{"id":"https://openalex.org/W7161144170","doi":"https://doi.org/10.48550/arxiv.2605.13810","title":"Provable Quantization with Randomized Hadamard Transform","display_name":"Provable Quantization with Randomized Hadamard Transform","publication_year":2026,"publication_date":"2026-05-13","ids":{"openalex":"https://openalex.org/W7161144170","doi":"https://doi.org/10.48550/arxiv.2605.13810"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.13810","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.13810","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100517074","display_name":"Feng Ying","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Ying","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136113734","display_name":"Piotr Indyk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Indyk, Piotr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086773451","display_name":"Michael Kapralov","orcid":"https://orcid.org/0009-0006-2882-0459"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kapralov, Michael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136163489","display_name":"Dmitry Krachun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krachun, Dmitry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5117692366","display_name":"Boris Prokhorov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Prokhorov, Boris","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8389999866485596,"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":0.8389999866485596,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.06210000067949295,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.0210999995470047,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.6035000085830688},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5701000094413757},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.5612999796867371},{"id":"https://openalex.org/keywords/dither","display_name":"Dither","score":0.5393999814987183},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5206000208854675},{"id":"https://openalex.org/keywords/random-projection","display_name":"Random projection","score":0.4251999855041504},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.3871000111103058},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.3804999887943268}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7249000072479248},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.6035000085830688},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5701000094413757},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.5612999796867371},{"id":"https://openalex.org/C70451592","wikidata":"https://www.wikidata.org/wiki/Q376493","display_name":"Dither","level":3,"score":0.5393999814987183},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5206000208854675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5031999945640564},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.4251999855041504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4009999930858612},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.3871000111103058},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C93372532","wikidata":"https://www.wikidata.org/wiki/Q6552455","display_name":"Linde\u2013Buzo\u2013Gray algorithm","level":3,"score":0.31540000438690186},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.30070000886917114},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.2985999882221222},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.13810","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"doi:10.48550/arxiv.2605.13810","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.5124688744544983,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Vector":[0],"quantization":[1,8,79,173],"via":[2],"random":[3,31,98,129],"projection":[4],"followed":[5],"by":[6],"scalar":[7,99],"is":[9,114],"a":[10,73,81,97,137],"fundamental":[11],"primitive":[12],"in":[13],"machine":[14],"learning,":[15],"with":[16,80,127],"applications":[17],"ranging":[18],"from":[19],"similarity":[20],"search":[21],"to":[22,49,61,91],"federated":[23],"learning":[24],"and":[25,59,95,116,166],"KV":[26],"cache":[27],"compression.":[28],"While":[29],"dense":[30],"rotations":[32],"yield":[33],"clean":[34],"theoretical":[35],"guarantees,":[36],"they":[37],"require":[38],"$\u0398(d^2)$":[39],"time.":[40],"The":[41],"randomized":[42,83],"Hadamard":[43,84],"transform":[44],"$HD$":[45,90],"reduces":[46],"this":[47,69,76,112],"cost":[48],"$O(d":[50],"\\log":[51],"d)$,":[52],"but":[53],"its":[54],"discrete":[55],"structure":[56],"complicates":[57],"analysis":[58],"leads":[60],"weaker":[62],"or":[63],"purely":[64],"empirical":[65],"compression":[66],"guarantees.":[67],"In":[68,132],"work,":[70],"we":[71,134],"study":[72],"variant":[74],"of":[75,140,172],"approach:":[77],"dithered":[78,138],"single":[82],"transform.":[85],"Specifically,":[86],"the":[87,92,157,170],"quantizer":[88],"applies":[89],"input":[93],"vector":[94],"subtracts":[96],"offset":[100],"before":[101],"quantizing,":[102],"injecting":[103],"additional":[104],"randomness":[105],"at":[106,151],"negligible":[107],"cost.":[108],"We":[109],"prove":[110,135],"that":[111,122,136],"approach":[113],"unbiased":[115],"provides":[117],"mean":[118,143],"squared":[119,144],"error":[120,145],"bounds":[121],"asymptotically":[123],"match":[124],"those":[125],"achievable":[126],"truly":[128],"rotation":[130],"matrices.":[131],"particular,":[133],"version":[139],"TurboQuant":[141],"achieves":[142],"$\\bigl(\u03c0\\sqrt{3}/2":[146],"+":[147],"o(1)\\bigr)":[148],"\\cdot":[149],"4^{-b}$":[150],"$b$":[152],"bits":[153],"per":[154],"coordinate,":[155],"where":[156],"$o(1)$":[158],"term":[159],"vanishes":[160],"uniformly":[161],"over":[162],"all":[163,167],"unit":[164],"vectors":[165],"dimensions":[168],"as":[169],"number":[171],"levels":[174],"grows.":[175]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-15T00:00:00"}