.png){kind=icon}
.png){kind=icon}
Return
STRASSEN'S ALGORITHM FOR TENSOR CONTRACTION
.png){kind=icon}
OA
AI
DOI：10.1137/17M1135578.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multidimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and practice, extending it to accelerate TC has not been previously pursued. Thus, we believe this to be the first paper to demonstrate how one can in practice speed up TC with Strassen's algorithm. By adopting a block-scatter-matrix format, a novel matrix-centric tensor layout, we can conceptually view TC as GEMM for a general stride storage, with an implicit tensor-to-matrix transformation. This insight enables us to tailor a recent state-of-the-art implementation of Strassen's algorithm to a recent state-of-the-art TC, avoiding explicit transpositions (permutations) and extra workspace, and reducing the overhead of memory movement that is incurred. Performance benefits are demonstrated with a performance model as well as in practice on modern single core, multicore, and distributed memory parallel architectures, achieving up to 1.3X speedup. The resulting implementations can serve as a drop-in replacement for various applications with significant speedup.
Keywords:
multilinear algebra
Strassen's algorithm
tensor contraction
matrix multiplication
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W