将张量关系计算自动转换为高效执行的张量-关系形式。
Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation
- 提出上标下标版EinSum，统一表达张量与关系运算。
- 自动重写计算式，使密集部分用高效数值核，稀疏部分由关系系统处理。
- 适合大规模稀疏张量计算，尤其适用于数据库+高性能计算场景。
张量-关系计算是一种每个元组携带向量、矩阵或高维数组的关系计算。其优势在于可在关系系统上执行整体计算，继承系统对超大规模稀疏输入的自动处理能力，同时利用高性能数值核（如优化的矩阵-矩阵乘法代码）完成大部分数学运算。本文引入上标下标版EinSum，即经典爱因斯坦求和记号的张量-关系版本。研究如何自动将爱因斯坦记号表达的计算重写为上标下标EinSum，使计算密集部分通过高效数值核执行，而稀疏性由关系系统管理。
原文摘要 · Abstract (English)
A \emph{tensor-relational} computation is a relational computation where individual tuples carry vectors, matrices, or higher-dimensional arrays. An advantage of tensor-relational computation is that the overall computation can be executed on top of a relational system, inheriting the system's ability to automatically handle very large inputs with high levels of sparsity while high-performance kernels (such as optimized matrix-matrix multiplication codes) can be used to perform most of the underlying mathematical operations. In this paper, we introduce upper-case-lower-case \texttt{EinSum}, which is a tensor-relational version of the classical Einstein Summation Notation. We study how to automatically rewrite a computation in Einstein Notation into upper-case-lower-case \texttt{EinSum} so that computationally intensive components are executed using efficient numerical kernels, while sparsity is managed relationally.
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