Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915849157214208 |
|---|---|
| author | Tang, Yuxin Xin, Zhiyuan Ding, Zhimin Yao, Xinyu Bourgeois, Daniel Patel, Tirthak Jermaine, Chris |
| author_facet | Tang, Yuxin Xin, Zhiyuan Ding, Zhimin Yao, Xinyu Bourgeois, Daniel Patel, Tirthak Jermaine, Chris |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08957 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation Tang, Yuxin Xin, Zhiyuan Ding, Zhimin Yao, Xinyu Bourgeois, Daniel Patel, Tirthak Jermaine, Chris Mathematical Software Artificial Intelligence Databases 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. |
| title | Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation |
| topic | Mathematical Software Artificial Intelligence Databases |
| url | https://arxiv.org/abs/2603.08957 |