5 papers
A Local Geometric Analysis of Maximal Coding Rate Reduction via Error Bounds
Peng Wang, Po Chen, Huikang Liu +1
While the maximal coding rate reduction (MCR) objective has become a useful principle for learning compact and discriminative representations, a theoretical understanding of it…
Benign Landscape of Quadratic Programs with Orthogonality Constraints and Its Application to Heteroscedastic Probabilistic PCA
Peng Wang, Po Chen, Rujun Jiang +1
In this work, we study the optimization landscape of homogeneous quadratic programs with orthogonality constraints (QPOC) and apply the resulting theory to heteroscedastic probabil…
A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization
Po Chen, Rujun Jiang, Peng Wang
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 thi…
Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks
Po Chen, Rujun Jiang, Peng Wang
The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzin…
Linear Convergence of the Proximal Gradient Method for Composite Optimization Under the Polyak-Łojasiewicz Inequality and Its Variant
Qingyuan Kong, Rujun Jiang, Yihan He
We study the linear convergence rates of the proximal gradient method for composite functions satisfying two classes of Polyak-Łojasiewicz (PL) inequality: the PL inequality, the v…