{"id":"https://openalex.org/W7165664229","doi":"https://doi.org/10.48550/arxiv.2606.21385","title":"Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability","display_name":"Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability","publication_year":2026,"publication_date":"2026-06-19","ids":{"openalex":"https://openalex.org/W7165664229","doi":"https://doi.org/10.48550/arxiv.2606.21385"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.21385","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.21385","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.21385","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062521686","display_name":"Mathieu Simon","orcid":"https://orcid.org/0000-0001-9797-540X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simon, Mathieu Cyrille","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000947076","display_name":"Pascal Frossard","orcid":"https://orcid.org/0000-0002-4010-714X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frossard, Pascal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012049713","display_name":"Christophe De Vleeschouwer","orcid":"https://orcid.org/0000-0001-5049-2929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"De Vleeschouwer, Christophe","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.5246999859809875,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.5246999859809875,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.13279999792575836,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.027699999511241913,"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/identifiability","display_name":"Identifiability","score":0.8765000104904175},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.7325000166893005},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6468999981880188},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5455999970436096},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.5436999797821045},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.4860000014305115},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4684999883174896},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.4059000015258789},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.3950999975204468}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.8765000104904175},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7325000166893005},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5455999970436096},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.5436999797821045},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5034999847412109},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5001000165939331},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.4860000014305115},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4684999883174896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46230000257492065},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.41679999232292175},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.4059000015258789},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.37130001187324524},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.36149999499320984},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C2779915298","wikidata":"https://www.wikidata.org/wiki/Q7604400","display_name":"Statistical learning theory","level":3,"score":0.31690001487731934},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2987000048160553},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.2815999984741211},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.21385","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.21385","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.21385","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.21385","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":"Preprint"},"sustainable_development_goals":[{"score":0.7425304055213928,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"explores":[2],"unsupervised":[3,96],"disentangled":[4],"representation":[5],"learning":[6],"from":[7],"a":[8,100],"functional":[9],"perspective.":[10],"We":[11,36],"define":[12],"latent":[13,57],"concepts":[14],"as":[15,25],"factors":[16],"that":[17,38],"influence":[18],"observations":[19],"through":[20],"locally":[21],"orthogonal":[22],"directions,":[23],"formalized":[24],"an":[26],"orthogonality":[27],"constraint":[28],"on":[29,83],"the":[30,33,56,72,84,91],"Jacobian":[31],"of":[32,43,62,77,86],"generative":[34,46],"mapping.":[35],"prove":[37],"this":[39],"condition":[40],"yields":[41],"identifiability":[42],"general":[44],"nonlinear":[45],"models,":[47],"without":[48],"requiring":[49],"statistical":[50],"independence":[51],"or":[52],"causal":[53],"assumptions,":[54],"provided":[55],"domain":[58],"admits":[59],"all":[60],"combinations":[61],"factor":[63],"values.":[64],"Experiments":[65],"with":[66],"orthogonality-regularized":[67],"normalizing":[68],"flows":[69],"empirically":[70],"confirm":[71],"theory,":[73],"demonstrate":[74],"reliable":[75],"recovery":[76],"ground-truth":[78],"factors,":[79],"and":[80,98],"shed":[81],"light":[82],"success":[85],"VAEs.":[87],"These":[88],"findings":[89],"challenge":[90],"prevailing":[92],"impossibility":[93],"claims":[94],"for":[95],"disentanglement":[97],"provide":[99],"principled":[101],"alternative":[102],"foundation.":[103]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-24T00:00:00"}