统一处理稀疏矩阵乘法，覆盖机器学习到生物计算的多种应用。
The Ubiquitous Sparse Matrix-Matrix Products
- 提出统一框架处理各类稀疏矩阵乘法
- 支持任意代数半环与异构数据域运算
- 适用于图算法、神经网络和生物序列分析
稀疏矩阵与另一矩阵（稠密或稀疏）相乘是许多数据科学应用的核心运算，包括图算法、稀疏连接神经网络、图神经网络、聚类以及生物测序数据的多对多比较。在多种应用场景中，矩阵乘法需在任意代数半环上进行，其中标量运算由具有特定性质的用户自定义函数重载，或在更一般的异构代数中，输入矩阵的定义域可不同。本文提供对稀疏矩阵-矩阵乘法及其丰富应用空间的统一处理，涵盖机器学习、计算生物学与化学、图算法及科学计算等领域。
原文摘要 · Abstract (English)
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.
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