Efficient and Portable Einstein Summation in SQL
Summary: Einstein summation for tensors is implemented in SQL with four mapping rules and a CTE-based decomposition, yielding portable, efficient expressions. Demonstrates use cases in triplestore queries, SAT solving, graphical-model inference, and quantum circuit simulation, and notes engine-dependent performance as a key SQL research challenge. (summarized by gpt-5-nano on Feb 09 2026)
Incoming Non-self Citations Over Time
Authors
- 1. Mark Blacher (University of Jena)
- 2. Julien Klaus (University of Jena)
- 3. Christoph Staudt (University of Jena)
- 4. Sören Laue (University of Hamburg)
- 5. Viktor Leis (Technical University of Munich)
- 6. Joachim Giesen (University of Jena)
BibTeX Citation
@inproceedings{blacher_sigmod23,
title = {{Efficient and Portable Einstein Summation in SQL}},
author = {Blacher, Mark and Klaus, Julien and Staudt, Christoph and Laue, Sören and Leis, Viktor and Giesen, Joachim},
series = {{SIGMOD} '23},
booktitle = {Proceedings of the {ACM} {SIGMOD} International Conference on Management of Data},
publisher = {Association for Computing Machinery},
doi = {10.1145/3589266},
url = {https://dl.acm.org/doi/10.1145/3589266},
year = {2023}
}Incoming Citations (Sorted by Pagerank)
Showing 8 of 8 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 6,614 | Mitigating the Impedance Mismatch between Prediction Query Execution and Database Engine | 2025 | SIGMOD | 5.8216658e-05 |
| 8,513 | Galley: Modern Query Optimization for Sparse Tensor Programs | 2025 | SIGMOD | 5.4119882e-05 |
| 9,834 | EinDecomp: Decomposition of Declaratively-Specified Machine Learning and Numerical Computations for Parallel Execution | 2025 | VLDB | 5.2112879e-05 |
| 10,232 | EncoderForge: Generating Efficient SQL for Encoders in Machine Learning Inference Pipelines | 2026 | SIGMOD | 5.093636e-05 |
| 10,292 | SPALM: A Sparsity-Pattern-Adaptive Library for Matrices | 2026 | SIGMOD | 5.093636e-05 |
| 10,514 | Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation | 2026 | VLDB | 5.093636e-05 |
| 10,731 | Qymera: Simulating Quantum Circuits using RDBMS | 2025 | SIGMOD | 5.093636e-05 |
| 10,836 | Quantum Data Management in the NISQ Era | 2025 | VLDB | 5.093636e-05 |
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Outgoing Citations (Sorted by Pagerank)
Showing 10 of 10 cited papers.
Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 71 | Including Group-By in Query Optimization | 1994 | VLDB | 0.00038021159 |
| 103 | DuckDB: an Embeddable Analytical Database | 2019 | SIGMOD | 0.00034161428 |
| 106 | The MADlib Analytics Library or MAD Skills, the SQL | 2012 | VLDB | 0.00033539462 |
| 155 | MAD Skills: New Analysis Practices for Big Data | 2009 | VLDB | 0.00028713176 |
| 518 | Towards a Unified Architecture for in-RDBMS Analytics | 2012 | SIGMOD | 0.00017167492 |
| 993 | Simulation of Database-Valued Markov Chains Using SimSQL | 2013 | SIGMOD | 0.00012789598 |
| 3,257 | One WITH RECURSIVE is Worth Many GOTOs | 2021 | SIGMOD | 7.590651e-05 |
| 4,897 | GLADE: Big Data Analytics Made Easy | 2012 | SIGMOD | 6.4546134e-05 |
| 5,684 | Snakes on a Plan: Compiling Python Functions into Plain SQL Queries | 2022 | SIGMOD | 6.1224825e-05 |
| 6,604 | Machine Learning, Linear Algebra, and More: Is SQL All You Need? | 2022 | CIDR | 5.8240599e-05 |
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