arXiv Machine Learning July 23, 2026 By Jingzhe Wang, Hung-Hsu Chou

Stability of Low-Rank Implicit Regularization in Perturbed Deep Matrix Factorization

Read the original on arXiv Machine Learning →

arXiv:2605. 28613v2 Announce Type: replace-cross Abstract: This paper studies the stability of low-rank implicit regularization in deep matrix factorization, a tractable model for understanding how gradient-based training can favor low-complexity structure.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

arXiv Machine Learning

Jul 1

Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics

arXiv:2606. 31390v1 Announce Type: cross Abstract: Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization.

By Yudong Wei, Liang Zhang, Bingcong Li, Niao He

arXiv Machine Learning

Aug 11

Understanding Alternating Minimization for Matrix Completion

arXiv:1312. 0925v4 Announce Type: replace Abstract: Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems.

By Moritz Hardt

arXiv Machine Learning

Jun 10

Sample-efficient inductive matrix completion with noise and inexact side-information

arXiv:2605. 17189v2 Announce Type: replace-cross Abstract: Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information.

By Yuepeng Yang, Cong Ma

arXiv Machine Learning

Jun 9

State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization

arXiv:2604. 26993v2 Announce Type: replace-cross Abstract: We study gradient descent for rank-1 matrix factorization through a state-dependent Lyapunov perspective.

By Jaehong Moon

arXiv Machine Learning

Jul 28

Weighted Low-Rank Matrix Approximation: Acceleration and Applications

arXiv:2109. 11057v2 Announce Type: replace-cross Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights.

By Elena Tuzhilina, Trevor Hastie

arXiv Machine Learning

Jul 10

Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

arXiv:2607. 08380v1 Announce Type: new Abstract: An important quantity in the theory of gradient descent (GD) is the \emph{sharpness}, defined as the largest eigenvalue of the objective Hessian.

By Lachlan Ewen MacDonald, Ren\'e Vidal

Related stories

Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics

Understanding Alternating Minimization for Matrix Completion

Sample-efficient inductive matrix completion with noise and inexact side-information

State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization

Weighted Low-Rank Matrix Approximation: Acceleration and Applications

Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima