{"id":"https://openalex.org/W7117574187","doi":"https://doi.org/10.1109/tit.2025.3649596","title":"Optimal Quantization for Matrix Multiplication","display_name":"Optimal Quantization for Matrix Multiplication","publication_year":2025,"publication_date":"2025-12-30","ids":{"openalex":"https://openalex.org/W7117574187","doi":"https://doi.org/10.1109/tit.2025.3649596"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2025.3649596","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3649596","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004351362","display_name":"Or Ordentlich","orcid":"https://orcid.org/0000-0002-5791-7923"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Or Ordentlich","raw_affiliation_strings":["Hebrew University of Jerusalem, Jerusalem, Israel"],"affiliations":[{"raw_affiliation_string":"Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031031216","display_name":"Yury Polyanskiy","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yury Polyanskiy","raw_affiliation_strings":["MIT, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210110987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004351362"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.84704567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"3","first_page":"1943","last_page":"1972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8252999782562256,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8252999782562256,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.042399998754262924,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.015399999916553497,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/quantization","display_name":"Quantization (signal processing)","score":0.6383000016212463},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.526199996471405},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.516700029373169},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5024999976158142},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.48910000920295715},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4611000120639801},{"id":"https://openalex.org/keywords/lossy-compression","display_name":"Lossy compression","score":0.44830000400543213},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.4442000091075897},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.424699991941452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639999747276306},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.6383000016212463},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5519000291824341},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.526199996471405},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.516700029373169},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5024999976158142},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.48910000920295715},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4611000120639801},{"id":"https://openalex.org/C165021410","wikidata":"https://www.wikidata.org/wiki/Q55564","display_name":"Lossy compression","level":2,"score":0.44830000400543213},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44670000672340393},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.4442000091075897},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37549999356269836},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C94835093","wikidata":"https://www.wikidata.org/wiki/Q3113333","display_name":"Data compression ratio","level":5,"score":0.33160001039505005},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.3025999963283539},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C93372532","wikidata":"https://www.wikidata.org/wiki/Q6552455","display_name":"Linde\u2013Buzo\u2013Gray algorithm","level":3,"score":0.2590999901294708},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.2567000091075897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3649596","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3649596","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.5426239967346191,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1512015702","https://openalex.org/W1634005169","https://openalex.org/W1809190717","https://openalex.org/W1977656318","https://openalex.org/W1984810686","https://openalex.org/W1985952257","https://openalex.org/W1999085092","https://openalex.org/W2011352281","https://openalex.org/W2012833704","https://openalex.org/W2018877773","https://openalex.org/W2029495080","https://openalex.org/W2035476608","https://openalex.org/W2036845965","https://openalex.org/W2042465463","https://openalex.org/W2059894101","https://openalex.org/W2064158368","https://openalex.org/W2064379477","https://openalex.org/W2078502923","https://openalex.org/W2093813380","https://openalex.org/W2103604544","https://openalex.org/W2109053700","https://openalex.org/W2116631972","https://openalex.org/W2119352491","https://openalex.org/W2122621581","https://openalex.org/W2124317079","https://openalex.org/W2124509324","https