Computer Science > Mathematical Software
arXiv:2603.08957 (cs)
[Submitted on 9 Mar 2026]
Title:Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation
Authors:Yuxin Tang, Zhiyuan Xin, Zhimin Ding, Xinyu Yao, Daniel Bourgeois, Tirthak Patel, Chris Jermaine
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Abstract: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.
| Subjects: | Mathematical Software (cs.MS); Artificial Intelligence (cs.AI); Databases (cs.DB) |
| Cite as: | arXiv:2603.08957 [cs.MS] |
| (or arXiv:2603.08957v1 [cs.MS] for this version) | |
| https://doi.org/10.48550/arXiv.2603.08957
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View a PDF of the paper titled Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation, by Yuxin Tang and 6 other authors
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