{"id":"https://openalex.org/W7128358724","doi":"https://doi.org/10.48550/arxiv.2602.06205","title":"Multi-Way Representation Alignment","display_name":"Multi-Way Representation Alignment","publication_year":2026,"publication_date":"2026-02-05","ids":{"openalex":"https://openalex.org/W7128358724","doi":"https://doi.org/10.48550/arxiv.2602.06205"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.06205","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.06205","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.06205","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046196341","display_name":"Akshit Achara","orcid":"https://orcid.org/0009-0006-4724-5621"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Achara, Akshit","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125421883","display_name":"Tatiana Gaintseva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gaintseva, Tatiana","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124313016","display_name":"Mat\u00e9o Mahaut","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mahaut, Mateo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084208139","display_name":"Pritish Chakraborty","orcid":"https://orcid.org/0000-0001-8875-5819"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chakraborty, Pritish","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125407635","display_name":"Viktor Stenby Johansson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johansson, Viktor Stenby","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008937016","display_name":"Melih Barsbey","orcid":"https://orcid.org/0000-0003-3404-8849"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barsbey, Melih","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125400611","display_name":"Emanuele Rodol\u00e0","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rodol\u00e0, Emanuele","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125428594","display_name":"Donato Crisostomi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Crisostomi, Donato","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5046196341"],"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1703999936580658,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1703999936580658,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.16179999709129333,"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/T11448","display_name":"Face recognition and analysis","score":0.13950000703334808,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6498000025749207},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5471000075340271},{"id":"https://openalex.org/keywords/procrustes-analysis","display_name":"Procrustes analysis","score":0.5268999934196472},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.46389999985694885},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4487000107765198},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4440999925136566},{"id":"https://openalex.org/keywords/canonical-correlation","display_name":"Canonical correlation","score":0.4332999885082245}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6498000025749207},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5471000075340271},{"id":"https://openalex.org/C2778585274","wikidata":"https://www.wikidata.org/wiki/Q2845240","display_name":"Procrustes analysis","level":2,"score":0.5268999934196472},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5098000168800354},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49320000410079956},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4733999967575073},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.46389999985694885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46000000834465027},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C153874254","wikidata":"https://www.wikidata.org/wiki/Q115542","display_name":"Canonical correlation","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C91682802","wikidata":"https://www.wikidata.org/wiki/Q620538","display_name":"Multidimensional scaling","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33000001311302185},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26750001311302185}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.06205","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.06205","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.06205","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.06205","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":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Platonic":[1],"Representation":[2],"Hypothesis":[3],"suggests":[4],"that":[5,66,80,126],"independently":[6],"trained":[7],"neural":[8],"networks":[9],"converge":[10],"to":[11,35,60],"increasingly":[12],"similar":[13],"latent":[14],"spaces.":[15],"However,":[16],"current":[17],"strategies":[18],"for":[19,72,86,120],"mapping":[20],"these":[21],"representations":[22],"are":[23],"inherently":[24],"pairwise,":[25],"scaling":[26],"quadratically":[27],"with":[28],"the":[29,46,68],"number":[30],"of":[31,48],"models":[32],"and":[33],"failing":[34],"yield":[36],"a":[37,62,111,117,134],"consistent":[38],"global":[39],"reference.":[40],"In":[41],"this":[42,100],"paper,":[43],"we":[44,102],"study":[45],"alignment":[47,83],"$M":[49],"\\ge":[50],"3$":[51],"models.":[52],"We":[53,77],"first":[54],"adapt":[55],"Generalized":[56],"Procrustes":[57,106],"Analysis":[58,94],"(GPA)":[59],"construct":[61],"shared":[63,136],"orthogonal":[64],"universe":[65,114],"preserves":[67],"internal":[69],"geometry":[70],"essential":[71],"tasks":[73],"like":[74,91],"model":[75],"stitching.":[76],"then":[78],"show":[79],"strict":[81],"isometric":[82],"is":[84],"suboptimal":[85],"retrieval,":[87],"where":[88],"agreement-maximizing":[89],"methods":[90],"Canonical":[92],"Correlation":[93],"(CCA)":[95],"typically":[96],"prevail.":[97],"To":[98],"bridge":[99],"gap,":[101],"finally":[103],"propose":[104],"Geometry-Corrected":[105],"Alignment":[107],"(GCPA),":[108],"which":[109],"establishes":[110],"robust":[112],"GPA-based":[113],"followed":[115],"by":[116],"post-hoc":[118],"correction":[119],"directional":[121],"mismatch.":[122],"Extensive":[123],"experiments":[124],"demonstrate":[125],"GCPA":[127],"consistently":[128],"improves":[129],"any-to-any":[130],"retrieval":[131],"while":[132],"retaining":[133],"practical":[135],"reference":[137],"space.":[138]},"counts_by_year":[],"updated_date":"2026-02-10T06:17:13.238206","created_date":"2026-02-10T00:00:00"}