{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T22:39:42Z","timestamp":1783204782876,"version":"3.54.6"},"reference-count":73,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T00:00:00Z","timestamp":1686614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100007569","name":"Carl-Zeiss-Stiftung","doi-asserted-by":"publisher","award":["Interactive Inference"],"award-info":[{"award-number":["Interactive Inference"]}],"id":[{"id":"10.13039\/100007569","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. ACM Manag. Data"],"published-print":{"date-parts":[[2023,6,13]]},"abstract":"<jats:p>Computational problems ranging from artificial intelligence to physics require efficient computations of large tensor expressions. These tensor expressions can often be represented in Einstein notation. To evaluate tensor expressions in Einstein notation, that is, for the actual Einstein summation, usually external libraries are used. Surprisingly, Einstein summation operations on tensors fit well with fundamental SQL constructs. We show that by applying only four mapping rules and a simple decomposition scheme using common table expressions, large tensor expressions in Einstein notation can be translated to portable and efficient SQL code. The ability to execute large Einstein summation queries opens up new possibilities to process data within SQL. We demonstrate the power of Einstein summation queries on four use cases, namely querying triplestore data, solving Boolean satisfiability problems, performing inference in graphical models, and simulating quantum circuits. The performance of Einstein summation queries, however, depends on the query engine implemented in the database system. Therefore, supporting efficient Einstein summation computations in database systems presents new research challenges for the design and implementation of query engines.<\/jats:p>","DOI":"10.1145\/3589266","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:26:45Z","timestamp":1687292805000},"page":"1-19","source":"Crossref","is-referenced-by-count":13,"title":["Efficient and Portable Einstein Summation in SQL"],"prefix":"10.1145","volume":"1","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-2009-7996","authenticated-orcid":false,"given":"Mark","family":"Blacher","sequence":"first","affiliation":[{"name":"Friedrich Schiller University Jena, Jena, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1498-2653","authenticated-orcid":false,"given":"Julien","family":"Klaus","sequence":"additional","affiliation":[{"name":"Friedrich Schiller University Jena, Jena, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4250-546X","authenticated-orcid":false,"given":"Christoph","family":"Staudt","sequence":"additional","affiliation":[{"name":"Friedrich Schiller University Jena, Jena, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4351-9868","authenticated-orcid":false,"given":"S\u00f6ren","family":"Laue","sequence":"additional","affiliation":[{"name":"University of Hamburg, Hamburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5676-8017","authenticated-orcid":false,"given":"Viktor","family":"Leis","sequence":"additional","affiliation":[{"name":"Technical University of Munich, Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6598-6833","authenticated-orcid":false,"given":"Joachim","family":"Giesen","sequence":"additional","affiliation":[{"name":"Friedrich Schiller University Jena, Jena, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Calculating fourier transforms in SQL,\" in ADBIS","author":"Marten D.","year":"2019","unstructured":"D. Marten, H. Meyer, and A. Heuer, \"Calculating fourier transforms in SQL,\" in ADBIS, 2019."