{"id":"https://openalex.org/W4302010773","doi":"https://doi.org/10.1038/s41586-022-05172-4","title":"Discovering faster matrix multiplication algorithms with reinforcement learning","display_name":"Discovering faster matrix multiplication algorithms with reinforcement learning","publication_year":2022,"publication_date":"2022-10-05","ids":{"openalex":"https://openalex.org/W4302010773","doi":"https://doi.org/10.1038/s41586-022-05172-4","pmid":"https://pubmed.ncbi.nlm.nih.gov/36198780"},"language":"en","primary_location":{"id":"doi:10.1038/s41586-022-05172-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41586-022-05172-4","pdf_url":"https://www.nature.com/articles/s41586-022-05172-4.pdf","source":{"id":"https://openalex.org/S137773608","display_name":"Nature","issn_l":"0028-0836","issn":["0028-0836","1476-4687"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.nature.com/articles/s41586-022-05172-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057393538","display_name":"Alhussein Fawzi","orcid":"https://orcid.org/0000-0001-7341-1917"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Alhussein Fawzi","raw_affiliation_strings":["DeepMind, London, UK. afawzi@deepmind.com","DeepMind, London, UK"],"raw_orcid":"https://orcid.org/0000-0001-7341-1917","affiliations":[{"raw_affiliation_string":"DeepMind, London, UK. afawzi@deepmind.com","institution_ids":["https://openalex.org/I4210090411"]},{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077302579","display_name":"Matej Balog","orcid":"https://orcid.org/0000-0002-5552-9855"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matej Balog","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006011042","display_name":"Aja Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Aja Huang","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083969139","display_name":"Thomas Hubert","orcid":"https://orcid.org/0000-0003-2209-3933"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thomas Hubert","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088601308","display_name":"Bernardino Romera\u2010Paredes","orcid":"https://orcid.org/0000-0003-3604-3590"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bernardino Romera-Paredes","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078666530","display_name":"Mohammadamin Barekatain","orcid":"https://orcid.org/0000-0002-8470-8203"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mohammadamin Barekatain","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":"https://orcid.org/0000-0002-8470-8203","affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101733098","display_name":"Alexander Novikov","orcid":"https://orcid.org/0009-0006-5256-7844"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexander Novikov","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101992030","display_name":"Francisco J. R. Ruiz","orcid":"https://orcid.org/0000-0002-2200-901X"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Francisco J. R. Ruiz","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080518618","display_name":"Julian Schrittwieser","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Julian Schrittwieser","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084747143","display_name":"Grzegorz \u015awirszcz","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Grzegorz Swirszcz","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091771290","display_name":"David Silver","orcid":"https://orcid.org/0000-0002-5197-2892"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David Silver","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":"https://orcid.org/0000-0002-5197-2892","affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005349213","display_name":"Demis Hassabis","orcid":"https://orcid.org/0000-0003-2812-9917"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Demis Hassabis","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":"https://orcid.org/0000-0003-2812-9917","affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013834379","display_name":"Pushmeet Kohli","orcid":"https://orcid.org/0000-0002-7466-7997"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"Google DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Pushmeet Kohli","raw_affiliation_strings":["DeepMind, London, UK"],"raw_orcid":"https://orcid.org/0000-0002-7466-7997","affiliations":[{"raw_affiliation_string":"DeepMind, London, UK","institution_ids":["https://openalex.org/I4210090411"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057393538"],"corresponding_institution_ids":["https://openalex.org/I4210090411"],"apc_list":{"value":9750,"currency":"EUR","value_usd":11690},"apc_paid":{"value":9750,"currency":"EUR","value_usd":11690},"fwci":53.7826,"has_fulltext":true,"cited_by_count":456,"citation_normalized_percentile":{"value":1.0,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"610","issue":"7930","first_page":"47","last_page":"53"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9970999956130981,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9739000201225281,"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/strassen-algorithm","display_name":"Strassen algorithm","score":0.8617415428161621},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7505675554275513},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.7394858002662659},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5391848683357239},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5055177211761475},{"id":"https://openalex.org/keywords/intuition","display_name":"Intuition","score":0.47716325521469116},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.45622214674949646},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41991090774536133},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35672762989997864},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35624411702156067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13726437091827393}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.8617415428161621},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7505675554275513},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.7394858002662659},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5391848683357239},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5055177211761475},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.47716325521469116},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.45622214674949646},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41991090774536133},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