{"id":"https://openalex.org/W4407091663","doi":"https://doi.org/10.1109/tit.2025.3649611","title":"Model Non-Collapse: Minimax Bounds for Recursive Discrete Distribution Estimation","display_name":"Model Non-Collapse: Minimax Bounds for Recursive Discrete Distribution Estimation","publication_year":2025,"publication_date":"2025-12-30","ids":{"openalex":"https://openalex.org/W4407091663","doi":"https://doi.org/10.1109/tit.2025.3649611"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3649611","doi":"https://doi.org/10.1109/tit.2025.3649611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3649611","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2501.19273","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038357013","display_name":"Millen Kanabar","orcid":"https://orcid.org/0000-0002-5915-0623","observed_orcids":["https://orcid.org/0000-0002-5915-0623"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Millen Kanabar","raw_affiliation_strings":["School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-5915-0623","affiliations":[{"raw_affiliation_string":"School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063528341","display_name":"Michael Gastpar","orcid":"https://orcid.org/0000-0002-5499-5336","observed_orcids":["https://orcid.org/0000-0002-5499-5336"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Michael Gastpar","raw_affiliation_strings":["School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-5499-5336","affiliations":[{"raw_affiliation_string":"School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01086678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"3","first_page":"1817","last_page":"1830"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.23280000686645508,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.23280000686645508,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.2273000031709671,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.0560000017285347,"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/discrete-distribution-estimation","display_name":"discrete distribution estimation","score":0.9190000295639038},{"id":"https://openalex.org/keywords/self-consumption","display_name":"self-consumption","score":0.8379999995231628},{"id":"https://openalex.org/keywords/synthetic-data","display_name":"synthetic data","score":0.46399998664855957},{"id":"https://openalex.org/keywords/model-collapse","display_name":"model collapse","score":0.7730000019073486},{"id":"https://openalex.org/keywords/minimax-lower-bounds","display_name":"minimax lower bounds","score":0.925000011920929},{"id":"https://openalex.org/keywords/recursive-estimation","display_name":"recursive estimation","score":0.7609999775886536},{"id":"https://openalex.org/keywords/data-accumulation","display_name":"data accumulation","score":0.7649999856948853},{"id":"https://openalex.org/keywords/data-replacement","display_name":"data replacement","score":0.9760000109672546},{"id":"https://openalex.org/keywords/generative-models","display_name":"generative models","score":0.6370000243186951},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.6000000238418579}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7750355005264282},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.6700314283370972},{"id":"https://openalex.org/C30772137","wikidata":"https://www.wikidata.org/wiki/Q5164762","display_name":"Consumption (sociology)","level":2,"score":0.6536571383476257},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5394049882888794},{"id":"https://openalex.org/C2984118289","wikidata":"https://www.wikidata.org/wiki/Q29954","display_name":"Power consumption","level":3,"score":0.41881343722343445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4120846390724182},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.376853346824646},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33353883028030396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3329349160194397},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3287407159805298},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3212859630584717},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.22013381123542786},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11301937699317932},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.10946092009544373},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10857221484184265},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2025.3649611","doi":"https://doi.org/10.1109/tit.2025