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Global Optimality of Local Search for Low Rank Matrix Recovery

Global Optimality of Local Search for Low Rank Matrix Recovery

23 May 2016
Srinadh Bhojanapalli
Behnam Neyshabur
Nathan Srebro
    ODL
ArXivPDFHTML

Papers citing "Global Optimality of Local Search for Low Rank Matrix Recovery"

50 / 58 papers shown
Title
Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization
Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization
G. Zhang
S. Fattahi
Richard Y. Zhang
40
34
0
13 Apr 2025
Compressible Dynamics in Deep Overparameterized Low-Rank Learning &
  Adaptation
Compressible Dynamics in Deep Overparameterized Low-Rank Learning & Adaptation
Can Yaras
Peng Wang
Laura Balzano
Qing Qu
AI4CE
37
12
0
06 Jun 2024
Wave Physics-informed Matrix Factorizations
Wave Physics-informed Matrix Factorizations
Harsha Vardhan Tetali
J. Harley
B. Haeffele
29
0
0
21 Dec 2023
Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled
  Gradient Descent, Even with Overparameterization
Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization
Cong Ma
Xingyu Xu
Tian Tong
Yuejie Chi
18
9
0
09 Oct 2023
Saddle-to-Saddle Dynamics in Diagonal Linear Networks
Saddle-to-Saddle Dynamics in Diagonal Linear Networks
Scott Pesme
Nicolas Flammarion
31
35
0
02 Apr 2023
A Newton-CG based barrier-augmented Lagrangian method for general
  nonconvex conic optimization
A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization
Chuan He
Heng Huang
Zhaosong Lu
14
1
0
10 Jan 2023
Escaping From Saddle Points Using Asynchronous Coordinate Gradient
  Descent
Escaping From Saddle Points Using Asynchronous Coordinate Gradient Descent
Marco Bornstein
Jin-Peng Liu
Jingling Li
Furong Huang
21
0
0
17 Nov 2022
Are All Losses Created Equal: A Neural Collapse Perspective
Are All Losses Created Equal: A Neural Collapse Perspective
Jinxin Zhou
Chong You
Xiao Li
Kangning Liu
Sheng Liu
Qing Qu
Zhihui Zhu
36
58
0
04 Oct 2022
Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape
  Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective
Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective
Yuetian Luo
Nicolas García Trillos
19
6
0
29 Sep 2022
A Validation Approach to Over-parameterized Matrix and Image Recovery
A Validation Approach to Over-parameterized Matrix and Image Recovery
Lijun Ding
Zhen Qin
Liwei Jiang
Jinxin Zhou
Zhihui Zhu
45
13
0
21 Sep 2022
Gradient-Free Methods for Deterministic and Stochastic Nonsmooth
  Nonconvex Optimization
Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization
Tianyi Lin
Zeyu Zheng
Michael I. Jordan
51
51
0
12 Sep 2022
Implicit Full Waveform Inversion with Deep Neural Representation
Implicit Full Waveform Inversion with Deep Neural Representation
Jian Sun
K. Innanen
AI4CE
34
32
0
08 Sep 2022
Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix
  Completion
Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion
G. Zhang
Hong-Ming Chiu
Richard Y. Zhang
16
10
0
24 Aug 2022
Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the
  Optimization Landscape Around the True Solution
Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the Optimization Landscape Around the True Solution
Jianhao Ma
S. Fattahi
42
5
0
15 Jul 2022
Preconditioned Gradient Descent for Overparameterized Nonconvex Burer--Monteiro Factorization with Global Optimality Certification
Preconditioned Gradient Descent for Overparameterized Nonconvex Burer--Monteiro Factorization with Global Optimality Certification
G. Zhang
S. Fattahi
Richard Y. Zhang
42
23
0
07 Jun 2022
On the Optimization Landscape of Neural Collapse under MSE Loss: Global
