ReSpar: Reordering Algorithm for ReRAM-based Sparse Matrix-Vector Multiplication Accelerator

Sparse matrix-vector multiplication (SpMV) serves as a crucial operation for several key application domains, such as graph analytics and scientific computing, in the era of big data. The performance of SpMV is bounded by the data transmissions across memory channels in conventional von Neumann systems. Emerging metal-oxide resistive random access memory (ReRAM) has shown its potential to address this memory wall challenge through performing SpMV directly within its crossbar arrays. However, due to the tightly coupled crossbar structure, it is unlikely to skip all redundant data loading and computations with zero-valued entries of the sparse matrix in such ReRAM-based processing-in-memory architecture. These unnecessary ReRAM writes and computations hurt the energy efficiency. As only the crossbar-sized sub-matrices with full-zero entries can be skipped, prior studies have proposed some matrix reordering methods to aggregate non-zero entries to few crossbar arrays, such that more full-zero crossbar arrays can be skipped. Nevertheless, the effectiveness of prior reordering methods is constrained by the original ordering of matrix rows. In this paper, we show that the amount of full-zero sub-matrices derived by these prior studies are less than a theoretical lower bound in some cases, indicating that there are still rooms for improvement. Hence, we propose a novel reordering algorithm, ReSpar, that aims to aggregate matrix rows with similar non-zero column entries together and concentrates the non-zeros columns to increase the zero-skipping opportunities. Results show that ReSpar achieves 1.68× and 1.37× more energy savings, while reducing the required number of crossbar loads by 40.4% and 27.2% on average.