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 |
|---|---|---|---|---|
| 6,742 | Mitigating the Impedance Mismatch between Prediction Query Execution and Database Engine | 2025 | SIGMOD | 5.6910432e-05 |
| 8,682 | Galley: Modern Query Optimization for Sparse Tensor Programs | 2025 | SIGMOD | 5.2905577e-05 |
| 9,227 | Qymera: Simulating Quantum Circuits using RDBMS | 2025 | SIGMOD | 5.2056825e-05 |
| 10,019 | EinDecomp: Decomposition of Declaratively-Specified Machine Learning and Numerical Computations for Parallel Execution | 2025 | VLDB | 5.0943606e-05 |
| 10,448 | EncoderForge: Generating Efficient SQL for Encoders in Machine Learning Inference Pipelines | 2026 | SIGMOD | 4.9793485e-05 |
| 10,504 | SPALM: A Sparsity-Pattern-Adaptive Library for Matrices | 2026 | SIGMOD | 4.9793485e-05 |
| 10,699 | Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation | 2026 | VLDB | 4.9793485e-05 |
| 11,243 | Quantum Data Management in the NISQ Era | 2025 | VLDB | 4.9793485e-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 | DuckDB: an Embeddable Analytical Database | 2019 | SIGMOD | 0.00037720227 |
| 73 | Including Group-By in Query Optimization | 1994 | VLDB | 0.00037522101 |
| 105 | The MADlib Analytics Library or MAD Skills, the SQL | 2012 | VLDB | 0.00033638251 |
| 154 | MAD Skills: New Analysis Practices for Big Data | 2009 | VLDB | 0.00028579704 |
| 503 | Towards a Unified Architecture for in-RDBMS Analytics | 2012 | SIGMOD | 0.00017202276 |
| 1,009 | Simulation of Database-Valued Markov Chains Using SimSQL | 2013 | SIGMOD | 0.00012539827 |
| 3,194 | One WITH RECURSIVE is Worth Many GOTOs | 2021 | SIGMOD | 7.5498012e-05 |
| 5,001 | GLADE: Big Data Analytics Made Easy | 2012 | SIGMOD | 6.3197648e-05 |
| 5,809 | Snakes on a Plan: Compiling Python Functions into Plain SQL Queries | 2022 | SIGMOD | 5.987479e-05 |
| 6,707 | Machine Learning, Linear Algebra, and More: Is SQL All You Need? | 2022 | CIDR | 5.7038956e-05 |
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