FaSTCC: Fast Sparse Tensor Contractions on CPUs

Sparse tensor contractions are a core computational primitive in scientific computing and machine learning. Effective optimization of such contractions through loop permutation/tiling remains an open challenge. Our work perform the first comprehensive comparative analysis of data access costs and memory requirements for loop permutations for sparse tensor contractions. Based on these insights, we develop FaSTCC, a novel hashing-based parallel implementation of sparse tensor contractions. FaSTCC introduces a new 2D tiled contraction-index-outer scheme and a corresponding tile-aware design. Using probabilistic modeling, our approach automatically chooses between dense and sparse output tile accumulators and selects suitable tile size. We evaluate FaSTCC across two CPU platforms and a range of real-world workloads, demonstrating significant speedups on benchmarks from FROSTT and from quantum chemistry.