{"id":"https://openalex.org/W7161807270","doi":"https://doi.org/10.48550/arxiv.2605.20151","title":"When Does Model Collapse Occur in Structured Interactive Learning?","display_name":"When Does Model Collapse Occur in Structured Interactive Learning?","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161807270","doi":"https://doi.org/10.48550/arxiv.2605.20151"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.20151","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20151","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.2605.20151","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136580990","display_name":"Yuchen Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Yuchen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059986401","display_name":"Kangjie Zhou","orcid":"https://orcid.org/0000-0002-2090-2920"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Kangjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136521634","display_name":"Weijie Su","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Su, Weijie","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.28679999709129333,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.28679999709129333,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.21410000324249268,"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":0.10639999806880951,"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/generative-grammar","display_name":"Generative grammar","score":0.6617000102996826},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.590499997138977},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5415999889373779},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.49889999628067017},{"id":"https://openalex.org/keywords/synthetic-data","display_name":"Synthetic data","score":0.44620001316070557},{"id":"https://openalex.org/keywords/natural","display_name":"Natural (archaeology)","score":0.39649999141693115},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.3650999963283539},{"id":"https://openalex.org/keywords/data-modeling","display_name":"Data modeling","score":0.36160001158714294}],"concepts":[{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.6617000102996826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.646399974822998},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.590499997138977},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5415999889373779},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5212000012397766},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.49889999628067017},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4074999988079071},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.39649999141693115},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2605000138282776}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.20151","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20151","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.2605.20151","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20151","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"proliferation":[1],"of":[2,58,120,173,199,207],"generative":[3,121,174],"artificial":[4],"intelligence":[5],"has":[6],"given":[7],"rise":[8],"to":[9,79,154],"an":[10,101,177,214],"interactive":[11,96,160,178],"learning":[12,97,179],"environment,":[13],"where":[14],"model":[15,64,112,135,140,147,156,189,200,222],"parameters":[16],"are":[17,45,127],"continuously":[18],"updated":[19],"using":[20,191],"not":[21],"only":[22],"data":[23,44,131],"generated":[24],"by":[25,33,133,169],"natural":[26],"processes,":[27],"but":[28],"also":[29],"synthetic":[30,82,130],"outputs":[31,83],"produced":[32,132],"other":[34],"models.":[35],"This":[36],"paradigm":[37],"introduces":[38],"two":[39],"major":[40],"challenges:":[41],"(1)":[42],"training":[43,65],"no":[46],"longer":[47],"drawn":[48],"exclusively":[49],"from":[50],"the":[51,118,171,197,205,208],"target":[52],"population,":[53],"undermining":[54],"a":[55,85,114,145],"core":[56],"assumption":[57],"classical":[59],"statistical":[60,91],"learning,":[61],"and":[62,194,217,225,232],"(2)":[63],"processes":[66],"become":[67],"inherently":[68],"correlated,":[69],"as":[70,125],"models":[71,122,175],"interact":[72],"with":[73,181],"one":[74],"another":[75],"through":[76,243],"repeated":[77],"exposure":[78],"each":[80],"other's":[81],"in":[84,93,116,158,176],"potentially":[86],"complex":[87],"manner.":[88],"Establishing":[89],"reliable":[90],"inference":[92],"such":[94],"structured":[95],"environments":[98],"therefore":[99],"remains":[100],"important":[102],"open":[103],"problem.":[104],"In":[105,162,185],"particular,":[106,186],"there":[107],"is":[108],"growing":[109],"concern":[110],"about":[111],"collapse,":[113],"phenomenon":[115],"which":[117],"performance":[119,157,172],"progressively":[123],"degrades":[124],"they":[126],"trained":[128,148],"on":[129,139,144,149,204],"earlier":[134],"generations.":[136],"Prior":[137],"work":[138],"collapse":[141,201,223],"primarily":[142],"focuses":[143],"single":[146],"its":[150],"own":[151],"output,":[152],"failing":[153],"capture":[155],"multi-model":[159],"settings.":[161],"this":[163,167],"work,":[164],"we":[165,187],"fill":[166],"gap":[168],"investigating":[170],"environment":[180],"general":[182,236],"interaction":[183,209],"patterns.":[184],"formalize":[188],"interactions":[190],"directed":[192],"graphs":[193],"show":[195],"that":[196],"occurrence":[198],"depends":[202],"critically":[203],"topology":[206],"graph.":[210],"We":[211,238],"further":[212],"derive":[213],"explicit":[215],"necessary":[216],"sufficient":[218],"condition":[219],"characterizing":[220],"when":[221],"occurs,":[224],"establish":[226],"finite-sample":[227],"results":[228],"for":[229,235],"linear":[230],"regression":[231],"asymptotic":[233],"guarantees":[234],"M-estimators.":[237],"support":[239],"our":[240],"theoretical":[241],"findings":[242],"extensive":[244],"numerical":[245],"experiments.":[246]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-21T00:00:00"}
