{"id":"https://openalex.org/W7128739328","doi":"https://doi.org/10.48550/arxiv.2602.11041","title":"Exploiting the Structure in Tensor Decompositions for Matrix Multiplication","display_name":"Exploiting the Structure in Tensor Decompositions for Matrix Multiplication","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128739328","doi":"https://doi.org/10.48550/arxiv.2602.11041"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2602.11041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.11041","pdf_url":"https://arxiv.org/pdf/2602.11041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.11041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007541022","display_name":"Manuel Kauers","orcid":"https://orcid.org/0000-0001-8641-6661","observed_orcids":["https://orcid.org/0000-0001-8641-6661"]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Kauers, Manuel","raw_affiliation_strings":["Institute for Algebra Johannes Kepler University , A4040 Linz , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Algebra Johannes Kepler University , A4040 Linz , Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076598862","display_name":"Jakob Moosbauer","orcid":"https://orcid.org/0000-0002-0634-4854","observed_orcids":["https://orcid.org/0000-0002-0634-4854"]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Moosbauer, Jakob","raw_affiliation_strings":["Institute for Algebra Johannes Kepler University , A4040 Linz , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Algebra Johannes Kepler University , A4040 Linz , Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125765237","display_name":"Isaac Wood","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Wood, Isaac","raw_affiliation_strings":["Institute for Algebra Johannes Kepler University , A4040 Linz , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Algebra Johannes Kepler University , A4040 Linz , Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.524399995803833,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.524399995803833,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.18549999594688416,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.07090000063180923,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fast-matrix-multiplication","display_name":"fast matrix multiplication","score":0.9010000228881836},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"tensor decomposition","score":0.7889999747276306},{"id":"https://openalex.org/keywords/matrix-multiplication-exponent","display_name":"matrix multiplication exponent","score":0.8009999990463257},{"id":"https://openalex.org/keywords/asymptotic-complexity","display_name":"asymptotic complexity","score":0.46399998664855957}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7141000032424927},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6963000297546387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6891000270843506},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6223000288009644},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5843999981880188},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5364999771118164},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4415000081062317},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.4278999865055084},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.3903999924659729},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3790999948978424},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.3199000060558319},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31040000915527344},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.305400013923645},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.30399999022483826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30390000343322754},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27649998664855957},{"id":"https://openalex.org/C113315163","wikidata":"https://www.wikidata.org/wiki/Q7625159","display_name":"Structure tensor","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2602.11041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.11041","pdf_url":"https://arxiv.org/pdf/2602.11041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2602.11041","doi":"https://doi.org/10.48550/arxiv.2602.11041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.11041","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2602.11041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.11041","pdf_url":"https://arxiv.org/pdf/2602.11041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3130385218","display_name":"Efficient Algorithms for Guessing, Inequalities, Summation","funder_award_id":"I6130","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7277916844","display_name":"Constructive Decomposition of Matrix Multiplication Tensors","funder_award_id":"PAT8258123","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G9000331260","display_name":null,"funder_award_id":"10.55776/PAT9952223","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128739328.pdf","grobid_xml":"https://content.openalex.org/works/W7128739328.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,58],"new":[3],"algorithm":[4,47],"for":[5,35],"fast":[6],"matrix":[7,38],"multiplication":[8,39],"using":[9],"tensor":[10,30],"decompositions":[11],"which":[12],"have":[13],"special":[14],"features.":[15],"Thanks":[16],"to":[17,54],"these":[18],"features":[19],"we":[20,40],"obtain":[21],"exponents":[22],"lower":[23],"than":[24],"what":[25],"the":[26,29,42,45],"rank":[27],"of":[28,44],"decomposition":[31],"suggests.":[32],"In":[33],"particular":[34],"$6\\times":[36],"6$":[37],"reduce":[41],"exponent":[43],"recent":[46],"by":[48],"Moosbauer":[49],"and":[50],"Poole":[51],"from":[52],"$2.8075$":[53],"$2.8019$,":[55],"while":[56],"retaining":[57],"reasonable":[59],"leading":[60],"coefficient.":[61]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2026-02-13T00:00:00"}
