3 papers
math.NA2026
Hierarchical Muon: Tiled Newton-Schulz Updates for Efficient Muon Optimization
Ziyuan Tang, Tianshi Xu, Yousef Saad +1
Muon-type optimizers construct update directions for dense neural-network weights by applying a finite Newton-Schulz map to momentum-gradient matrices. For an matrix,…
math.NA2025
Preconditioned Truncated Single-Sample Estimators for Scalable Stochastic Optimization
Tianshi Xu, Difeng Cai, Hua Huang +2
Many large-scale stochastic optimization algorithms involve repeated solutions of linear systems or evaluations of log-determinants. In these regimes, computing exact solutions is…
math.NA2025
Mixed Precision Orthogonalization-Free Projection Methods for Eigenvalue and Singular Value Problems
Tianshi Xu, Zechen Zhang, Jie Chen +2
Mixed-precision arithmetic offers significant computational advantages for large-scale matrix computation tasks, yet preserving accuracy and stability in eigenvalue problems and th…