Rethinking Tiling and Dataflow for SpMM Acceleration: A Graph Transformation Framework

Sparse Matrix Dense Matrix Multiplication (SpMM) is a fundamental computation kernel across various domains, including scientific computing, machine learning, and graph processing.Despite extensive research, existing approaches optimize SpMM using loop transformations and linear algebra principles, which (1) poorly handle unstructured sparsity patterns, (2) rely on empirical methods to explore data reuse opportunities, and (3) enforce rigid coordinate alignment, compromising data locality.In this paper, we demonstrate that these limitations stem from the fundamental matrix representation and traditional dataflows of SpMM (e.g., inner-product, outer-product, and Gustavson).We propose Aquila, a graph transformation framework that reformulates SpMM computations as a graph optimization problem, leveraging graph theory to reinterpret tiling and dataflow.First, on the theoretical side, we introduce vertex decomposition and adaptive depth traversal (ADT) to enable non-contiguous tiling, where nonzero elements from discontinuous rows and columns are clustered by connectivity rather than following matrix dimensionality.This approach quantifies data reuse and improves data locality beyond traditional loop transformations while maintaining output equivalence.Second, on the algorithm side, we develop a pull-after-push (PaP) dataflow that simultaneously enhances the dense matrix data reuse while eliminating synchronization issues in output matrix accumulation.Third, building on our theoretical approach and dataflow, we present a versatile accelerator architecture that handles a variety of SpMM kernels with diverse data sizes and sparsity patterns in a unified architecture.Additionally, we introduce a bidirectional fiber tree (BFT) format to support the proposed graph-oriented dataflow in contrast to traditional column or row-major access.Evaluation across diverse sparse datasets shows Aquila achieves speedups of 4.3×, 3.4×, 3.7×, 2.9×, and 2.7× in execution time and up to 4.8× * Both authors contributed equally to this research.