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Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed matrix, HMatrix, is used to reduce the computational complexity of operations such as HMatrix-matrix multiplications with tuneable accuracy in an evaluation phase. Existing implementations of HMatrix evaluations do not preserve locality and often lead to unbalanced parallel execution with high synchronization. Also, current solutions require the compression phase to re-execute if the kernel method or the required accuracy change. In this work, we describe MatRox, a framework that uses novel structure analysis strategies, blocking and coarsen, with code specialization and a storage format to improve locality and create load-balanced parallel tasks for HMatrix-matrix multiplications. Modularization of the matrix compression phase enables the reuse of computations when there are changes to the input accuracy and the kernel function. The MatRox-generated code for matrix-matrix multiplication is 2.98×, 1.60×, and 5.98× faster than library implementations available in GOFMM, SMASH, and STRUMPACK respectively. Additionally, the ability to reuse portions of the compression computation for changes to the accuracy leads to up to 2.64× improvement with MatRox over five changes to accuracy using GOFMM.

This program is tentative and subject to change.

Wed 26 Feb

11:20 - 12:35: Main Conference - Matrix Multiplication and Approximation (Mediterranean Ballroom)
Chair(s): Albert CohenGoogle
PPoPP-2020-papers11:20 - 11:45
Mathias PargerGraz University of Technology, Martin WinterGraz University of Technology, Austria, Daniel MlakarGraz University of Technology, Austria, Markus SteinbergerGraz University of Technology, Austria
PPoPP-2020-papers11:45 - 12:10
Peng JiangThe University of Iowa, Changwan HongThe Ohio State University, Gagan AgrawalThe Ohio State University
PPoPP-2020-papers12:10 - 12:35
Bangtian LiuUniversity of Toronto, Kazem CheshmiUniversity of Toronto, Saeed SooriUniversity of Toronto, Michelle StroutUniversity of Arizona, Maryam Mehri DehnaviUniversity of Toronto