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)

Paper ID: 6624
Venue: SIGMOD
Year: 2023
Pagerank: 6.0953447e-05
Overall Rank: 4,548 | 68.37%
DOI: 10.1145/3589266

Incoming Non-self Citations Over Time

Authors

Incoming Citations (Sorted by Pagerank)

Showing 6 of 6 citing papers.

Rank	Citing Paper	Year	Venue	Pagerank
6,378	Mitigating the Impedance Mismatch between Prediction Query Execution and Database Engine	2025	SIGMOD	5.0909804e-05
8,279	Galley: Modern Query Optimization for Sparse Tensor Programs	2025	SIGMOD	4.5435639e-05
9,694	EinDecomp: Decomposition of Declaratively-Specified Machine Learning and Numerical Computations for Parallel Execution	2025	VLDB	4.3025567e-05
10,226	Automated Tensor-Relational Decomposition for Large-Scale Sparse Tensor Computation	2026	VLDB	4.1945683e-05
10,450	Qymera: Simulating Quantum Circuits using RDBMS	2025	SIGMOD	4.1945683e-05
10,571	Quantum Data Management in the NISQ Era	2025	VLDB	4.1945683e-05

Outgoing Citations (Sorted by Pagerank)

Showing 11 of 11 cited papers.

Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.

Rank	Cited Paper	Year	Venue	Pagerank
51	Including Group-By in Query Optimization	1994	VLDB	0.00067123727
140	The MADlib Analytics Library or MAD Skills, the SQL	2012	VLDB	0.00042270404
168	MAD Skills: New Analysis Practices for Big Data	2009	VLDB	0.00038946305
185	DuckDB: an Embeddable Analytical Database	2019	SIGMOD	0.00036538405
658	Towards a Unified Architecture for in-RDBMS Analytics	2012	SIGMOD	0.00018506577
1,158	Simulation of Database-Valued Markov Chains Using SimSQL	2013	SIGMOD	0.0001361064
3,648	One WITH RECURSIVE is Worth Many GOTOs	2021	SIGMOD	6.8831123e-05
4,409	Declarative Recursive Computation on an RDBMS	2019	VLDB	6.2104034e-05
5,294	GLADE: Big Data Analytics Made Easy	2012	SIGMOD	5.5810654e-05
6,212	Snakes on a Plan: Compiling Python Functions into Plain SQL Queries	2022	SIGMOD	5.1552576e-05
6,990	Machine Learning, Linear Algebra, and More: Is SQL All You Need?	2022	CIDR	4.8704904e-05

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