{"id":"https://openalex.org/W7123254502","doi":"https://doi.org/10.48550/arxiv.2601.05328","title":"Bi-Orthogonal Factor Decomposition for Vision Transformers","display_name":"Bi-Orthogonal Factor Decomposition for Vision Transformers","publication_year":2026,"publication_date":"2026-01-08","ids":{"openalex":"https://openalex.org/W7123254502","doi":"https://doi.org/10.48550/arxiv.2601.05328"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.05328","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.05328","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.2601.05328","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122796936","display_name":"Fenil R. Doshi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Doshi, Fenil R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116144107","display_name":"Thomas Fel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fel, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002461431","display_name":"Talia Konkle","orcid":"https://orcid.org/0000-0003-1738-4744"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konkle, Talia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122829445","display_name":"George Alvarez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alvarez, George","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/T11094","display_name":"Face Recognition and Perception","score":0.304500013589859,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11094","display_name":"Face Recognition and Perception","score":0.304500013589859,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"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/T11605","display_name":"Visual Attention and Saliency Detection","score":0.22499999403953552,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.09950000047683716,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.612500011920929},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.4952999949455261},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.42829999327659607},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.40880000591278076},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.40380001068115234},{"id":"https://openalex.org/keywords/computational-model","display_name":"Computational model","score":0.3919000029563904},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.32420000433921814}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6898999810218811},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.612500011920929},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5338000059127808},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.4952999949455261},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.42829999327659607},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.3919000029563904},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C5339829","wikidata":"https://www.wikidata.org/wiki/Q1425977","display_name":"Machine vision","level":2,"score":0.3125},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2924000024795532},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.2858999967575073},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.27619999647140503},{"id":"https://openalex.org/C107457646","wikidata":"https://www.wikidata.org/wiki/Q207434","display_name":"Human\u2013computer interaction","level":1,"score":0.274399995803833},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.2612000107765198}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.05328","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.05328","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.2601.05328","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.05328","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Self-attention":[0],"is":[1],"the":[2,70],"central":[3],"computational":[4],"primitive":[5],"of":[6,15,69,89],"Vision":[7],"Transformers,":[8],"yet":[9],"we":[10,93],"lack":[11],"a":[12,49,131],"principled":[13],"understanding":[14],"what":[16],"information":[17],"attention":[18,112,183],"mechanisms":[19,137],"exchange":[20],"between":[21],"tokens.":[22],"Attention":[23,104,136],"maps":[24],"describe":[25],"where":[26],"weight":[27],"mass":[28],"concentrates;":[29],"they":[30],"do":[31],"not":[32],"reveal":[33,79],"whether":[34],"queries":[35],"and":[36,64,91,100,127,145,184],"keys":[37],"trade":[38],"position,":[39],"content,":[40,92],"or":[41,190],"both.":[42],"We":[43],"introduce":[44],"Bi-orthogonal":[45],"Factor":[46],"Decomposition":[47],"(BFD),":[48],"two-stage":[50],"analytical":[51],"framework:":[52],"first,":[53],"an":[54],"ANOVA-based":[55],"decomposition":[56],"statistically":[57],"disentangles":[58],"token":[59],"activations":[60],"into":[61,142,199],"orthogonal":[62],"positional":[63,169,189],"content":[65],"factors;":[66],"second,":[67],"SVD":[68],"query-key":[71],"interaction":[72],"matrix":[73],"QK^T":[74],"exposes":[75,178],"bi-orthogonal":[76],"modes":[77,150],"that":[78,166],"how":[80,179],"these":[81],"factors":[82,187],"mediate":[83,193],"communication.":[84],"After":[85],"validating":[86],"proper":[87],"isolation":[88],"position":[90],"apply":[94],"BFD":[95,177],"to":[96,122],"state-of-the-art":[97],"vision":[98,200],"models":[99,126],"uncover":[101],"three":[102],"phenomena.(i)":[103],"operates":[105],"primarily":[106],"through":[107,182],"content.":[108,175],"Content-content":[109],"interactions":[110],"dominate":[111],"energy,":[113],"followed":[114],"by":[115],"content-position":[116,123],"coupling.":[117],"DINOv2":[118],"allocates":[119],"more":[120],"energy":[121],"than":[124],"supervised":[125],"distributes":[128],"computation":[129],"across":[130],"richer":[132],"mode":[133],"spectrum.":[134],"(ii)":[135],"exhibit":[138],"specialization:":[139],"heads":[140,152],"differentiate":[141],"content-content,":[143],"content-position,":[144],"position-position":[146],"operators,":[147],"while":[148,171],"singular":[149],"within":[151],"show":[153],"analogous":[154],"specialization.":[155],"(iii)":[156],"DINOv2's":[157],"superior":[158],"holistic":[159],"shape":[160],"processing":[161],"emerges":[162],"from":[163],"intermediate":[164],"layers":[165],"simultaneously":[167],"preserve":[168],"structure":[170],"contextually":[172],"enriching":[173],"semantic":[174,191],"Overall,":[176],"tokens":[180],"interact":[181],"which":[185],"informational":[186],"-":[188,192],"their":[194],"communication,":[195],"yielding":[196],"practical":[197],"insights":[198],"transformer":[201],"mechanisms.":[202]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-01-13T00:00:00"}