No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis

3 April 2017

Papers citing "No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis"

50 / 220 papers shown

Title
Nonnegative Low-rank Matrix Recovery Can Have Spurious Local Minima Richard Y. Zhang 36 0 0 06 May 2025
Euclidean Distance Matrix Completion via Asymmetric Projected Gradient Descent Yicheng Li Xinghua Sun 39 0 0 28 Apr 2025
Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization G. Zhang S. Fattahi Richard Y. Zhang 45 36 0 13 Apr 2025
Can Diffusion Models Disentangle? A Theoretical Perspective Liming Wang Muhammad Jehanzeb Mirza Yishu Gong Yuan Gong Jiaqi Zhang Brian Tracey Katerina Placek Marco Vilela James Glass DiffM CoGe 87 0 0 31 Mar 2025
Recommendations from Sparse Comparison Data: Provably Fast Convergence for Nonconvex Matrix Factorization Suryanarayana Sankagiri Jalal Etesami Matthias Grossglauser 40 0 0 27 Feb 2025
$k$ -SVD with Gradient Descent Emily Gan Yassir Jedra Devavrat Shah 66 0 0 01 Feb 2025
Disentangling Interpretable Factors with Supervised Independent Subspace Principal Component Analysis Jiayu Su David A. Knowles Raul Rabadan 21 0 0 31 Oct 2024
On the Crucial Role of Initialization for Matrix Factorization Bingcong Li Liang Zhang Aryan Mokhtari Niao He 31 1 0 24 Oct 2024
Implicit Regularization of Sharpness-Aware Minimization for Scale-Invariant Problems Bingcong Li Liang Zhang Niao He 58 3 0 18 Oct 2024
On the Learn-to-Optimize Capabilities of Transformers in In-Context Sparse Recovery Renpu Liu Ruida Zhou Cong Shen Jing Yang 30 0 0 17 Oct 2024
Noise is All You Need: Private Second-Order Convergence of Noisy SGD Dmitrii Avdiukhin Michael Dinitz Chenglin Fan G. Yaroslavtsev 34 0 0 09 Oct 2024
$$\ell_1$-norm rank-one symmetric matrix factorization has no spurious second-order stationary points$ $\ell_1$ -norm rank-one symmetric matrix factorization has no spurious second-order stationary points Jiewen Guan Anthony Man-Cho So 39 2 0 07 Oct 2024
Federated Representation Learning in the Under-Parameterized Regime Renpu Liu Cong Shen Jing Yang 26 4 0 07 Jun 2024
Compressible Dynamics in Deep Overparameterized Low-Rank Learning & Adaptation Can Yaras Peng Wang Laura Balzano Qing Qu AI4CE 37 13 0 06 Jun 2024
A Global Geometric Analysis of Maximal Coding Rate Reduction Peng Wang Huikang Liu Druv Pai Yaodong Yu Zhihui Zhu Q. Qu Yi Ma 34 6 0 04 Jun 2024
Low solution rank of the matrix LASSO under RIP with consequences for rank-constrained algorithms Andrew D. McRae 53 1 0 19 Apr 2024
cuFastTuckerPlus: A Stochastic Parallel Sparse FastTucker Decomposition Using GPU Tensor Cores Zixuan Li Mingxing Duan Huizhang Luo Wangdong Yang KenLi Li Keqin Li 34 0 0 15 Apr 2024
Robust Second-Order Nonconvex Optimization and Its Application to Low Rank Matrix Sensing Shuyao Li Yu Cheng Ilias Diakonikolas Jelena Diakonikolas Rong Ge Stephen J. Wright 44 2 0 12 Mar 2024
Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses Ziye Ma Ying Chen Javad Lavaei Somayeh Sojoudi 33 1 0 10 Mar 2024
Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape Juno Kim Taiji Suzuki 18 18 0 02 Feb 2024
Learning Rich Rankings Arjun Seshadri Stephen Ragain J. Ugander 27 12 0 22 Dec 2023
Wave Physics-informed Matrix Factorizations Harsha Vardhan Tetali J. Harley B. Haeffele 46 0 0 21 Dec 2023
High Probability Guarantees for Random Reshuffling Hengxu Yu Xiao Li 45 2 0 20 Nov 2023
A randomized algorithm for nonconvex minimization with inexact evaluations and complexity guarantees Shuyao Li Stephen J. Wright 24 3 0 28 Oct 2023
Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function Liu Liu Xuanqing Liu Cho-Jui Hsieh Dacheng Tao 23 3 0 18 Oct 2023
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
How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing: The Curses of Symmetry and Initialization Nuoya Xiong Lijun Ding Simon S. Du 48 11 0 03 Oct 2023
Global Optimality in Bivariate Gradient-based DAG Learning Chang Deng Kevin Bello Bryon Aragam Pradeep Ravikumar 38 8 0 30 Jun 2023
Curvature-Independent Last-Iterate Convergence for Games on Riemannian Manifolds Yong Cai Michael I. Jordan Tianyi Lin Argyris Oikonomou Emmanouil-Vasileios Vlatakis-Gkaragkounis 30 4 0 29 Jun 2023
Bootstrapped Representations in Reinforcement Learning Charline Le Lan Stephen Tu Mark Rowland Anna Harutyunyan Rishabh Agarwal Marc G. Bellemare Will Dabney OffRL OOD SSL 77 10 0 16 Jun 2023
The Law of Parsimony in Gradient Descent for Learning Deep Linear Networks Can Yaras Peng Wang Wei Hu Zhihui Zhu Laura Balzano Qing Qu 40 17 0 01 Jun 2023
Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming Yubo Zhuang Xiaohui Chen Yun Yang Richard Y. Zhang 19 3 0 29 May 2023
Personalized Dictionary Learning for Heterogeneous Datasets Geyu Liang Naichen Shi Raed Al Kontar S. Fattahi 25 6 0 24 May 2023
Accelerated Algorithms for Nonlinear Matrix Decomposition with the ReLU function Giovanni Seraghiti Atharva Awari A. Vandaele M. Porcelli Nicolas Gillis 23 7 0 15 May 2023
Greedy Pruning with Group Lasso Provably Generalizes for Matrix Sensing Nived Rajaraman Devvrit Aryan Mokhtari Kannan Ramchandran 25 0 0 20 Mar 2023
Can Learning Be Explained By Local Optimality In Robust Low-rank Matrix Recovery? Jianhao Ma S. Fattahi 36 1 0 21 Feb 2023
Efficient displacement convex optimization with particle gradient descent Hadi Daneshmand J. Lee Chi Jin 26 5 0 09 Feb 2023
$Approximate message passing from random initialization with applications to $\mathbb{Z}_{2}$ synchronization$ Approximate message passing from random initialization with applications to $\mathbb{Z}_{2}$ synchronization Gen Li Wei Fan Yuting Wei 26 10 0 07 Feb 2023
Understanding Incremental Learning of Gradient Descent: A Fine-grained Analysis of Matrix Sensing Jikai Jin Zhiyuan Li Kaifeng Lyu S. Du Jason D. Lee MLT 54 34 0 27 Jan 2023
Decentralized Nonconvex Optimization with Guaranteed Privacy and Accuracy Yongqiang Wang Tamer Basar 26 21 0 14 Dec 2022
Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models Qiong Wu Jian Li Zhenming Liu Jun Luo Mihai Cucuringu 34 4 0 01 Dec 2022
Simple Alternating Minimization Provably Solves Complete Dictionary Learning Geyu Liang G. Zhang S. Fattahi Richard Y. Zhang 15 5 0 23 Oct 2022
Are All Losses Created Equal: A Neural Collapse Perspective Jinxin Zhou Chong You Xiao Li Kangning Liu Sheng Liu Qing Qu Zhihui Zhu 36 59 0 04 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
Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective Yuetian Luo Nicolas García Trillos 24 6 0 29 Sep 2022
A Validation Approach to Over-parameterized Matrix and Image Recovery Lijun Ding Zhen Qin Liwei Jiang Jinxin Zhou Zhihui Zhu 48 13 0 21 Sep 2022
Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization Tianyi Lin Zeyu Zheng Michael I. Jordan 59 52 0 12 Sep 2022
Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion G. Zhang Hong-Ming Chiu Richard Y. Zhang 27 10 0 24 Aug 2022
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing Baturalp Yalcin Ziye Ma Javad Lavaei Somayeh Sojoudi 32 7 0 15 Aug 2022
Gradient descent provably escapes saddle points in the training of shallow ReLU networks Patrick Cheridito Arnulf Jentzen Florian Rossmannek 36 5 0 03 Aug 2022