  Optimality with Unconstrained Features
On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features
Jinxin Zhou
Xiao Li
Tian Ding
Chong You
Qing Qu
Zhihui Zhu
24
97
0
02 Mar 2022
Escape saddle points by a simple gradient-descent based algorithm
Escape saddle points by a simple gradient-descent based algorithm
Chenyi Zhang
Tongyang Li
ODL
23
15
0
28 Nov 2021
Faster Perturbed Stochastic Gradient Methods for Finding Local Minima
Faster Perturbed Stochastic Gradient Methods for Finding Local Minima
Zixiang Chen
Dongruo Zhou
Quanquan Gu
35
1
0
25 Oct 2021
Nonconvex Factorization and Manifold Formulations are Almost Equivalent
  in Low-rank Matrix Optimization
Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization
Yuetian Luo
Xudong Li
Anru R. Zhang
25
9
0
03 Aug 2021
Small random initialization is akin to spectral learning: Optimization
  and generalization guarantees for overparameterized low-rank matrix
  reconstruction
Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction
Dominik Stöger
Mahdi Soltanolkotabi
ODL
36
75
0
28 Jun 2021
Escaping Saddle Points with Compressed SGD
Escaping Saddle Points with Compressed SGD
Dmitrii Avdiukhin
G. Yaroslavtsev
8
4
0
21 May 2021
Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery
  Problems with Corrupted Measurements
Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements
Ziye Ma
Yingjie Bi
Javad Lavaei
Somayeh Sojoudi
21
14
0
18 May 2021
Sharp Global Guarantees for Nonconvex Low-rank Recovery in the Noisy Overparameterized Regime
Sharp Global Guarantees for Nonconvex Low-rank Recovery in the Noisy Overparameterized Regime
Richard Y. Zhang
39
1
0
21 Apr 2021
Group-Sparse Matrix Factorization for Transfer Learning of Word
  Embeddings
Group-Sparse Matrix Factorization for Transfer Learning of Word Embeddings
Kan Xu
Xuanyi Zhao
Hamsa Bastani
Osbert Bastani
25
6
0
18 Apr 2021
Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian
  Optimization
Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization
Jian-Feng Cai
Jingyang Li
Dong Xia
49
30
0
16 Mar 2021
HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise
HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise
David Hong
Kyle Gilman
Laura Balzano
Jeffrey A. Fessler
32
18
0
10 Jan 2021
Recursive Importance Sketching for Rank Constrained Least Squares:
  Algorithms and High-order Convergence
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
Yuetian Luo
Wen Huang
Xudong Li
Anru R. Zhang
23
15
0
17 Nov 2020
Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled
  Gradient Descent
Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent
Tian Tong
Cong Ma
Yuejie Chi
19
113
0
18 May 2020
On the Sample Complexity and Optimization Landscape for Quadratic
  Feasibility Problems
On the Sample Complexity and Optimization Landscape for Quadratic Feasibility Problems
Parth Thaker
Gautam Dasarathy
Angelia Nedić
16
5
0
04 Feb 2020
Revisiting Landscape Analysis in Deep Neural Networks: Eliminating
  Decreasing Paths to Infinity
Revisiting Landscape Analysis in Deep Neural Networks: Eliminating Decreasing Paths to Infinity
Shiyu Liang
Ruoyu Sun
R. Srikant
25
19
0
31 Dec 2019
Manifold Gradient Descent Solves Multi-Channel Sparse Blind
  Deconvolution Provably and Efficiently
Manifold Gradient Descent Solves Multi-Channel Sparse Blind Deconvolution Provably and Efficiently
Laixi Shi
Yuejie Chi
22
26
0
25 Nov 2019
Global Optimality Guarantees For Policy Gradient Methods
Global Optimality Guarantees For Policy Gradient Methods
Jalaj Bhandari
Daniel Russo
35
185
0
05 Jun 2019
Implicit Regularization in Deep Matrix Factorization
