{"id":"https://openalex.org/W7131400476","doi":"https://doi.org/10.48550/arxiv.2602.19393","title":"In Defense of Cosine Similarity: Normalization Eliminates the Gauge Freedom","display_name":"In Defense of Cosine Similarity: Normalization Eliminates the Gauge Freedom","publication_year":2026,"publication_date":"2026-02-23","ids":{"openalex":"https://openalex.org/W7131400476","doi":"https://doi.org/10.48550/arxiv.2602.19393"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.19393","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19393","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.19393","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125146797","display_name":"Taha Bouhsine","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bouhsine, Taha","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5125146797"],"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":0.14090000092983246,"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":0.14090000092983246,"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/T10656","display_name":"Child and Animal Learning Development","score":0.13910000026226044,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.11159999668598175,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.7440000176429749},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.7008000016212463},{"id":"https://openalex.org/keywords/cosine-similarity","display_name":"Cosine similarity","score":0.6431999802589417},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5289999842643738},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5217000246047974},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.46309998631477356},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.40310001373291016},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.39419999718666077},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.3797999918460846}],"concepts":[{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.7440000176429749},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.7008000016212463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.671500027179718},{"id":"https://openalex.org/C2780762811","wikidata":"https://www.wikidata.org/wiki/Q1784941","display_name":"Cosine similarity","level":3,"score":0.6431999802589417},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5289999842643738},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5217000246047974},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.3797999918460846},{"id":"https://openalex.org/C28726691","wikidata":"https://www.wikidata.org/wiki/Q1268231","display_name":"Modified discrete cosine transform","level":5,"score":0.3734999895095825},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.364300012588501},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C91458471","wikidata":"https://www.wikidata.org/wiki/Q17096468","display_name":"Lapped transform","level":5,"score":0.310699999332428},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3046000003814697},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3005000054836273},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2791999876499176},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.19393","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19393","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.19393","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19393","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5882368683815002,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Steck,":[0],"Ekanadham,":[1],"and":[2,30,101,118],"Kallus":[3],"[arXiv:2403.05440]":[4],"demonstrate":[5],"that":[6,47,77,116],"cosine":[7,36,52,69,102,130,134],"similarity":[8,37,53,131],"of":[9,59,68],"learned":[10],"embeddings":[11,39,79],"from":[12],"matrix":[13,24],"factorization":[14],"models":[15],"can":[16],"be":[17],"rendered":[18],"arbitrary":[19],"by":[20],"a":[21],"diagonal":[22],"``gauge''":[23],"$D$.":[25],"Their":[26],"result":[27],"is":[28,132,137],"correct":[29],"important":[31],"for":[32],"practitioners":[33],"who":[34],"compute":[35],"on":[38,71,124],"trained":[40],"with":[41,64,92,129],"dot-product":[42],"objectives.":[43],"However,":[44],"we":[45],"argue":[46],"their":[48],"conclusion,":[49],"cautioning":[50],"against":[51],"in":[54],"general,":[55],"conflates":[56],"the":[57,65,72,83,96,108,138],"pathology":[58],"an":[60,93],"incompatible":[61],"training":[62,91],"objective":[63],"geometric":[66],"validity":[67],"distance":[70,103],"unit":[73,84],"sphere.":[74],"We":[75],"prove":[76],"when":[78],"are":[80,122],"constrained":[81],"to":[82,105,140],"sphere":[85],"$\\mathbb{S}^{d-1}$":[86],"(either":[87],"during":[88],"or":[89],"after":[90],"appropriate":[94],"objective),":[95],"$D$-matrix":[97],"ambiguity":[98],"vanishes":[99],"identically,":[100],"reduces":[104],"exactly":[106],"half":[107],"squared":[109],"Euclidean":[110],"distance.":[111],"This":[112],"monotonic":[113],"equivalence":[114],"implies":[115],"cosine-based":[117],"Euclidean-based":[119],"neighbor":[120],"rankings":[121],"identical":[123],"normalized":[125],"embeddings.":[126],"The":[127],"``problem''":[128],"not":[133],"similarity,":[135],"it":[136],"failure":[139],"normalize.":[141]},"counts_by_year":[],"updated_date":"2026-02-26T06:34:08.959763","created_date":"2026-02-26T00:00:00"}
