Fast Eigenvalue Decomposition via WY Representation on Tensor Core
Symmetric eigenvalue decomposition (EVD) is a fundamental analytic and numerical tool used in many scientific areas. The state-of-the-art algorithm in terms of performance is typically the two-stage tridiagonalization method. The first stage in the two-stage tridiagonalization is called successive band reduction (SBR), which reduces a symmetric matrix to a band form, and its computational cost usually dominates. When Tensor Core (specialized matrix computational accelerator) is used to accelerate the expensive EVD, the conventional ZY-representation-based method results in suboptimal performance due to unfavorable shapes of the matrix computations. In this paper, we propose a new method that uses WY representation instead of ZY representation (see Section~\ref{WY} for details), which can provide a better combination of locality and parallelism so as to perform better on Tensor Cores. Experimentally, the proposed method can bring up to 3.7x speedup in SBR and 2.3x in the entire EVD compared to state-of-the-art implementations.
Tue 28 FebDisplayed time zone: Eastern Time (US & Canada) change
13:50 - 15:10 | Session 5: DecompositionsMain Conference at Montreal 4 Chair(s): Milind Chabbi Uber Technologies Inc. | ||
13:50 20mTalk | TDC: Towards Extremely Efficient CNNs on GPUs via Hardware-Aware Tucker Decomposition Main Conference Lizhi Xiang University of utah, Miao Yin Rutgers University, Chengming Zhang Indiana University, Aravind Sukumaran-Rajam Meta, Saday Sadayappan University of Utah, USA, Bo Yuan Rutgers University, Dingwen Tao Indiana University | ||
14:10 20mTalk | Improving Energy Saving of One-sided Matrix Decompositions on CPU-GPU Heterogeneous Systems Main Conference Jieyang Chen University of Alabama at Birmingham, Xin Liang University of Kentucky, Kai Zhao University of Alabama at Birmingham, Hadi Zamani Sabzi University of California Riverside, Laxmi Bhuyan University of California, Riverside, zizhong chen University of California, Riverside | ||
14:30 20mTalk | End-to-End LU Factorization of Large Matrices on GPUs Main Conference Yang Xia , Peng Jiang The University of Iowa, Rajiv Ramnath The Ohio State University, Gagan Agrawal Augusta University | ||
14:50 20mTalk | Fast Eigenvalue Decomposition via WY Representation on Tensor Core Main Conference Shaoshuai Zhang University of Houston, Ruchi Shah University of Houston, Hiroyuki Ootomo Tokyo Institute of Technology, Rio Yokota Tokyo Institute of Technology, Panruo Wu University of Houston |