Efficient Tiled Sparse Matrix Multiplication through Matrix Signatures

Abstract

Tiling is a key technique to reduce data movement in matrix computations. While tiling is well understood and widely used for dense matrix/tensor computations, effective tiling of sparse matrix computations remains a challenging problem. This paper proposes a novel method to efficiently summarize the impact of the sparsity structure of a matrix on achievable data reuse as a one-dimensional signature, which is then used to build an analytical cost model for tile size optimization for sparse matrix computations. The proposed model-driven approach to sparse tiling is evaluated on two key sparse matrix kernels: Sparse Matrix-Dense Matrix Multiplication (SpMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). Experimental results demonstrate that model-based tiled SpMM and SDDMM achieve high performance relative to the current state-of-the-art.

Efficiency of Various Tiling Strategies for the Zuker Algorithm Optimization

“…The paper [29] contributes to the efficient use of multilevel memory and optimization of data exchanges in both sequential and parallel programming. Experimental results demonstrate that the model-based tiled Sparse Matrix-Dense Matrix Multiplication (SpMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM) achieve high performance relative to the current state-of-the-art methods [30]. In paper [31], the authors introduce monoparametric tiling, a restricted parametric tiling transformation for polyhedral programs that retains the closure properties of the polyhedral model.…”

Heterogeneous computing with graphical processing unit: improvised back-propagation algorithm for water level prediction

“…12, No. 4, August 2022: 4090-4098 4092 has been applied to augment the size of tile for matrix multiplication on different kernels i.e., sparse matrixdense (SpMM) and sampled dense-dense (SDDMM)[27].…”