The Ubiquitous Sparse Matrix-Matrix Products

Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected neural networks, graph neural networks, clustering, and many-to-many comparisons of biological sequencing data.In many application scenarios, the matrix multiplication takes places on an arbitrary algebraic semiring where the scalar operations are overloaded with user-defined functions with certain properties or a more general heterogenous algebra where even the domains of the input matrices can be different. Here, we provide a unifying treatment of the sparse matrix-matrix operation and its rich application space including machine learning, computational biology and chemistry, graph algorithms, and scientific computing.