35672762989997864},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35624411702156067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13726437091827393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1038/s41586-022-05172-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41586-022-05172-4","pdf_url":"https://www.nature.com/articles/s41586-022-05172-4.pdf","source":{"id":"https://openalex.org/S137773608","display_name":"Nature","issn_l":"0028-0836","issn":["0028-0836","1476-4687"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":"journal-article"},{"id":"pmid:36198780","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36198780","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":null},{"id":"pmh:oai:RePEc:nat:nature:v:610:y:2022:i:7930:d:10.1038_s41586-022-05172-4","is_oa":false,"landing_page_url":"https://www.nature.com/articles/s41586-022-05172-4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9534758","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9534758","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Nature","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1038/s41586-022-05172-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41586-022-05172-4","pdf_url":"https://www.nature.com/articles/s41586-022-05172-4.pdf","source":{"id":"https://openalex.org/S137773608","display_name":"Nature","issn_l":"0028-0836","issn":["0028-0836","1476-4687"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320317153","display_name":"DeepMind","ror":"https://ror.org/00971b260"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4302010773.pdf","grobid_xml":"https://content.openalex.org/works/W4302010773.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W569478347","https://openalex.org/W1492936035","https://openalex.org/W1983419392","https://openalex.org/W1986272312","https://openalex.org/W1989290453","https://openalex.org/W2004948173","https://openalex.org/W2019865138","https://openalex.org/W2023724794","https://openalex.org/W2024165284","https://openalex.org/W2035476608","https://openalex.org/W2058790613","https://openalex.org/W2077071943","https://openalex.org/W2079705627","https://openalex.org/W2080063509","https://openalex.org/W2120248756","https://openalex.org/W2201600774","https://openalex.org/W2257979135","https://openalex.org/W2747592475","https://openalex.org/W2763778230","https://openalex.org/W2765302304","https://openalex.org/W2773987374","https://openalex.org/W2805516822","https://openalex.org/W2902907165","https://openalex.org/W2950034300","https://openalex.org/W2961408814","https://openalex.org/W2962764565","https://openalex.org/W2963407845","https://openalex.org/W2963576499","https://openalex.org/W2964309316","https://openalex.org/W3014127403","https://openalex.org/W3035156307","https://openalex.org/W3093790569","https://openalex.org/W3100751385","https://openalex.org/W3102252921","https://openalex.org/W3103766662","https://openalex.org/W3104956673","https://openalex.org/W3116253690","https://openalex.org/W3169240678","https://openalex.org/W3171752851","https://openalex.org/W3181416008","https://openalex.org/W3193556752","https://openalex.org/W4248316278","https://openalex.org/W6713134421","https://openalex.org/W6794153505"],"related_works":["https://openalex.org/W2392656174","https://openalex.org/W2772956802","https://openalex.org/W2962985479","https://openalex.org/W1995312928","https://openalex.org/W1523285705","https://openalex.org/W2332964641","https://openalex.org/W1989290453","https://openalex.org/W4386087921","https://openalex.org/W1997032216","https://openalex.org/W2165928982"],"abstract_inverted_index":{"Abstract":[0],"Improving":[1],"the":[2,18,53,62,69,76,103,119,135,145,165,182,217],"efficiency":[3,200],"of":[4,21,25,47,55,78,105,147,184,219,225],"algorithms":[5,48,80,101,132,189],"for":[6,95,102,138,164,193,205,230],"fundamental":[7],"computations":[8],"can":[9,16],"have":[10],"a":[11,22,86,115,126,153,223],"widespread":[12],"impact,":[13],"as":[14,75],"it":[15],"affect":[17],"overall":[19],"speed":[20],"large":[23],"amount":[24],"computations.":[26],"Matrix":[27],"multiplication":[28,104,196,204],"is":[29,73,81,111,121,144],"one":[30],"such":[31],"primitive":[32],"task,":[33],"occurring":[34],"in":[35,152],"many":[36,139],"systems\u2014from":[37],"neural":[38],"networks":[39],"to":[40,113,168,215,228],"scientific":[41],"computing":[42],"routines.":[43],"The":[44],"automatic":[45],"discovery":[46,71,173,221],"using":[49],"machine":[50],"learning":[51,89],"offers":[52],"prospect":[54],"reaching":[56],"beyond":[57],"human":[58],"intuition":[59],"and":[60,98,197,227],"outperforming":[61],"current":[63],"best":[64],"human-designed":[65],"algorithms.":[66],"However,":[67],"automating":[68],"algorithm":[70,158,163],"procedure":[72],"intricate,":[74],"space":[77],"possible":[79],"enormous.":[82],"Here":[83],"we":[84],"report":[85],"deep":[87],"reinforcement":[88],"approach":[90],"based":[91],"on":[92,160,207,222],"AlphaZero":[93],"1":[94],"discovering":[96],"efficient":[97],"provably":[99],"correct":[100],"arbitrary":[106],"matrices.":[107],"Our":[108,210],"agent,":[109],"AlphaTensor,":[110],"trained":[112],"play":[114],"single-player":[116],"game":[117],"where":[118,156],"objective":[120],"finding":[122],"tensor":[123],"decompositions":[124],"within":[125],"finite":[127,154],"factor":[128],"space.":[129],"AlphaTensor":[130,185],"discovered":[131],"that":[133],"outperform":[134],"state-of-the-art":[136,191],"complexity":[137,192],"matrix":[140,195,203],"sizes.":[141],"Particularly":[142],"relevant":[143],"case":[146],"4":[148,150],"\u00d7":[149],"matrices":[151],"field,":[155],"AlphaTensor\u2019s":[157,213],"improves":[159],"Strassen\u2019s":[161],"two-level":[162],"first":[166],"time,":[167],"our":[169],"knowledge,":[170],"since":[171],"its":[172],"50":[174],"years":[175],"ago":[176],"2":[177],".":[178],"We":[179],"further":[180],"showcase":[181],"flexibility":[183],"through":[186],"different":[187,231],"use-cases:":[188],"with":[190],"structured":[194],"improved":[198],"practical":[199],"by":[201],"optimizing":[202],"runtime":[206],"specific":[208],"hardware.":[209],"results":[211],"highlight":[212],"ability":[214],"accelerate":[216],"process":[218],"algorithmic":[220],"range":[224],"problems,":[226],"optimize":[229],"criteria.":[232]},"counts_by_year":[{"year":2026,"cited_by_count":43},{"year":2025,"cited_by_count":117},{"year":2024,"cited_by_count":134},{"year":2023,"cited_by_count":151},{"year":2022,"cited_by_count":8},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}