},{"key":"e_1_2_2_2_1","volume-title":"Recursive sql for data mining,\" in SSDBM","author":"Sch\u00fcle M. E.","year":"2022","unstructured":"M. E. Sch\u00fcle, A. Kemper, and T. Neumann, \"Recursive sql for data mining,\" in SSDBM, 2022."},{"key":"e_1_2_2_3_1","volume-title":"Machine learning, linear algebra, and more: Is SQL all you need?,\" in CIDR","author":"Blacher M.","year":"2022","unstructured":"M. Blacher, J. Giesen, S. Laue, J. Klaus, and V. Leis, \"Machine learning, linear algebra, and more: Is SQL all you need?,\" in CIDR, 2022."},{"key":"e_1_2_2_4_1","volume-title":"Snakes on a plan: Compiling python functions into plain SQL queries,\" in SIGMOD","author":"Fischer T.","year":"2022","unstructured":"T. Fischer, D. Hirn, and T. Grust, \"Snakes on a plan: Compiling python functions into plain SQL queries,\" in SIGMOD, 2022."},{"key":"e_1_2_2_5_1","volume-title":"In-database machine learning: Gradient descent and tensor algebra for main memory database systems,\" in BTW","author":"Sch\u00fcle M. E.","year":"2019","unstructured":"M. E. Sch\u00fcle, F. Simonis, T. Heyenbrock, A. Kemper, S. G\u00fcnnemann, and T. Neumann, \"In-database machine learning: Gradient descent and tensor algebra for main memory database systems,\" in BTW, 2019."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2018.2827988"},{"key":"e_1_2_2_7_1","volume-title":"One WITH RECURSIVE is worth many GOTOs,\" in SIGMOD","author":"Hirn D.","year":"2021","unstructured":"D. Hirn and T. Grust, \"One WITH RECURSIVE is worth many GOTOs,\" in SIGMOD, 2021."},{"key":"e_1_2_2_8_1","volume-title":"Array programming with NumPy,\" Nature","author":"Harris C. R.","year":"2020","unstructured":"C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, et al., \"Array programming with NumPy,\" Nature, 2020."},{"key":"e_1_2_2_9_1","volume-title":"TensorFlow: Large-scale machine learning on heterogeneous systems","author":"Abadi M.","year":"2015","unstructured":"M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, et al., \"TensorFlow: Large-scale machine learning on heterogeneous systems,\" 2015. Software available from tensorflow.org."},{"key":"e_1_2_2_10_1","volume-title":"Pytorch: An imperative style, high-performance deep learning library","author":"Paszke A.","year":"2019","unstructured":"A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, et al., \"Pytorch: An imperative style, high-performance deep learning library,\" 2019."},{"key":"e_1_2_2_11_1","volume-title":"JAX: composable transformations of Python+NumPy programs","author":"Bradbury J.","year":"2018","unstructured":"J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, \"JAX: composable transformations of Python+NumPy programs,\" 2018."},{"key":"e_1_2_2_12_1","volume-title":"Parallel Computation with Blocked algorithms and Task Scheduling,\" in Proceedings of the 14th Python in Science Conference","author":"Rocklin Matthew","year":"2015","unstructured":"Matthew Rocklin, \"Dask: Parallel Computation with Blocked algorithms and Task Scheduling,\" in Proceedings of the 14th Python in Science Conference, 2015."},{"key":"e_1_2_2_13_1","volume-title":"A numpy-compatible library for nvidia gpu calculations,\" Workshop on machine learning systems (LearningSys) in Neural Information Processing Systems (NIPS)","author":"Nishino R.","year":"2017","unstructured":"R. Nishino and S. H. C. Loomis, \"Cupy: A numpy-compatible library for nvidia gpu calculations,\" Workshop on machine learning systems (LearningSys) in Neural Information Processing Systems (NIPS), 2017."},{"key":"e_1_2_2_14_1","volume-title":"Tentris - A tensor-based triple store,\" in ISWC","author":"Bigerl A.","year":"2020","unstructured":"A. Bigerl, F. Conrads, C. Behning, M. A. Sherif, M. Saleem, and A. N. Ngomo, \"Tentris - A tensor-based triple store,\" in ISWC, 2020."