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Efficient parallel sparse tensor contraction

Authors: Singh, Somesh; Uçar, Bora;

Efficient parallel sparse tensor contraction

Abstract

We investigate the performance of algorithms for sparse tensor-sparse tensor multiplication (SpGeTT). This operation, also called sparse tensor contraction, is a higher order analogue of the sparse matrix-sparsematrix multiplication (SpGeMM) operation. Therefore,SpGeTT can be performed by first converting the input tensors into matrices, then invoking high performancevariants of SpGeMM, and finally reconverting the resultant matrix into a tensor.Alternatively, one can carry out the scalar operations underlying SpGeTT in the realm of tensors withoutmatrix formulation.We discuss the building blocks in both approaches and formulate a hashing-based method to avoid costly searchor redirection operations.We present performance results with the current state-of-the-art SpGeMM-based approaches, existing SpGeTT approaches,and a carefully implemented SpGeTT approach with a new fine-tuned hashing method, proposed in this paper.We evaluate the methods on real world tensors, contracting a tensor with itself along various dimensions.Our proposed hashing-based method for SpGETT consistently outperforms the state-of-the-art method, achieving a 25% reduction in sequential execution time on average and a 21% reduction in parallel execution time on average across a variety of input instances.

Keywords

tensor contraction, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], hashing

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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