FIST-HOSVD: Fused In-place Sequentially Truncated Higher Order Singular Value Decomposition
Cobb, Benjamin,
Kolla, Hemanth,
Phipps, Eric,
and Çatalyürek, Ümit V.
In Platform for Advanced Scientific Computing (PASC’22)
2022
In this paper, several novel methods of improving the memory lo- cality of the
Sequentially Truncated Higher Order Singular Value Decomposition (ST-HOSVD) algorithm for
computing the Tucker decomposition are presented. We show how the two primary com- putational
kernels of the ST-HOSVD can be fused together into a single kernel to significantly improve
memory locality. We then extend matrix tiling techniques to tensors to further improve cache
utilization. This block-based approach is then coupled with a novel in-place transpose algorithm
to drastically reduce the memory re- quirements of the algorithm by overwriting the original
tensor with the result. Our approach’s effectiveness is demonstrated by compar- ing the
multi-threaded performance of our optimized ST-HOSVD algorithm to TuckerMPI, a state-of-the-art
ST-HOSVD implemen- tation, in compressing two combustion simulation datasets. We demonstrate up
to 135x reduction in auxiliary memory consump- tion thereby increasing the problem size that
can be computed for a given memory allocation by up to 3x, whilst maintaining comparable
runtime performance.