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-015-1276-z"},{"key":"e_1_2_2_16_1","first-page":"01437","article-title":"Duality of graphical models and tensor networks","volume":"1710","author":"Robeva E.","year":"2017","unstructured":"E. Robeva and A. Seigal, \"Duality of graphical models and tensor networks,\" CoRR, vol. abs\/1710.01437, 2017.","journal-title":"CoRR"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/050644756"},{"key":"e_1_2_2_18_1","doi-asserted-by":"crossref","unstructured":"A. Einstein \"The foundation of the general theory of relativity \" Annalen der Physik 1916.","DOI":"10.4324\/9780203198711"},{"key":"e_1_2_2_19_1","unstructured":"O. Bilaniuk \"Einstein summation in numpy.\" https:\/\/obilaniu6266h16.wordpress.com\/2016\/02\/04\/einstein-summation-in-numpy\/ 2016."},{"key":"e_1_2_2_20_1","unstructured":"Torch Contributors \"Bilinear.\" https:\/\/pytorch.org\/docs\/stable\/generated\/torch.nn.Bilinear.html 2019."},{"key":"e_1_2_2_21_1","volume-title":"Carving-width and contraction trees for tensor networks,\" arXiv","author":"Jakes-Schauer J.","year":"2019","unstructured":"J. Jakes-Schauer, D. Anekstein, and P. Wocjan, \"Carving-width and contraction trees for tensor networks,\" arXiv, 2019."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iay009"},{"key":"e_1_2_2_23_1","article-title":"On optimizing a class of multi-dimensional loops with reductions for parallel execution","author":"Lam C.","year":"1997","unstructured":"C. Lam, P. Sadayappan, and R. Wenger, \"On optimizing a class of multi-dimensional loops with reductions for parallel execution,\" Parallel Process. Lett., 1997.","journal-title":"Parallel Process. Lett."},{"key":"e_1_2_2_24_1","volume-title":"Algorithms for tensor network contraction ordering,\" Machine Learning: Science and Technology","author":"Schindler F.","year":"2020","unstructured":"F. Schindler and A. S. Jermyn, \"Algorithms for tensor network contraction ordering,\" Machine Learning: Science and Technology, 2020."},{"key":"e_1_2_2_25_1","article-title":"Sparse and dense linear algebra for machine learning on parallel-rdbms using SQL","author":"Marten D.","year":"2019","unstructured":"D. Marten, H. Meyer, D. Dietrich, and A. Heuer, \"Sparse and dense linear algebra for machine learning on parallel-rdbms using SQL,\" Open J. Big Data, 2019.","journal-title":"Open J. Big Data"},{"key":"e_1_2_2_26_1","volume-title":"ACM Program. Lang.","author":"Chou S.","year":"2018","unstructured":"S. Chou, F. Kjolstad, and S. P. Amarasinghe, \"Format abstraction for sparse tensor algebra compilers,\" Proc. ACM Program. Lang., 2018."},{"key":"e_1_2_2_27_1","volume-title":"Open Source Softw.","author":"Smith D. G. A.","year":"2018","unstructured":"D. G. A. Smith and J. Gray, \"opt_einsum - A python package for optimizing contraction order for einsum-like expressions,\" J. Open Source Softw., 2018."},{"key":"e_1_2_2_28_1","unstructured":"D. G. A. Smith \"opt_einsum docs.\" https:\/\/optimized-einsum.readthedocs.io 2018."},{"key":"e_1_2_2_29_1","volume-title":"HyPer: A hybrid OLTP&OLAP main memory database system based on virtual memory snapshots,\" in ICDE","author":"Kemper A.","year":"2011","unstructured":"A. Kemper and T. Neumann, \"HyPer: A hybrid OLTP&OLAP main memory database system based on virtual memory snapshots,\" in ICDE, 2011."},{"key":"e_1_2_2_30_1","volume-title":"Sparql 1.1 query language,\" W3C","author":"Harris S.","year":"2013","unstructured":"S. Harris and A. Seaborne, \"Sparql 1.1 query language,\" W3C, 2013."},{"key":"e_1_2_2_31_1","volume-title":"Extended example on Tentris.