Zu Chongzhi Research Seminar

Date and Time (China standard time): Thursday, May 28, 2:00 – 3:00 pm

Location: WDR 1007

Title: Improved Global Landscape Guarantees for Low-rank Factorization in Synchronization

Speaker: Shuyang Ling, NYU Shanghai

Abstract: Orthogonal group synchronization seeks to recover $d\times d$ orthogonal matrices from noisy pairwise products and arises in signal processing, computer vision, and network analysis. Semidefinite relaxation (SDR) enjoys strong recovery guarantees but is often not scalable, whereas low-rank Burer–Monteiro factorization is computationally efficient but nonconvex. Understanding when this low-rank formulation has a benign landscape, free of spurious local minima, is therefore crucial.

We study the low-rank factorization over the product Stiefel manifold ${\rm St}(p,d)^{\otimes n}$. By reformulating the landscape analysis as a convex optimization problem, we provide a unified characterization of landscape benignness for all $(p,d)$ with $p\geq d+2$ for $d\geq 1$, and with $p=d+1$ for $1\leq d\leq 3$. Our results yield a substantially improved dependence on the Hessian condition number at the global minimizer. They recover the sharp known bound for $d=1$, with implications for Kuramoto synchronization, and significantly improve existing guarantees for general $d\geq 2$. The framework is broadly applicable to a range of synchronization problems.

Bio: Shuyang Ling is currently an Assistant Professor of Data Science at NYU Shanghai. He received Ph.D. degree in 2017 at Department of Mathematics, University of California, Davis, under the supervision of Prof. Thomas Strohmer. After that, he worked as a Courant Instructor at Courant Institute of Mathematical Sciences (CIMS) and Center for Data Science from 2017 to 2019. His research interests focus on the mathematics of data science and machine learning, optimization, and probability. His research has been supported by NSFC, National Major R&D Program, and national/Shanghai talent programs.