# Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation

arXiv: https://arxiv.org/abs/2603.08957 · HTML: https://mlsanity.com/paper/2603.08957/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [AliGraph: A Comprehensive Graph Neural Network Platform](https://mlsanity.com/paper/1902.08730/) (2019)
- [SparseTIR: Composable Abstractions for Sparse Compilation in Deep Learning](https://mlsanity.com/paper/2207.04606/) (2022)
- [SystemDS: A Declarative Machine Learning System for the End-to-End Data Science Lifecycle](https://mlsanity.com/paper/1909.02976/) (2019)
- [Format Abstraction for Sparse Tensor Algebra Compilers](https://mlsanity.com/paper/1804.10112/) (2018)
- [Tensor Relational Algebra for Machine Learning System Design](https://mlsanity.com/paper/2009.00524/) (2020)
- [Optimizing Tensor Programs on Flexible Storage](https://mlsanity.com/paper/2210.06267/) (2022)
- [PlinyCompute: A Platform for High-Performance, Distributed, Data-Intensive Tool Development](https://mlsanity.com/paper/1711.05573/) (2017)
- [TorchGT: A Holistic System for Large-scale Graph Transformer Training](https://mlsanity.com/paper/2407.14106/) (2024)
- [PyTond: Efficient Python Data Science on the Shoulders of Databases](https://mlsanity.com/paper/2407.11616/) (2024)
- [The Duck's Brain: Training and Inference of Neural Networks in Modern Database Engines](https://mlsanity.com/paper/2312.17355/) (2023)
- [EinDecomp: Decomposition of Declaratively-Specified Machine Learning and Numerical Computations for Parallel Execution](https://mlsanity.com/paper/2410.02682/) (2024)
- [Galley: Modern Query Optimization for Sparse Tensor Programs](https://mlsanity.com/paper/2408.14706/) (2024)

## Abstract (arXiv)

A 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 textttEinSum, 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 textttEinSum so that computationally intensive components are executed using efficient numerical kernels, while sparsity is managed relationally.