{"id":"https://openalex.org/W7165205879","doi":"https://doi.org/10.48550/arxiv.2606.18509","title":"Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation","display_name":"Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation","publication_year":2026,"publication_date":"2026-06-16","ids":{"openalex":"https://openalex.org/W7165205879","doi":"https://doi.org/10.48550/arxiv.2606.18509"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.18509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18509","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,"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.2606.18509","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071277091","display_name":"Soheun Yi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi, Soheun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138918862","display_name":"Yizhou Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Yizhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058350509","display_name":"Chandler Squires","orcid":"https://orcid.org/0000-0002-1783-2802"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Squires, Chandler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138836376","display_name":"Pradeep Ravikumar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ravikumar, Pradeep","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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.5742999911308289,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.5742999911308289,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.09260000288486481,"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":0.06239999830722809,"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/identifiability","display_name":"Identifiability","score":0.9602000117301941},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.6462000012397766},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.5378999710083008},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44209998846054077},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.38769999146461487},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.3743000030517578},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.3677000105381012},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.34380000829696655}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.9602000117301941},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.6462000012397766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6381000280380249},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.5378999710083008},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44209998846054077},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.38769999146461487},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.3743000030517578},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34119999408721924},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31709998846054077},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3093000054359436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3028999865055084},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2822999954223633},{"id":"https://openalex.org/C70727504","wikidata":"https://www.wikidata.org/wiki/Q1806878","display_name":"Latent class model","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27570000290870667},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.26649999618530273},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.2590000033378601}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.18509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18509","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,"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.2606.18509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18509","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,"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":{"Reliable":[0],"generalization":[1],"in":[2,42,182],"conditional":[3,52,66,94],"latent":[4,19,53,81,106],"variable":[5,54],"models":[6,60,68],"requires":[7],"understanding":[8],"both":[9],"identifiability":[10,32,92,170],"and":[11,21,33,50,84,171],"extrapolation:":[12,140],"how":[13,22],"observed":[14,87,102],"variation":[15],"across":[16],"attributes":[17,76,103,144],"determines":[18,25],"structure,":[20],"that":[23,98],"structure":[24,70],"distributions":[26],"at":[27,142],"unseen":[28,143],"attributes.":[29,155],"However,":[30],"existing":[31,169],"extrapolation":[34,159,172],"guarantees":[35],"are":[36],"largely":[37],"model-specific,":[38],"with":[39,69,177],"separate":[40],"analyses":[41],"nonlinear":[43],"ICA,":[44],"causal":[45],"representation":[46],"learning,":[47],"perturbation":[48],"modeling,":[49],"related":[51],"models.":[55],"We":[56,114],"introduce":[57],"concept":[58,82,107,125],"modulation":[59],"(CMMs),":[61],"an":[62],"attribute-indexed":[63],"class":[64],"of":[65],"generative":[67],"$A\\to":[71],"\u039b\\to":[72],"C\\to":[73],"X$,":[74],"where":[75],"select":[77],"modulators,":[78],"modulators":[79],"induce":[80],"laws,":[83,126],"concepts":[85],"generate":[86],"features.":[88],"CMMs":[89],"lift":[90],"transition-based":[91],"to":[93,153],"settings":[95],"by":[96,110],"showing":[97],"feature":[99],"agreement":[100,141],"on":[101],"induces":[104],"a":[105],"transition":[108],"constrained":[109],"the":[111,128,148,162,178],"CMM":[112],"class.":[113],"express":[115],"these":[116],"constraints":[117],"through":[118],"attribute":[119],"potentials,":[120],"log-density":[121],"ratios":[122],"between":[123],"attribute-conditioned":[124],"separating":[127],"generic":[129],"lifting":[130],"step":[131],"from":[132],"model-specific":[133,179],"rigidity":[134,180],"arguments.":[135],"The":[136],"same":[137],"potentials":[138],"control":[139],"holds":[145],"exactly":[146],"when":[147,175],"transported":[149],"attribute-potential":[150],"identities":[151],"extend":[152],"those":[154,183],"This":[156],"yields":[157],"algebraic":[158],"criteria,":[160],"identifies":[161],"common":[163],"potential-based":[164],"proof":[165],"objects":[166],"behind":[167],"several":[168],"results,":[173],"and,":[174],"combined":[176],"arguments":[181],"works,":[184],"recovers":[185],"their":[186],"stated":[187],"conclusions.":[188]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-19T00:00:00"}