{"id":"https://openalex.org/W4415368924","doi":"https://doi.org/10.1109/isit63088.2025.11195282","title":"High-Rate Nested-Lattice Quantized Matrix Multiplication with Small Lookup Tables","display_name":"High-Rate Nested-Lattice Quantized Matrix Multiplication with Small Lookup Tables","publication_year":2025,"publication_date":"2025-06-22","ids":{"openalex":"https://openalex.org/W4415368924","doi":"https://doi.org/10.1109/isit63088.2025.11195282"},"language":null,"primary_location":{"id":"doi:10.1109/isit63088.2025.11195282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195282","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/A5086364920","display_name":"Itay Kaplan","orcid":"https://orcid.org/0000-0002-7032-1710"},"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":"Iris Kaplan","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/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":false,"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086364920"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":3.3332,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.93709791,"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/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9388999938964844,"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":0.9269000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lookup-table","display_name":"Lookup table","score":0.6082000136375427},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5288000106811523},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.48559999465942383},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.4357999861240387},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.43529999256134033},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.3977000117301941},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3736000061035156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6342999935150146},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.6082000136375427},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5288000106811523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5185999870300293},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.4357999861240387},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3935000002384186},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34299999475479126},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C1306188","wikidata":"https://www.wikidata.org/wiki/Q4060687","display_name":"Nested loop join","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2565999925136566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit63088.2025.11195282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195282","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1634005169","https://openalex.org/W1977182282","https://openalex.org/W2035422657","https://openalex.org/W2036845965","https://openalex.org/W2053691921","https://openalex.org/W2113885918","https://openalex.org/W2124509324","https://openalex.org/W2142276208","https://openalex.org/W2151252184","https://openalex.org/W2732156181","https://openalex.org/W2963122961","https://openalex.org/W4237963784","https://openalex.org/W4254197176","https://openalex.org/W4415367973"],"related_works":[],"abstract_inverted_index":{"Recent":[0],"work":[1],"have":[2],"shown":[3],"that":[4,37,164],"the":[5,30,53,148,151,179],"quantization":[6,112],"for":[7,140],"matrix":[8,21],"multiplication":[9],"problem":[10],"can":[11,59],"be":[12,60],"optimally":[13],"solved":[14],"by":[15],"quantizing":[16],"each":[17,20,116],"column":[18],"in":[19,89,186],"using":[22,129],"a":[23,64,104],"nested":[24,110,157],"lattice":[25,111,158],"code,":[26],"and":[27,46,55,123,160],"then":[28],"multiplying":[29],"de-quantized":[31],"matrices.":[32],"It":[33],"was":[34],"further":[35],"demonstrated":[36],"when":[38,80],"product":[39,57,94,127],"codes":[40],"of":[41,68,132,150],"sub-dimension":[42],"<tex":[43,48,70,81,106,119,134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[44,49,71,82,107,120,135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$d$</tex>":[45],"rate":[47,105],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$R$</tex>":[50,108],"are":[51],"used,":[52],"de-quantization":[54],"inner":[56,93,126],"operations":[58],"implemented":[61],"with":[62],"querying":[63],"lookup":[65],"table":[66],"(LUT)":[67],"size":[69,133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$2^{2":[72,136],"d":[73,137],"R}$</tex>,":[74],"but":[75],"this":[76,100,165],"is":[77,85,167,184],"only":[78],"useful":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$d":[83],"R$</tex>":[84],"sufficiently":[86],"small.":[87],"This":[88],"turn":[90],"limits":[91],"LUT-based":[92,125],"decoding":[95,128],"to":[96,118,155,173],"low-rate":[97],"quantizers.":[98],"In":[99],"work,":[101],"we":[102],"develop":[103],"hierarchical":[109],"framework,":[113],"which":[114],"quantizes":[115],"vector":[117],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$M$</tex>":[121],"layers,":[122],"admits":[124],"an":[130],"LUT":[131],"\\frac{R}{M}}$</tex>,":[138],"allowing":[139],"high-rate":[141],"quantization.":[142],"We":[143],"provide":[144],"analytic":[145],"bounds":[146],"on":[147],"loss":[149,166],"developed":[152],"scheme":[153,171],"compared":[154],"standard":[156],"quantizers,":[159],"also":[161],"numerically":[162],"illustrate":[163],"negligible.":[168],"Thus,":[169],"our":[170],"enables":[172],"use":[174],"small":[175],"LUTs":[176],"without":[177],"compromising":[178],"overall":[180],"distortion.":[181],"Python":[182],"code":[183],"available":[185],"https://github.com/iriskaplan/LatticeQuant.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-21T00:00:00"}
