Sparta: high-performance, element-wise sparse tensor contraction on heterogeneous memory

Sparse tensor contractions appear commonly in many applications. Efficiently computing a two sparse tensor product is challenging: It not only inherits the challenges from common sparse matrix-matrix multiplication (SpGEMM), i.e., indirect memory access and unknown output size before computation, but also raises new challenges because of high dimensionality of tensors, expensive multi-dimensional index search, and massive intermediate and output data. To address the above challenges, we introduce three optimization techniques by using multi-dimensional, efficient hashtable representation for the accumulator and larger input tensor, and all-stage parallelization. Evaluating with 15 datasets, we show that Sparta brings 28 -- 576× speedup over the traditional sparse tensor contraction with sparse accumulator. With our proposed algorithm- and memory heterogeneity-aware data management, Sparta brings extra performance improvement on the heterogeneous memory with DRAM and Intel Optane DC Persistent Memory Module (PMM) over a state-of-the-art software-based data management solution, a hardware-based data management solution, and PMM-only by 30.7% (up to 98.5%), 10.7% (up to 28.3%) and 17% (up to 65.1%) respectively.