Implicit Regularization in Deep Matrix Factorization
Sanjeev Arora
Nadav Cohen
Wei Hu
Yuping Luo
AI4CE
24
491
0
31 May 2019
Stabilized SVRG: Simple Variance Reduction for Nonconvex Optimization
Stabilized SVRG: Simple Variance Reduction for Nonconvex Optimization
Rong Ge
Zhize Li
Weiyao Wang
Xiang Wang
17
33
0
01 May 2019
A Deterministic Gradient-Based Approach to Avoid Saddle Points
A Deterministic Gradient-Based Approach to Avoid Saddle Points
L. Kreusser
Stanley J. Osher
Bao Wang
ODL
24
3
0
21 Jan 2019
On the Global Convergence of Imitation Learning: A Case for Linear
  Quadratic Regulator
On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulator
Qi Cai
Mingyi Hong
Yongxin Chen
Zhaoran Wang
19
34
0
11 Jan 2019
Convergence of Cubic Regularization for Nonconvex Optimization under KL
  Property
Convergence of Cubic Regularization for Nonconvex Optimization under KL Property
Yi Zhou
Zhe Wang
Yingbin Liang
24
23
0
22 Aug 2018
Optimistic mirror descent in saddle-point problems: Going the extra
  (gradient) mile
Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile
P. Mertikopoulos
Bruno Lecouat
Houssam Zenati
Chuan-Sheng Foo
V. Chandrasekhar
Georgios Piliouras
19
290
0
07 Jul 2018
On the Implicit Bias of Dropout
On the Implicit Bias of Dropout
Poorya Mianjy
R. Arora
René Vidal
27
66
0
26 Jun 2018
Stochastic Nested Variance Reduction for Nonconvex Optimization
Stochastic Nested Variance Reduction for Nonconvex Optimization
Dongruo Zhou
Pan Xu
Quanquan Gu
25
146
0
20 Jun 2018
Improved Learning of One-hidden-layer Convolutional Neural Networks with
  Overlaps
Improved Learning of One-hidden-layer Convolutional Neural Networks with Overlaps
S. Du
Surbhi Goel
MLT
20
17
0
20 May 2018
The Global Optimization Geometry of Shallow Linear Neural Networks
The Global Optimization Geometry of Shallow Linear Neural Networks
Zhihui Zhu
Daniel Soudry
Yonina C. Eldar
M. Wakin
ODL
18
36
0
13 May 2018
Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase
  Procrustes Flow
Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow
Xiao Zhang
S. Du
Quanquan Gu
23
24
0
03 Mar 2018
Smoothed analysis for low-rank solutions to semidefinite programs in
  quadratic penalty form
Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form
Srinadh Bhojanapalli
Nicolas Boumal
Prateek Jain
Praneeth Netrapalli
23
42
0
01 Mar 2018
Stochastic Variance-Reduced Cubic Regularization for Nonconvex
  Optimization
Stochastic Variance-Reduced Cubic Regularization for Nonconvex Optimization
Zhe Wang
Yi Zhou
Yingbin Liang
Guanghui Lan
32
46
0
20 Feb 2018
Spurious Local Minima are Common in Two-Layer ReLU Neural Networks
Spurious Local Minima are Common in Two-Layer ReLU Neural Networks
Itay Safran
Ohad Shamir
31
261
0
24 Dec 2017
A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with
  the Trace Norm
A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm
Wenjie Zheng
A. Bellet
Patrick Gallinari
18
19
0
20 Dec 2017
Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient
  Descent
Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent
Chi Jin
Praneeth Netrapalli
Michael I. Jordan
ODL
29
261
0
28 Nov 2017
On the Gap Between Strict-Saddles and True Convexity: An Omega(log d)
  Lower Bound for Eigenvector Approximation
On the Gap Between Strict-Saddles and True Convexity: An Omega(log d) Lower Bound for Eigenvector Approximation
Max Simchowitz
A. Alaoui
Benjamin Recht
18
13
0
14 Apr 2017
No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified
  Geometric Analysis
No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis
Rong Ge
Chi Jin
Yi Zheng
36
433
0
03 Apr 2017
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