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CP tensor decomposition with alternating least squares (ALS) is dominated incost by the matricized-tensor times Khatri-Rao product (MTTKRP) kernel that isnecessary to set up the quadratic optimization subproblems. State-of-artparallel ALS implementations use dimension trees to avoid redundantcomputations across MTTKRPs within each ALS sweep. In this paper, we proposetwo new parallel algorithms to accelerate CP-ALS. We introduce the multi-sweepdimension tree (MSDT) algorithm, which requires the contraction between anorder N input tensor and the first-contracted input matrix once every (N-1)/Nsweeps. This algorithm reduces the leading order computational cost by a factorof 2(N-1)/N relative to the best previously known approach. In addition, weintroduce a more communication-efficient approach to parallelizing anapproximate CP-ALS algorithm, pairwise perturbation. This technique usesperturbative corrections to the subproblems rather than recomputing thecontractions, and asymptotically accelerates ALS. Our benchmark results showthat the per-sweep time achieves 1.25X speed-up for MSDT and 1.94X speed-up forpairwise perturbation compared to the state-of-art dimension trees running on1024 processors on the Stampede2 supercomputer.

Efficient parallel CP decomposition with pairwise perturbation and multi-sweep dimension tree