Optical Realization And Application Research Of Sparse Matrix Multiplication

In numerical analysis and scientific computing,a sparse matrix is a matrix with the majority of its elements being zero.Sparse matrix multiplication,as a universal operation,is widely used in scientific computing,financial modeling,and information retrieval,such as web search ranking,graph algorithms and recommendation systems,machine learning algorithms such as computer vision,and more.While integrated electronic technology currently dominates the computing field,optical processors that are not limited by electrical interconnect energy bandwidth can bring the advantages of optical processing into the computing domain.Optical computing features high speed,high bandwidth,low power consumption,and multidimensional parallelism,making it an effective means to accelerate matrix operations and perfectly meet the computational demands of matrix multiplication.Based on this,this paper proposes an optical implementation of sparse matrix multiplication and applies it to the typical sparse matrix application scenario of graph neural networks.The main contributions of this work are as follows:First,this paper presents an optical implementation of the Sparse Matrix-Vector Multiplication(SpMV)scheme,which has been simulated and experimentally verified,by thoroughly studying the computational model of sparse matrix multiplication.The main innovations of the scheme are:(1)to construct a parallel computing framework by using multiple dimensions of time domain,frequency domain and space domain to improve the arithmetic power;(2)to support non-regular sparse matrices of different sizes and sparse distributions through reconfigurable interconnection structures,and to improve the hardware utilization by targeting the non-zero elements of the matrix during the computation.Second,this paper proposes a parallel computation scheme for graph neighborhood aggregation algorithm based on the optical sparse matrix multiplication method.The efficient computation of Graph Neural Network(GNN)remains a problem due to the structureless nature of graphs.Unlike the traditional dense matrix neural network computation,GNNs need to perform iterative neighborhood aggregation operations,in which each node aggregates its neighboring node features.Real-life graphs do not have a fixed structure,and the distribution of connections between nodes is mostly highly sparse,which leads to a large number of invalid zero operations and limits the overall performance.Therefore,this paper uses optical SpMV multipliers to compute the GNN neighborhood aggregation algorithm.In addition,to address the current problem that large-scale graph neural networks are difficult to compute,this scheme introduces a graph partitioning algorithm to slice the complete graph into multiple small-scale subgraphs,using multiple wavelengths for parallel processing,and completes testing and verification on the graph node classification task.