.3649611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3649611","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2501.19273","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.19273","pdf_url":"https://arxiv.org/pdf/2501.19273","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:20.500.14299/262234","doi":null,"is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/262234","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"},{"id":"doi:10.48550/arxiv.2501.19273","doi":"https://doi.org/10.48550/arxiv.2501.19273","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2501.19273","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2501.19273","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.19273","pdf_url":"https://arxiv.org/pdf/2501.19273","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3113097525","display_name":null,"funder_award_id":"200364","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407091663.pdf","grobid_xml":"https://content.openalex.org/works/W4407091663.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3007895144","https://openalex.org/W2886368732","https://openalex.org/W2990563962","https://openalex.org/W4391987634","https://openalex.org/W2164234199","https://openalex.org/W4414582027","https://openalex.org/W7204934882","https://openalex.org/W2419099043","https://openalex.org/W2769916633","https://openalex.org/W840677367"],"abstract_inverted_index":{"Learning":[0],"discrete":[1,124],"distributions":[2],"from":[3,36,48],"i.i.d.":[4],"samples":[5,35,168,221,254],"is":[6,32,137,202,230,255],"a":[7,24,59,203,236,262],"well-understood":[8],"problem.":[9],"However,":[10],"advances":[11],"in":[12,63,77,100,127,206,243],"generative":[13],"machine":[14,65],"learning":[15,66],"prompt":[16],"an":[17,29],"interesting":[18],"new,":[19],"non-i.i.d.":[20],"setting:":[21],"after":[22],"receiving":[23],"certain":[25],"number":[26],"of":[27,53,88,122,167,253],"samples,":[28],"estimated":[30],"distribution":[31,125],"fixed,":[33],"and":[34,41,147,178,219,224,257],"this":[37,115,228],"estimate":[38,271],"are":[39,169,182,222],"drawn":[40],"introduced":[42],"into":[43],"the":[44,64,103,119,140,143,155,160,188,207,212,240,244,250,266],"sample":[45],"corpus,":[46],"undifferentiated":[47],"real":[49,109,218],"samples.":[50],"Subsequent":[51],"generations":[52],"estimators":[54],"now":[55],"face":[56],"contaminated":[57],"environments,":[58],"scenario":[60],"referred":[61],"to":[62,95,211,260],"literature":[67],"as":[68,154],"self-consumption.":[69],"Empirically,":[70],"it":[71,259],"has":[72,92],"been":[73,93],"observed":[74],"that":[75,132,181],"models":[76],"fully":[78],"synthetic":[79,220],"self-consuming":[80,123],"loops":[81],"collapse\u2014their":[82],"performance":[83],"deteriorates":[84],"with":[85,146],"each":[86],"batch":[87,156,252],"training\u2014but":[89],"accumulating":[90],"data":[91,161,245],"shown":[94],"prevent":[96],"complete":[97],"degeneration.":[98],"This,":[99],"turn,":[101],"begs":[102],"question:":[104],"What":[105],"happens":[106],"when":[107,134],"fresh":[108],"samplesareadded":[110],"at":[111,192],"every":[112,193],"stage?":[113],"In":[114,159],"paper,":[116],"we":[117,173],"study":[118],"minimax":[120,144,175,215,241],"loss":[121,216,242,268],"estimation":[126],"such":[128],"loops.":[129],"We":[130,195,233],"show":[131],"even":[133],"model":[135],"collapse":[136],"consciously":[138],"averted,":[139],"ratios":[141],"between":[142],"losses":[145],"without":[148],"source":[149],"information":[150],"can":[151],"grow":[152],"unbounded":[153],"size":[157],"increases.":[158],"accumulation":[162],"setting,":[163,247],"where":[164,200,217,227,248],"all":[165],"batches":[166],"available":[170],"for":[171,187,198,265,269],"estimation,":[172],"provide":[174,196,225,235],"lower":[176,237,263],"bounds":[177,180],"upper":[179],"order-optimal":[183],"under":[184],"mild":[185],"conditions":[186,197],"expected":[189],"\u211322and":[190],"\u21131losses":[191],"stage.":[194],"regimes":[199],"there":[201],"strict":[204],"gap":[205,229],"convergence":[208],"rates":[209],"compared":[210],"corresponding":[213],"oracle-assisted":[214],"differentiated,":[223],"examples":[226],"easily":[231],"observed.":[232],"also":[234],"bound":[238,264],"on":[239],"replacement":[246],"only":[249],"latest":[251],"available,":[256],"use":[258],"find":[261],"worst-case":[267],"bounded":[270],"trajectories.":[272]},"counts_by_year":[],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2025-02-04T00:00:00"}
