
Yuanyuan Lin
Jian Huang
483
85
0
14 Apr 2021
A Local Convergence Theory for Mildly Over-Parameterized Two-Layer
  Neural Network
A Local Convergence Theory for Mildly Over-Parameterized Two-Layer Neural NetworkAnnual Conference Computational Learning Theory (COLT), 2021
Mo Zhou
Rong Ge
Chi Jin
398
53
0
04 Feb 2021
Particle Dual Averaging: Optimization of Mean Field Neural Networks with
  Global Convergence Rate Analysis
Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate AnalysisNeural Information Processing Systems (NeurIPS), 2020
Atsushi Nitanda
Denny Wu
Taiji Suzuki
550
31
0
31 Dec 2020
Mathematical Models of Overparameterized Neural Networks
Mathematical Models of Overparameterized Neural NetworksProceedings of the IEEE (Proc. IEEE), 2020
Cong Fang
Hanze Dong
Tong Zhang
340
26
0
27 Dec 2020
Global optimality of softmax policy gradient with single hidden layer
  neural networks in the mean-field regime
Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime
Andrea Agazzi
Jianfeng Lu
259
19
0
22 Oct 2020
A Dynamical Central Limit Theorem for Shallow Neural Networks
A Dynamical Central Limit Theorem for Shallow Neural Networks
Zhengdao Chen
Grant M. Rotskoff
Joan Bruna
Eric Vanden-Eijnden
364
30
0
21 Aug 2020
A Note on the Global Convergence of Multilayer Neural Networks in the
  Mean Field Regime
A Note on the Global Convergence of Multilayer Neural Networks in the Mean Field Regime
H. Pham
Phan-Minh Nguyen
MLTAI4CE
173
4
0
16 Jun 2020
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