From the 1 of 5 linked papers with an AI index.
5 papers
Graph Neural Multilevel Preconditioners for Iterative Solvers
Zechen Zhang, Rui Peng Li, Yousef Saad
The paper proposes a Graph Neural Multilevel Preconditioner that integrates an algebraic multigrid hierarchy into a learned GNN framework to improve the convergence of iterative so…
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,…
Design Criteria for SGD Preconditioners: Local Conditioning, Noise Floors, and Basin Stability
Mitchell Scott, Tianshi Xu, Ziyuan Tang +4
Stochastic Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise. We analyze preconditioned SGD in the geometry induced b…
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…
Straggler-tolerant stationary methods for linear systems
Vassilis Kalantzis, Yuanzhe Xi, Lior Horesh +1
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partia…