A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization

Understand

Despite its wide range of applications across various domains, the optimization foundations of deep matrix factorization (DMF) remain largely open.

• In this work, we aim to fill this gap by conducting a comprehensive study of the loss landscape of the regularized DMF problem.
• Toward this goal, we first provide a closed-form characterization of all critical points of the problem.
• Building on this, we establish precise conditions under which a critical point is a local minimizer, a global minimizer, a strict saddle point, or a non-strict saddle point.