A multi-dimensional Morton-ordered block storage for mode-oblivious tensor computations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of computational science Year : 2019

A multi-dimensional Morton-ordered block storage for mode-oblivious tensor computations

Abstract

Computation on tensors, treated as multidimensional arrays, revolve around generalized basic linear algebra subroutines (BLAS). We propose a novel data structure in which tensors are blocked and blocks are stored in an order determined by Morton order. This is not only proposed for efficiency reasons, but also to induce efficient performance regardless of which mode a generalized BLAS call is invoked for; we coin the term mode-oblivious to describe data structures and algorithms that induce such behavior. Experiments on one of the most bandwidth-bound generalized BLAS kernel, the tensor–vector multiplication, not only demonstrate superior performance over two state-of-the-art variants by up to 18%, but additionally show that the proposed data structure induces a 71% less sample standard deviation for tensor–vector multiplication across d modes, where d varies from 2 to 10. Finally, we show our data structure naturally expands to other tensor kernels and demonstrate up to 38% higher performance for the higher-order power method.
Fichier principal
Vignette du fichier
pawlowskiUcarYzelman-jocs.pdf (599.95 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02082524 , version 1 (28-03-2019)

Identifiers

Cite

Filip Pawlowski, Bora Uçar, Albert-Jan Yzelman. A multi-dimensional Morton-ordered block storage for mode-oblivious tensor computations. Journal of computational science, 2019, 33, pp.34-44. ⟨10.1016/j.jocs.2019.02.007⟩. ⟨hal-02082524⟩
93 View
385 Download

Altmetric

Share

Gmail Facebook X LinkedIn More