Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

22 September 2020

Chao Ma

Papers citing "Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't"

29 / 29 papers shown

Title
Sharp higher order convergence rates for the Adam optimizer Steffen Dereich Arnulf Jentzen Adrian Riekert ODL 61 0 0 28 Apr 2025
Robust Concept Erasure Using Task Vectors Minh Pham Kelly O. Marshall Chinmay Hegde Niv Cohen 117 17 0 21 Feb 2025
High-dimensional classification problems with Barron regular boundaries under margin conditions Jonathan García Philipp Petersen 74 0 0 10 Dec 2024
Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss T. Getu Georges Kaddoum M. Bennis 32 1 0 13 Sep 2023
Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization Leyang Zhang Yaoyu Zhang Tao Luo 18 2 0 01 Sep 2023
Embeddings between Barron spaces with higher order activation functions T. J. Heeringa L. Spek Felix L. Schwenninger C. Brune 19 3 0 25 May 2023
Reinforcement Learning with Function Approximation: From Linear to Nonlinear Jihao Long Jiequn Han 19 5 0 20 Feb 2023
Infinite-width limit of deep linear neural networks Lénaïc Chizat Maria Colombo Xavier Fernández-Real Alessio Figalli 31 14 0 29 Nov 2022
To be or not to be stable, that is the question: understanding neural networks for inverse problems David Evangelista J. Nagy E. Morotti E. L. Piccolomini 23 4 0 24 Nov 2022
Duality for Neural Networks through Reproducing Kernel Banach Spaces L. Spek T. J. Heeringa Felix L. Schwenninger C. Brune 11 13 0 09 Nov 2022
Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling Giulia Bertaglia AI4CE 10 5 0 17 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 46 6 0 17 Sep 2022
SRMD: Sparse Random Mode Decomposition Nicholas Richardson Hayden Schaeffer Giang Tran 19 11 0 12 Apr 2022
HARFE: Hard-Ridge Random Feature Expansion Esha Saha Hayden Schaeffer Giang Tran 38 14 0 06 Feb 2022
Optimal learning of high-dimensional classification problems using deep neural networks P. Petersen F. Voigtlaender 25 9 0 23 Dec 2021
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions Martin Hutzenthaler Arnulf Jentzen Katharina Pohl Adrian Riekert Luca Scarpa MLT 34 6 0 13 Dec 2021
Embedding Principle: a hierarchical structure of loss landscape of deep neural networks Yaoyu Zhang Yuqing Li Zhongwang Zhang Tao Luo Z. Xu 21 21 0 30 Nov 2021
Conditioning of Random Feature Matrices: Double Descent and Generalization Error Zhijun Chen Hayden Schaeffer 35 12 0 21 Oct 2021
On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime Zhiyan Ding Shi Chen Qin Li S. Wright MLT AI4CE 30 11 0 06 Oct 2021
Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations Georg Gottwald Sebastian Reich AI4CE 40 37 0 08 Aug 2021
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation Arnulf Jentzen Adrian Riekert 19 23 0 09 Jul 2021
Generalization Error of GAN from the Discriminator's Perspective Hongkang Yang Weinan E GAN 38 13 0 08 Jul 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems Jianfeng Lu Yulong Lu 29 29 0 04 May 2021
Learning with invariances in random features and kernel models Song Mei Theodor Misiakiewicz Andrea Montanari OOD 46 89 0 25 Feb 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 23 37 0 05 Jan 2021
Cutting-edge 3D Medical Image Segmentation Methods in 2020: Are Happy Families All Alike? Jun Ma 64 25 0 01 Jan 2021
Machine Learning and Computational Mathematics Weinan E PINN AI4CE 18 61 0 23 Sep 2020
On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima N. Keskar Dheevatsa Mudigere J. Nocedal M. Smelyanskiy P. T. P. Tang ODL 281 2,888 0 15 Sep 2016
The Loss Surfaces of Multilayer Networks A. Choromańska Mikael Henaff Michaël Mathieu Gerard Ben Arous Yann LeCun ODL 179 1,185 0 30 Nov 2014