{"id":"https://openalex.org/W7220995153","doi":"https://doi.org/10.48550/arxiv.2610.10033","title":"Gaussian Equivalence for Multi-Head Self-Attention","display_name":"Gaussian Equivalence for Multi-Head Self-Attention","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220995153","doi":"https://doi.org/10.48550/arxiv.2610.10033"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10033","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10033","pdf_url":"https://arxiv.org/pdf/2610.10033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10033","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061058801","display_name":"Tomohiro Hayase","orcid":"https://orcid.org/0000-0001-6453-4317","observed_orcids":["https://orcid.org/0000-0001-6453-4317"]},"institutions":[{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"id":"https://openalex.org/I4405268240","display_name":"Artificial Intelligence Research Center","ror":"https://ror.org/009x1ke56","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4405268240"]},{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hayase, Tomohiro","raw_affiliation_strings":["Artificial Intelligence Research Center (AIRC) , AIST RIKEN AIP"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Artificial Intelligence Research Center (AIRC) , AIST RIKEN AIP","institution_ids":["https://openalex.org/I4210110652","https://openalex.org/I4210126580","https://openalex.org/I4405268240","https://openalex.org/I73613424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037944527","display_name":"Ryo Karakida","orcid":"https://orcid.org/0000-0003-2294-8946","observed_orcids":["https://orcid.org/0000-0003-2294-8946"]},"institutions":[{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"id":"https://openalex.org/I4405268240","display_name":"Artificial Intelligence Research Center","ror":"https://ror.org/009x1ke56","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4405268240"]},{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Karakida, Ryo","raw_affiliation_strings":["Artificial Intelligence Research Center (AIRC) , AIST RIKEN AIP"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Artificial Intelligence Research Center (AIRC) , AIST RIKEN AIP","institution_ids":["https://openalex.org/I4210110652","https://openalex.org/I4210126580","https://openalex.org/I4405268240","https://openalex.org/I73613424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11716","display_name":"Random Matrices and Applications","score":0.8148999810218811,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.8148999810218811,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.05180000141263008,"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/T10028","display_name":"Topic Modeling","score":0.030400000512599945,"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/multi-head-self-attention","display_name":"multi-head self-attention","score":0.9919999837875366},{"id":"https://openalex.org/keywords/random-matrix-theory","display_name":"random matrix theory","score":0.8920000195503235},{"id":"https://openalex.org/keywords/softmax-attention","display_name":"softmax attention","score":0.7979999780654907},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.6480000019073486},{"id":"https://openalex.org/keywords/transformer","display_name":"transformer models","score":0.5339999794960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6837999820709229},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6492000222206116},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5759000182151794},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.42890000343322754},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.4205000102519989},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40450000762939453},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3984000086784363},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3336000144481659},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3158999979496002},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30709999799728394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29910001158714294},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2651999890804291},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2556999921798706},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C11902944","wikidata":"https://www.wikidata.org/wiki/Q5121662","display_name":"Circular ensemble","level":4,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10033","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10033","pdf_url":"https://arxiv.org/pdf/2610.10033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.10033","doi":"https://doi.org/10.48550/arxiv.2610.10033","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10033","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10033","pdf_url":"https://arxiv.org/pdf/2610.10033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220995153.pdf","grobid_xml":"https://content.openalex.org/works/W7220995153.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W3030163527","https://openalex.org/W4362679054","https://openalex.org/W4389157038","https://openalex.org/W4396815229","https://openalex.org/W6948168608"],"related_works":["https://openalex.org/W4415316575","https://openalex.org/W6893511161","https://openalex.org/W4390911450","https://openalex.org/W7204883366","https://openalex.org/W7162000890","https://openalex.org/W7148748946","https://openalex.org/W7083807327","https://openalex.org/W4392341757","https://openalex.org/W4387838886","https://openalex.org/W7107866822"],"abstract_inverted_index":{"A":[0],"theoretical":[1],"understanding":[2],"of":[3,11,40,63],"multi-head":[4,24],"self-attention":[5],"is":[6],"fundamental":[7],"to":[8],"the":[9,36,41,55,61],"study":[10],"modern":[12],"neural":[13],"networks.":[14],"Using":[15],"random":[16],"matrix":[17],"theory,":[18],"we":[19],"establish":[20],"Gaussian":[21,33],"equivalence":[22,45],"for":[23],"self-attention:":[25],"replacing":[26],"softmax":[27],"attention":[28],"with":[29],"rescaled":[30],"scores":[31],"plus":[32],"noise":[34],"preserves":[35],"limiting":[37],"spectral":[38],"law":[39],"centered":[42],"output.":[43],"This":[44],"also":[46],"covers":[47],"value":[48],"and":[49,66,69],"output":[50],"projections":[51],"that":[52],"depend":[53],"on":[54],"keys.":[56],"The":[57],"resulting":[58],"laws":[59],"separate":[60],"effects":[62],"head":[64],"allocation":[65],"projection":[67],"widths,":[68],"distinguish":[70],"spectrum-preserving":[71],"across-head":[72],"sharing":[73],"from":[74],"within-head":[75],"key--value":[76],"dependence.":[77]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}