{"id":"https://openalex.org/W4415367973","doi":"https://doi.org/10.1109/isit63088.2025.11195544","title":"Optimal Quantization for Matrix Multiplication","display_name":"Optimal Quantization for Matrix Multiplication","publication_year":2025,"publication_date":"2025-06-22","ids":{"openalex":"https://openalex.org/W4415367973","doi":"https://doi.org/10.1109/isit63088.2025.11195544"},"language":null,"primary_location":{"id":"doi:10.1109/isit63088.2025.11195544","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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,Computer Science and Engineering,Jerusalem,Israel"],"affiliations":[{"raw_affiliation_string":"Hebrew University of Jerusalem,Computer Science and Engineering,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,Dept. EECS,Cambridge,MA,USA"],"affiliations":[{"raw_affiliation_string":"MIT,Dept. EECS,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":2.856,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.92375925,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9491000175476074,"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"}},"topics":[{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9491000175476074,"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"}},{"id":"https://openalex.org/T12702","display_name":"Brain Tumor Detection and Classification","score":0.9458000063896179,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9235000014305115,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.5958999991416931},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.554099977016449},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5482000112533569},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5257999897003174},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.4830000102519989},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4603999853134155},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.44179999828338623},{"id":"https://openalex.org/keywords/lossy-compression","display_name":"Lossy compression","score":0.42309999465942383},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.38679999113082886}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7371000051498413},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5958999991416931},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.554099977016449},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5482000112533569},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5267000198364258},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5257999897003174},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.4830000102519989},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4603999853134155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4546000063419342},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.44179999828338623},{"id":"https://openalex.org/C165021410","wikidata":"https://www.wikidata.org/wiki/Q55564","display_name":"Lossy compression","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38179999589920044},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C94835093","wikidata":"https://www.wikidata.org/wiki/Q3113333","display_name":"Data compression ratio","level":5,"score":0.2824000120162964},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2743000090122223},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.2554999887943268},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit63088.2025.11195544","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1512015702","https://openalex.org/W1984810686","https://openalex.org/W1985952257","https://openalex.org/W2012833704","https://openalex.org/W2035476608","https://openalex.org/W2036845965","https://openalex.org/W2042465463","https://openalex.org/W2109053700","https://openalex.org/W2124317079","https://openalex.org/W2162006472","https://openalex.org/W2201600774","https://openalex.org/W2564985867","https://openalex.org/W2784935051","https://openalex.org/W2963122961","https://openalex.org/W3108353645","https://openalex.org/W3202306058","https://openalex.org/W4237963784","https://openalex.org/W4244670803","https://openalex.org/W4302010773","https://openalex.org/W4390098349","https://openalex.org/W4390575692","https://openalex.org/W4401692979","https://openalex.org/W4406168614","https://openalex.org/W4415367973","https://openalex.org/W4415368924"],"related_works":[],"abstract_inverted_index":{"Recent":[0],"work":[1],"in":[2,185,264],"machine":[3],"learning":[4],"community":[5],"proposed":[6],"multiple":[7],"methods":[8],"for":[9,21,143,173,237],"performing":[10],"lossy":[11],"compression":[12,56],"(quantization)":[13],"of":[14,27,38,53,76,90,132,138,146,170,177,187,206,240,259],"large":[15,28],"matrices.":[16],"This":[17],"quantization":[18,47],"is":[19,32,58,86,262],"important":[20],"accelerating":[22],"matrix":[23,70,112,238],"multiplication":[24,239],"(main":[25],"component":[26],"language":[29],"models),":[30],"which":[31,244],"often":[33],"bottlenecked":[34],"by":[35,107],"the":[36,51,65,108,128,144,222,234],"speed":[37],"loading":[39],"these":[40,54],"matrices":[41,66,78,147,178,218],"from":[42],"memory.":[43],"Unlike":[44],"classical":[45],"vector":[46],"and":[48,194,225],"rate-distortion":[49,235],"theory,":[50],"goal":[52],"new":[55],"algorithms":[57],"to":[59,62,88,110],"be":[60],"able":[61],"approximate":[63],"not":[64],"themselves,":[67],"but":[68],"their":[69],"product.":[71],"Specifically,":[72],"given":[73],"a":[74,123,136,159],"pair":[75,176],"real":[77],"<tex":[79,96,114,140,148,179,182,191,195,200,207,250],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[80,97,115,141,149,180,183,192,196,201,208,251],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$A,":[81,150,209],"B$</tex>":[82,151,210],"an":[83,167,246],"encoder":[84],"(compressor)":[85],"applied":[87],"each":[89],"them":[91],"independently":[92],"producing":[93],"descriptions":[94],"with":[95,152,166,211],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$R$</tex>":[98],"bits":[99],"per":[100],"entry.":[101],"These":[102],"representations":[103],"subsequently":[104],"are":[105,204],"used":[106],"decoder":[109],"estimate":[111],"product":[113],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$A^{\\top}":[116],"B$</tex>.":[117],"In":[118,230],"this":[119,133,260],"work,":[120],"we":[121,157,232],"provide":[122],"non-asymptotic":[124],"lower":[125,223],"bound":[126,224],"on":[127,163],"mean":[129],"squared":[130],"error":[131,172],"approximation":[134,171],"(as":[135],"function":[137,236],"rate":[139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$R$</tex>)":[142],"case":[145],"iid":[153,216,241],"Gaussian":[154,217,242],"entries.":[155],"Algorithmically,":[156],"construct":[158],"universal":[160],"quantizer":[161,220],"based":[162],"nested":[164],"lattices":[165],"explicit":[168],"guarantee":[169],"any":[174],"(non-random)":[175],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$A$</tex>,":[181],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$B$</tex>":[184],"terms":[186],"only":[188],"Frobenius":[189],"norms":[190],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\vert\\bar{A}\\vert_{F},\\vert\\bar{B}\\vert_{F}$</tex>":[193],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\left\\vert\\bar{A}^{\\top}":[197],"\\bar{B}\\right\\vert_{F}$</tex>,":[198],"where":[199],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\bar{A},":[202],"\\bar{B}$</tex>":[203],"versions":[205],"zerocentered":[212],"columns,":[213],"respectively.":[214],"For":[215],"our":[219],"achieves":[221],"is,":[226],"thus,":[227],"asymptotically":[228],"optimal.":[229],"particular,":[231],"derive":[233],"matrices,":[243],"exhibits":[245],"interesting":[247],"phase-transition":[248],"at":[249],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$R":[252],"\\approx":[253],"0.906$</tex>":[254],"bit/entry.":[255],"An":[256],"extended":[257],"version":[258],"paper":[261],"available":[263],"[1].":[265]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-21T00:00:00"}
