InnerSP: A Memory Efficient Sparse Matrix Multiplication Accelerator with Locality-aware Inner Product Processing

Abstract

Sparse matrix multiplication is one of the key computational kernels in large-scale data analytics. However, a naive implementation suffers from the overheads of irregular memory accesses due to the representation of sparsity. To mitigate the memory access overheads, recent accelerator designs advocated the outer product processing which minimizes input accesses but generates intermediate products to be merged to the final output matrix. Using real-world sparse matrices, this study first identifies the memory bloating problem of the outer product designs due to the unpredictable intermediate products. Such an unpredictable increase in memory requirement during computation can limit the applicability of accelerators. To address the memory bloating problem, this study revisits an alternative inner product approach, and proposes a new accelerator design called InnerSP. This study shows that nonzero element distributions in real-world sparse matrices have a certain level of locality. Using a smart caching scheme designed for inner product, the locality is effectively exploited with a modest on-chip cache. However, the row-wise inner product relies on on-chip aggregation of intermediate products. Due to uneven sparsity per row, overflows or underflows of the on-chip storage for aggregation can occur. To maximize the parallelism while avoiding costly overflows, the proposed accelerator uses pre-scanning for row splitting and merging. The simulation results show that the performance of InnerSP can exceed or be similar to those of the prior outer product approaches without any memory bloating problem.