://openalex.org/W2129344187","https://openalex.org/W2162006472","https://openalex.org/W2201600774","https://openalex.org/W2301261742","https://openalex.org/W2317486283","https://openalex.org/W2543481766","https://openalex.org/W2564985867","https://openalex.org/W2784935051","https://openalex.org/W2963122961","https://openalex.org/W2963129746","https://openalex.org/W2963455674","https://openalex.org/W2964133401","https://openalex.org/W3100495456","https://openalex.org/W3108353645","https://openalex.org/W3164043532","https://openalex.org/W3202306058","https://openalex.org/W4237963784","https://openalex.org/W4244670803","https://openalex.org/W4254362479","https://openalex.org/W4293259454","https://openalex.org/W4302010773","https://openalex.org/W4313598801","https://openalex.org/W4382809751","https://openalex.org/W4390098349","https://openalex.org/W4390575692","https://openalex.org/W4401692979","https://openalex.org/W4401989792","https://openalex.org/W4405908657","https://openalex.org/W4406168614","https://openalex.org/W4415368924"],"related_works":[],"abstract_inverted_index":{"Recent":[0],"work":[1],"in":[2,190,285],"machine":[3],"learning":[4],"community":[5],"proposed":[6],"multiple":[7],"methods":[8],"for":[9,21,147,178,259],"performing":[10],"lossy":[11],"compression":[12,56],"(quantization)":[13],"of":[14,27,38,53,76,91,136,142,150,175,182,192,215,244,262,280],"large":[15,28],"matrices.":[16],"This":[17],"quantization":[18,47],"is":[19,32,58,87],"important":[20],"accelerating":[22],"matrix":[23,70,113,260],"multiplication":[24,261],"(main":[25],"component":[26],"language":[29],"models),":[30],"which":[31,266],"often":[33],"bottlenecked":[34],"by":[35,108],"the":[36,51,65,109,132,148,232,286],"speed":[37],"loading":[39],"these":[40,54],"matrices":[41,66,78,151,183,228],"from":[42],"memory.":[43],"Unlike":[44],"classical":[45],"vector":[46],"and":[48,202,235],"rate-distortion":[49,257],"theory,":[50],"goal":[52],"new":[55],"algorithms":[57],"to":[59,62,89,111,251],"be":[60],"able":[61],"approximate":[63],"not":[64],"themselves,":[67],"but":[68],"their":[69],"product.":[71],"Specifically,":[72],"given":[73],"a":[74,127,140,164],"pair":[75,181],"real":[77],"<italic":[79,97,115,144,152,184,187,210,216,272],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[80,82,98,116,118,120,145,153,155,185,188,197,200,204,206,211,217,219,273],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>,<italic":[81,154,218],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">B</i>":[83,156,189,212,220],"an":[84,172,268],"encoder":[85],"(compressor)":[86],"applied":[88],"each":[90],"them":[92],"independently":[93],"producing":[94],"descriptions":[95],"with":[96,157,171,221],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R</i>":[99,274],"bits":[100],"per":[101],"entry.":[102],"These":[103],"representations":[104],"subsequently":[105],"are":[106,213],"used":[107],"decoder":[110],"estimate":[112],"product":[114],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i><sup":[117],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u22a4</sup><italic":[119],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">B</i>.":[121],"In":[122,253],"this":[123,137],"work,":[124],"we":[125,162,255],"provide":[126],"non-asymptotic":[128],"lower":[129,233],"bound":[130,234],"on":[131,168],"mean":[133],"squared":[134],"error":[135,177],"approximation":[138,176],"(as":[139],"function":[141,258],"rate":[143],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R</i>)":[146],"case":[149],"iid":[158,226,263],"Gaussian":[159,227,264],"entries.":[160],"Algorithmically,":[161],"construct":[163],"universal":[165],"quantizer":[166,230,246],"based":[167],"nested":[169],"lattices":[170],"explicit":[173],"guarantee":[174],"any":[179],"(non-random)":[180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>,":[186],"terms":[191],"only":[193],"Frobenius":[194],"norms":[195],"\u2225\u0100\u2225<sub":[196],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>F</i></sub>,":[198,207],"\u2225B\u2225<sub":[199],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>F</i></sub>":[201],"\u2225\u0100\u22a4<italic":[203],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">B</i>\u2225<sub":[205],"where":[208],"\u0100,":[209],"versions":[214],"zero-centered":[222],"columns,":[223],"respectively.":[224],"For":[225],"our":[229,245],"achieves":[231,247],"is,":[236],"thus,":[237],"asymptotically":[238],"optimal.":[239,252],"A":[240],"practical":[241],"low-complexity":[242],"version":[243],"performance":[248],"quite":[249],"close":[250],"addition,":[254],"derive":[256],"matrices,":[265],"exhibits":[267],"interesting":[269],"phase-transition":[270],"at":[271],"\u2248":[275],"0.906":[276],"bit/entry,":[277],"showing":[278],"necessity":[279],"Johnson-Lindestrauss":[281],"dimensionality":[282],"reduction":[283],"(sketching)":[284],"low-rate":[287],"regime.":[288]},"counts_by_year":[],"updated_date":"2026-02-20T06:14:18.993340","created_date":"2025-12-30T00:00:00"}