\" https:\/\/tentris.dice-research.org\/iswc2020\/","author":"Bigerl A.","year":"2020","unstructured":"A. Bigerl, F. Conrads, C. Behning, M. A. Sherif, M. Saleem, and A. N. Ngomo, \"Extended example on Tentris.\" https:\/\/tentris.dice-research.org\/iswc2020\/, 2020."},{"key":"e_1_2_2_32_1","unstructured":"A. Addlesee \"Creating linked data.\" https:\/\/medium.com\/wallscope\/creating-linked-data-31c7dd479a9e. Accessed: 2022-08-04."},{"key":"e_1_2_2_33_1","unstructured":"R. Griffin \"120 years of olympic history: athletes and results.\" https:\/\/www.kaggle.com\/datasets\/heesoo37\/120-years-of-olympic-history-athletes-and-results. Accessed: 2022-08-04."},{"key":"e_1_2_2_34_1","doi-asserted-by":"crossref","unstructured":"S. A. Cook \"The complexity of theorem-proving procedures \" in Proceedings of the 3rd Annual ACM Symposium on Theory of Computing 1971.","DOI":"10.1145\/800157.805047"},{"key":"e_1_2_2_35_1","volume-title":"Comput. Sci.","author":"Valiant L. G.","year":"1979","unstructured":"L. G. Valiant, \"The complexity of computing the permanent,\" Theor. Comput. Sci., 1979."},{"key":"e_1_2_2_36_1","unstructured":"\"Anaconda software distribution \" 2020."},{"key":"e_1_2_2_37_1","volume-title":"UCI machine learning repository","author":"Dua D.","year":"2017","unstructured":"D. Dua and C. Graff, \"UCI machine learning repository,\" 2017."},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2020.104601"},{"key":"e_1_2_2_39_1","volume-title":"Pareto-efficient quantum circuit simulation using tensor contraction deferral,\" arXiv","author":"Pednault E.","year":"2017","unstructured":"E. Pednault, J. A. Gunnels, G. Nannicini, L. Horesh, T. Magerlein, E. Solomonik, E. W. Draeger, E. T. Holland, and R. Wisnieff, \"Pareto-efficient quantum circuit simulation using tensor contraction deferral,\" arXiv, 2017."},{"key":"e_1_2_2_40_1","volume-title":"computer software","author":"Liakh D.","year":"2019","unstructured":"D. Liakh and USDOE, \"Exatensor. computer software,\" 2019."},{"key":"e_1_2_2_41_1","volume-title":"A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware,\" npj Quantum Information","author":"Villalonga B.","year":"2019","unstructured":"B. Villalonga, S. Boixo, B. Nelson, C. Henze, E. Rieffel, R. Biswas, and S. Mandr\u00e0, \"A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware,\" npj Quantum Information, 2019."},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.090502"},{"key":"e_1_2_2_43_1","volume-title":"Quantum theory based on real numbers can be experimentally falsified,\" Nature","author":"Renou M.-O.","year":"2021","unstructured":"M.-O. Renou, D. Trillo, M. Weilenmann, T. P. Le, A. Tavakoli, N. Gisin, A. Ac\u00edn, and M. Navascu\u00e9s, \"Quantum theory based on real numbers can be experimentally falsified,\" Nature, 2021."},{"key":"e_1_2_2_44_1","article-title":"Ruling out real-valued standard formalism of quantum theory","author":"Chen M.-C.","year":"2022","unstructured":"M.-C. Chen, C. Wang, F.-M. Liu, J.-W. Wang, C. Ying, Z.-X. Shang, Y. Wu, M. Gong, H. Deng, F.-T. Liang, et al., \"Ruling out real-valued standard formalism of quantum theory,\" Physical Review Letters, 2022.","journal-title":"Physical Review Letters"},{"key":"e_1_2_2_45_1","article-title":"Testing real quantum theory in an optical quantum network","author":"Li Z.-D.","year":"2022","unstructured":"Z.-D. Li, Y.-L. Mao, M. Weilenmann, A. Tavakoli, H. Chen, L. Feng, S.-J. Yang, M.-O. Renou, D. Trillo, T. P. Le, et al., \"Testing real quantum theory in an optical quantum network,\" Physical Review Letters, 2022.","journal-title":"Physical Review Letters"},{"key":"e_1_2_2_46_1","volume-title":"Database languages -- SQL -- Part 2: Foundation","author":"IEC","year":"2016","unstructured":"ISO\/IEC 9075--2:2016, Database languages -- SQL -- Part 2: Foundation. 