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Sparse Matrix-Matrix Multiplication (SpMM) has served as fundamentalcomponents in various domains. Many previous studies exploit GPUs for SpMMacceleration because GPUs provide high bandwidth and parallelism. We point outthat a static design does not always improve the performance of SpMM ondifferent input data (e.g., >85\% performance loss with a single algorithm). Inthis paper, we consider the challenge of input dynamics from a novelauto-tuning perspective, while following issues remain to be solved: (1)Orthogonal design principles considering sparsity. Orthogonal design principlesfor such a sparse problem should be extracted to form different algorithms, andfurther used for performance tuning. (2) Nontrivial implementations in thealgorithm space. Combining orthogonal design principles to create newalgorithms needs to tackle with new challenges like thread race handling. (3)Heuristic adaptability to input dynamics. The heuristic adaptability isrequired to dynamically optimize code for input dynamics.  To tackle these challenges, we first propose a novel three-loop model toextract orthogonal design principles for SpMM on GPUs. The model not onlycovers previous SpMM designs, but also comes up with new designs absent fromprevious studies. We propose techniques like conditional reduction to implementalgorithms missing in previous studies. We further propose DA-SpMM, aData-Aware heuristic GPU kernel for SpMM. DA-SpMM adaptively optimizes codeconsidering input dynamics. Extensive experimental results show that, DA-SpMMachieves 1.26x~1.37x speedup compared with the best NVIDIA cuSPARSE algorithmon average, and brings up to 5.59x end-to-end speedup to applications likeGraph Neural Networks.

Heuristic Adaptability to Input Dynamics for SpMM on GPUs