Fetching the paper…
Reading the bibliography…
We study the asymmetric low-rank factorization problem: \[\min_{\mathbf{U} \in \mathbb{R}^{m \times d}, \mathbf{V} \in \mathbb{R}^{n \times d}} \frac{1}{2}\|\mathbf{U}\mathbf{V}^\top -\mathbf{\Sigma}\|_F^2\] where $\mathbf{\Sigma}$ is a given matrix of size $m \times n$ and rank $d$.
Linear Algebra and Its Applications
P.D. Lax · 2007
Earlier work this paper cites.
Topics in random matrix theory , volume 132
Terence Tao · 2012
Earlier work this paper cites.
Escaping from saddle points − - online stochastic gradient for tensor decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
Earlier work this paper cites.
Nonconvex low rank matrix factorization via inexact first order oracle
Tuo Zhao, Zhaoran Wang, and Han Liu · 2015
Earlier work this paper cites.
Dropping convexity for faster semi-definite optimization
Srinadh Bhojanapalli, Anastasios Kyrillidis, and Sujay Sanghavi · 2016
Earlier work this paper cites.
Matrix completion has no spurious local minimum
Rong Ge, Jason D Lee, and Tengyu Ma · 2016
Earlier work this paper cites.
Gradient descent only converges to minimizers
Jason D Lee, Max Simchowitz, Michael I Jordan, and Benjamin Recht · 2016
Earlier work this paper cites.
Gradient descent only converges to minimizers: Non-isolated critical points and invariant regions
Ioannis Panageas and Georgios Piliouras · 2016
Cited alongside, same era.
Guaranteed matrix completion via non-convex factorization
Ruoyu Sun and Zhi-Quan Luo · 2016
Cited alongside, same era.
Low-rank solutions of linear matrix equations via Procrustes flow
Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Benjamin Recht · 2016
Cited alongside, same era.
Qinqing Zheng and John Lafferty · 2016
Cited alongside, same era.
Gradient descent can take exponential time to escape saddle points
Simon S Du, Chi Jin, Jason D Lee, Michael I Jordan, Barnabas Poczos, and Aarti Singh · 2017
Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach
Dohyung Park, Anastasios Kyrillidis, Constantine Carmanis, and Sujay Sanghavi · 2017
Later among the works it cites.
Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced
Simon S Du, Wei Hu, and Jason D Lee · 2018
Later among the works it cites.
Algorithmic regularization in over-parameterized matrix sensing and neural networks with quadratic activations
Yuanzhi Li, Tengyu Ma, and Hongyang Zhang · 2018
Later among the works it cites.
Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval
Yuxin Chen, Yuejie Chi, Jianqing Fan, and Cong Ma · 2019
Later among the works it cites.
Polynomial time guarantees for the burer-monteiro method
Diego Cifuentes and Ankur Moitra · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Global convergence of non-convex gradient descent for computing matrix squareroot
Prateek Jain, Chi Jin, Sham Kakade, and Praneeth Netrapalli · 2017
Cited alongside, same era.
How to escape saddle points efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M. Kakade, and Michael I. Jordan · 2017
Cited alongside, same era.
No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng
Cited in the paper.
Learning one-hidden-layer neural networks with landscape design
Rong Ge, Jason D Lee, and Tengyu Ma
Cited in the paper.
The non-convex geometry of low-rank matrix optimization
Qiuwei Li, Zhihui Zhu, and Gongguo Tang
Cited in the paper.
Symmetry, saddle points, and global optimization landscape of nonconvex matrix factorization
Xingguo Li, Junwei Lu, Raman Arora, Jarvis Haupt, Han Liu, Zhaoran Wang, and Tuo Zhao
Cited in the paper.
Beyond procrustes: Balancing-free gradient descent for asymmetric low-rank matrix sensing
Cong Ma, Yuanxin Li, and Yuejie Chi · 2021
Closest in time.