Spurious Local Minima are Common in Two-Layer ReLU Neural Networks

24 December 2017

Papers citing "Spurious Local Minima are Common in Two-Layer ReLU Neural Networks"

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Title
Mean-Field Analysis for Learning Subspace-Sparse Polynomials with Gaussian Input Ziang Chen Rong Ge MLT 61 1 0 10 Jan 2025
Learning Gaussian Multi-Index Models with Gradient Flow: Time Complexity and Directional Convergence Berfin Simsek Amire Bendjeddou Daniel Hsu 44 0 0 13 Nov 2024
$How does promoting the minority fraction affect generalization? A theoretical study of the one-hidden-layer neural network on group imbalance$ How does promoting the minority fraction affect generalization? A theoretical study of the one-hidden-layer neural network on group imbalance Hongkang Li Shuai Zhang Yihua Zhang Meng Wang Sijia Liu Pin-Yu Chen 41 4 0 12 Mar 2024
How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing: The Curses of Symmetry and Initialization Nuoya Xiong Lijun Ding Simon S. Du 35 11 0 03 Oct 2023
Worrisome Properties of Neural Network Controllers and Their Symbolic Representations J. Cyranka Kevin E. M. Church J. Lessard 39 0 0 28 Jul 2023
NTK-SAP: Improving neural network pruning by aligning training dynamics Yite Wang Dawei Li Ruoyu Sun 34 19 0 06 Apr 2023
Over-Parameterization Exponentially Slows Down Gradient Descent for Learning a Single Neuron Weihang Xu S. Du 37 16 0 20 Feb 2023
An SDE for Modeling SAM: Theory and Insights Enea Monzio Compagnoni Luca Biggio Antonio Orvieto F. Proske Hans Kersting Aurelien Lucchi 23 13 0 19 Jan 2023
Regression as Classification: Influence of Task Formulation on Neural Network Features Lawrence Stewart Francis R. Bach Quentin Berthet Jean-Philippe Vert 27 24 0 10 Nov 2022
When Expressivity Meets Trainability: Fewer than $n$ Neurons Can Work Jiawei Zhang Yushun Zhang Mingyi Hong Ruoyu Sun Zhi-Quan Luo 26 10 0 21 Oct 2022
Annihilation of Spurious Minima in Two-Layer ReLU Networks Yossi Arjevani M. Field 16 8 0 12 Oct 2022
Behind the Scenes of Gradient Descent: A Trajectory Analysis via Basis Function Decomposition Jianhao Ma Li-Zhen Guo S. Fattahi 38 4 0 01 Oct 2022
On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias Itay Safran Gal Vardi Jason D. Lee MLT 59 23 0 18 May 2022
Self-scalable Tanh (Stan): Faster Convergence and Better Generalization in Physics-informed Neural Networks Raghav Gnanasambandam Bo Shen Jihoon Chung Xubo Yue Zhenyu Zhen Kong LRM 34 12 0 26 Apr 2022
On Feature Learning in Neural Networks with Global Convergence Guarantees Zhengdao Chen Eric Vanden-Eijnden Joan Bruna MLT 36 13 0 22 Apr 2022
Exact Solutions of a Deep Linear Network Liu Ziyin Botao Li Xiangmin Meng ODL 19 21 0 10 Feb 2022
Understanding Deep Contrastive Learning via Coordinate-wise Optimization Yuandong Tian 52 34 0 29 Jan 2022
Improved Overparametrization Bounds for Global Convergence of Stochastic Gradient Descent for Shallow Neural Networks Bartlomiej Polaczyk J. Cyranka ODL 33 3 0 28 Jan 2022
How does unlabeled data improve generalization in self-training? A one-hidden-layer theoretical analysis Shuai Zhang Hao Wu Sijia Liu Pin-Yu Chen Jinjun Xiong SSL MLT 41 22 0 21 Jan 2022
Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape Devansh Bisla Jing Wang A. Choromańska 25 34 0 20 Jan 2022
Mode connectivity in the loss landscape of parameterized quantum circuits Kathleen E. Hamilton E. Lynn R. Pooser 25 3 0 09 Nov 2021
Path Regularization: A Convexity and Sparsity Inducing Regularization for Parallel ReLU Networks Tolga Ergen Mert Pilanci 32 16 0 18 Oct 2021
Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Pruned Neural Networks Shuai Zhang Meng Wang Sijia Liu Pin-Yu Chen Jinjun Xiong UQCV MLT 31 13 0 12 Oct 2021
Global Optimality Beyond Two Layers: Training Deep ReLU Networks via Convex Programs Tolga Ergen Mert Pilanci OffRL MLT 29 32 0 11 Oct 2021
Exponentially Many Local Minima in Quantum Neural Networks Xuchen You Xiaodi Wu 72 51 0 06 Oct 2021
Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks: A Tale of Symmetry II Yossi Arjevani M. Field 28 18 0 21 Jul 2021
Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of $S_n$ Yossi Arjevani M. Field 27 8 0 06 Jul 2021
A Geometric Analysis of Neural Collapse with Unconstrained Features Zhihui Zhu Tianyu Ding Jinxin Zhou Xiao Li Chong You Jeremias Sulam Qing Qu 24 194 0 06 May 2021
Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions Patrick Cheridito Arnulf Jentzen Florian Rossmannek 24 10 0 19 Mar 2021
Understanding self-supervised Learning Dynamics without Contrastive Pairs Yuandong Tian Xinlei Chen Surya Ganguli SSL 138 281 0 12 Feb 2021
A Convergence Theory Towards Practical Over-parameterized Deep Neural Networks Asaf Noy Yi Tian Xu Y. Aflalo Lihi Zelnik-Manor R. L. Jin 31 3 0 12 Jan 2021
The Nonconvex Geometry of Linear Inverse Problems Armin Eftekhari Peyman Mohajerin Esfahani 20 1 0 07 Jan 2021
Learning Graph Neural Networks with Approximate Gradient Descent Qunwei Li Shaofeng Zou Leon Wenliang Zhong GNN 32 1 0 07 Dec 2020
PAC Confidence Predictions for Deep Neural Network Classifiers Sangdon Park Shuo Li Insup Lee Osbert Bastani UQCV 24 25 0 02 Nov 2020
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't E. Weinan Chao Ma Stephan Wojtowytsch Lei Wu AI4CE 22 133 0 22 Sep 2020
Non-convergence of stochastic gradient descent in the training of deep neural networks Patrick Cheridito Arnulf Jentzen Florian Rossmannek 14 37 0 12 Jun 2020
Symmetry & critical points for a model shallow neural network Yossi Arjevani M. Field 31 13 0 23 Mar 2020
Optimization for deep learning: theory and algorithms Ruoyu Sun ODL 16 168 0 19 Dec 2019
Growing axons: greedy learning of neural networks with application to function approximation Daria Fokina Ivan V. Oseledets 18 18 0 28 Oct 2019
The Local Elasticity of Neural Networks Hangfeng He Weijie J. Su 40 44 0 15 Oct 2019
Hessian based analysis of SGD for Deep Nets: Dynamics and Generalization Xinyan Li Qilong Gu Yingxue Zhou Tiancong Chen A. Banerjee ODL 34 51 0 24 Jul 2019
Neural ODEs as the Deep Limit of ResNets with constant weights B. Avelin K. Nystrom ODL 37 31 0 28 Jun 2019
Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks Sanjeev Arora S. Du Wei Hu Zhiyuan Li Ruosong Wang MLT 35 962 0 24 Jan 2019
Width Provably Matters in Optimization for Deep Linear Neural Networks S. Du Wei Hu 16 93 0 24 Jan 2019
Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks Difan Zou Yuan Cao Dongruo Zhou Quanquan Gu ODL 24 446 0 21 Nov 2018
Gradient Descent Finds Global Minima of Deep Neural Networks S. Du J. Lee Haochuan Li Liwei Wang M. Tomizuka ODL 35 1,122 0 09 Nov 2018
A Closer Look at Deep Policy Gradients Andrew Ilyas Logan Engstrom Shibani Santurkar Dimitris Tsipras Firdaus Janoos Larry Rudolph Aleksander Madry 22 50 0 06 Nov 2018
On the Convergence Rate of Training Recurrent Neural Networks Zeyuan Allen-Zhu Yuanzhi Li Zhao-quan Song 18 191 0 29 Oct 2018
Benefits of over-parameterization with EM Ji Xu Daniel J. Hsu A. Maleki 32 29 0 26 Oct 2018
Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity Chulhee Yun S. Sra Ali Jadbabaie 18 117 0 17 Oct 2018