2016."},{"key":"e_1_2_2_47_1","volume-title":"Quantum supremacy using a programmable superconducting processor,\" Nature","author":"Arute F.","year":"2019","unstructured":"F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., \"Quantum supremacy using a programmable superconducting processor,\" Nature, 2019."},{"key":"e_1_2_2_48_1","volume-title":"Efficient Framework for Quantum Algorithm Design,\" Quantum","author":"Luo X.-Z.","year":"2020","unstructured":"X.-Z. Luo, J.-G. Liu, P. Zhang, and L. Wang, \"Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design,\" Quantum, 2020."},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/3299869.3320212"},{"key":"e_1_2_2_50_1","volume-title":"Hyper-optimized tensor network contraction,\" Quantum","author":"Gray J.","year":"2021","unstructured":"J. Gray and S. Kourtis, \"Hyper-optimized tensor network contraction,\" Quantum, 2021."},{"key":"e_1_2_2_51_1","volume-title":"k-way hypergraph partitioning via n-level recursive bisection,\" in ALENEX","author":"Schlag S.","year":"2016","unstructured":"S. Schlag, V. Henne, T. Heuer, H. Meyerhenke, P. Sanders, and C. Schulz, \"k-way hypergraph partitioning via n-level recursive bisection,\" in ALENEX, 2016."},{"key":"e_1_2_2_52_1","volume-title":"Skew strikes back: new developments in the theory of join algorithms,\" SIGMOD Rec","author":"Ngo H. Q.","year":"2013","unstructured":"H. Q. Ngo, C. R\u00e9, and A. Rudra, \"Skew strikes back: new developments in the theory of join algorithms,\" SIGMOD Rec., 2013."},{"key":"e_1_2_2_53_1","volume-title":"Including group-by in query optimization,\" in VLDB","author":"Chaudhuri S.","year":"1994","unstructured":"S. Chaudhuri and K. Shim, \"Including group-by in query optimization,\" in VLDB, 1994."},{"key":"e_1_2_2_54_1","volume-title":"Performing group-by before join,\" in ICDE","author":"Yan W. P.","year":"1994","unstructured":"W. P. Yan and P. Larson, \"Performing group-by before join,\" in ICDE, 1994."},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00778-017-0476-3"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-01869-5"},{"key":"e_1_2_2_57_1","article-title":"Machine learning on large databases: Transforming hidden markov models to SQL statements","author":"Marten D.","year":"2017","unstructured":"D. Marten and A. Heuer, \"Machine learning on large databases: Transforming hidden markov models to SQL statements,\" Open J. Databases, 2017.","journal-title":"Open J. Databases"},{"key":"e_1_2_2_58_1","volume-title":"Reimagining deep learning with old-school SQL,\" arXiv","author":"Du L.","year":"2020","unstructured":"L. Du, \"In-machine-learning database: Reimagining deep learning with old-school SQL,\" arXiv, 2020."},{"key":"e_1_2_2_59_1","volume-title":"VLDB Endow.","author":"Jankov D.","year":"2019","unstructured":"D. Jankov, S. Luo, B. Yuan, Z. Cai, J. Zou, C. Jermaine, and Z. J. Gao, \"Declarative recursive computation on an RDBMS,\" Proc. VLDB Endow., 2019."},{"key":"e_1_2_2_60_1","volume-title":"In-database machine learning with SQL on gpus,\" in SSDBM","author":"Sch\u00fcle M. E.","year":"2021","unstructured":"M. E. Sch\u00fcle, H. Lang, M. Springer, A. Kemper, T. Neumann, and S. G\u00fcnnemann, \"In-database machine learning with SQL on gpus,\" in SSDBM, 2021."},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/2000824.2000828"},{"key":"e_1_2_2_62_1","volume-title":"Simulation of database-valued markov chains using simsql,\" in SIGMOD","author":"Cai Z.","year":"2013","unstructured":"Z. Cai, Z. Vagena, L. L. Perez, S. Arumugam, P. J. Haas, and C. M. Jermaine, \"Simulation of database-valued markov chains using simsql,\" in SIGMOD, 2013."},{"key":"e_1_2_2_63_1","volume-title":"Scalable linear algebra on a relational database system,\" in ICDE","author":"Luo S.","year":"2017","unstructured":"S. Luo, Z. J. Gao, M. N. Gubanov, L. L. Perez, and C. M. Jermaine, \"Scalable linear algebra on a relational database system,\" in ICDE, 2017."},{"key":"e_1_2_2_64_1","doi-asserted-by":"publisher","DOI":"10.14778\/1687553.1687576"},{"key":"e_1_2_2_65_1","volume-title":"VLDB Endow.","author":"Hellerstein J. M.","year":"2012","unstructured":"J. M. Hellerstein, C. R\u00e9, F. Schoppmann, D. Z. Wang, E. Fratkin, A. Gorajek, K. S. Ng, C. Welton, X. Feng, K. Li, and A. Kumar, \"The madlib analytics library or MAD skills, the SQL,\" Proc. VLDB Endow., 2012."},{"key":"e_1_2_2_66_1","volume-title":"Towards a unified architecture for in-rdbms analytics,\" in SIGMOD","author":"Feng X.","year":"2012","unstructured":"X. Feng, A. Kumar, B. Recht, and C. R\u00e9, \"Towards a unified architecture for in-rdbms analytics,\" in SIGMOD, 2012."},{"key":"e_1_2_2_67_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213836.2213936"},{"key":"e_1_2_2_68_1","volume-title":"ACM","author":"Abadi D.","year":"2022","unstructured":"D. Abadi, A. Ailamaki, D. Andersen, P. Bailis, M. Balazinska, P. A. Bernstein, P. Boncz, S. Chaudhuri, A. Cheung, A. Doan, et al., \"The seattle report on database research,\" Commun. ACM, August 2022."},{"key":"e_1_2_2_69_1","volume-title":"Tensorizing neural networks,\" in Neural Information Processing Systems (NIPS)","author":"Novikov A.","year":"2015","unstructured":"A. Novikov, D. Podoprikhin, A. Osokin, and D. P. Vetrov, \"Tensorizing neural networks,\" in Neural Information Processing Systems (NIPS), 2015."},{"key":"e_1_2_2_70_1","volume-title":"Supervised learning with tensor networks,\" in Neural Information Processing Systems (NIPS)","author":"Stoudenmire E. M.","year":"2016","unstructured":"E. M. Stoudenmire and D. J. Schwab, \"Supervised learning with tensor networks,\" in Neural Information Processing Systems (NIPS), 2016."},{"key":"e_1_2_2_71_1","article-title":"Tree tensor networks for generative modeling","author":"Cheng S.","year":"2019","unstructured":"S. Cheng, L. Wang, T. Xiang, and P. Zhang, \"Tree tensor networks for generative modeling,\" Phys. Rev. B, 2019.","journal-title":"Phys. Rev. B"},{"key":"e_1_2_2_72_1","volume-title":"Towards quantum machine learning with tensor networks,\" Quantum Science and Technology","author":"Huggins W.","year":"2019","unstructured":"W. Huggins, P. Patil, B. Mitchell, K. B. Whaley, and E. M. Stoudenmire, \"Towards quantum machine learning with tensor networks,\" Quantum Science and Technology, 2019."},{"key":"e_1_2_2_73_1","volume-title":"From probabilistic graphical models to generalized tensor networks for supervised learning,\" IEEE Access","author":"Glasser I.","year":"2020","unstructured":"I. Glasser, N. Pancotti, and J. I. Cirac, \"From probabilistic graphical models to generalized tensor networks for supervised learning,\" IEEE Access, 2020."}],"container-title":["Proceedings of the ACM on Management of Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3589266","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3589266","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:48:54Z","timestamp":1750182534000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3589266"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,13]]},"references-count":73,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6,13]]}},"alternative-id":["10.1145\/3589266"],"URL":"https:\/\/doi.org\/10.1145\/3589266","relation":{},"ISSN":["2836-6573"],"issn-type":[{"value":"2836-6573","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,13]]}}}