{"id":"https://openalex.org/W3168792393","doi":"https://doi.org/10.1145/3406325.3465360","title":"Learnability can be independent of set theory (invited paper)","display_name":"Learnability can be independent of set theory (invited paper)","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3168792393","doi":"https://doi.org/10.1145/3406325.3465360","mag":"3168792393"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3465360","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3465360","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-abstract","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112193907","display_name":"Shai Ben-David","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shai Ben-David","raw_affiliation_strings":["University of Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103278473","display_name":"Pavel Hrube\u0161","orcid":"https://orcid.org/0000-0003-4526-4934"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210154638","display_name":"Engineering Academy of the Czech Republic","ror":"https://ror.org/04dea3c58","country_code":"CZ","type":"nonprofit","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210154638"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Pavel Hrubes","raw_affiliation_strings":["Czech Academy of Sciences, Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Czech Academy of Sciences, Czechia","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210154638"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047793114","display_name":"Shay Moran","orcid":"https://orcid.org/0000-0002-8662-2737"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shay Moran","raw_affiliation_strings":["Technion, Israel"],"raw_orcid":"https://orcid.org/0000-0002-8662-2737","affiliations":[{"raw_affiliation_string":"Technion, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004182247","display_name":"Amir Shpilka","orcid":"https://orcid.org/0000-0003-2384-425X"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amir Shpilka","raw_affiliation_strings":["Tel Aviv University, Israel"],"raw_orcid":"https://orcid.org/0000-0003-2384-425X","affiliations":[{"raw_affiliation_string":"Tel Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041051779","display_name":"Amir Yehudayoff","orcid":"https://orcid.org/0000-0002-0177-1814"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amir Yehudayoff","raw_affiliation_strings":["Technion, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"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":"11","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9818999767303467,"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":0.9818999767303467,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9325000047683716,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/learnability","display_name":"Learnability","score":0.9690514206886292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.539375364780426},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5181576013565063},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4178313910961151},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.41083937883377075},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3958017826080322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32144421339035034},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30536890029907227}],"concepts":[{"id":"https://openalex.org/C2777723229","wikidata":"https://www.wikidata.org/wiki/Q4367921","display_name":"Learnability","level":2,"score":0.9690514206886292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.539375364780426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5181576013565063},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4178313910961151},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.41083937883377075},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3958017826080322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32144421339035034},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30536890029907227},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3406325.3465360","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3465360","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4302791369","https://openalex.org/W2951285859","https://openalex.org/W2766040214","https://openalex.org/W72092541","https://openalex.org/W37360785","https://openalex.org/W1973394166","https://openalex.org/W1996805091","https://openalex.org/W24519920","https://openalex.org/W2087778462"],"abstract_inverted_index":{"A":[0],"fundamental":[1],"result":[2,26],"in":[3,42,95,168],"statistical":[4,65],"learning":[5,123],"theory":[6,54,150],"is":[7,103,144],"the":[8,17,63,106,129,138,141,148,173],"equivalence":[9],"of":[10,13,19,40,52,60,72,112,132,140,147,176],"PAC":[11],"learnability":[12,41,131,167],"a":[14,36,43,49,69,169],"class":[15],"with":[16],"finiteness":[18],"its":[20,99],"Vapnik-Chervonenkis":[21],"dimension.":[22],"However,":[23],"this":[24],"clean":[25],"applies":[27],"only":[28],"to":[29,105,172],"binary":[30,177],"classification":[31,178],"problems.":[32,124],"In":[33],"search":[34],"for":[35,55],"similar":[37,171],"combinatorial":[38,162],"characterization":[39,175],"more":[44],"general":[45,58],"setting,":[46],"we":[47,126],"discovered":[48],"surprising":[50],"independence":[51],"set":[53,149],"some":[56,78,133],"basic":[57],"notion":[59],"learnability.":[61,179],"Consider":[62],"following":[64],"estimation":[66],"problem:":[67],"given":[68],"family":[70],"F":[71,96],"real":[73],"valued":[74],"random":[75],"variables":[76],"over":[77,91,109],"domain":[79],"X":[80],"and":[81,143],"an":[82,87],"i.i.d.":[83],"sample":[84],"drawn":[85],"from":[86],"unknown":[88],"distribution":[89],"P":[90,102],"X,":[92],"find":[93],"f":[94],"such":[97],"that":[98,128,156,157,164],"expectation":[100,108],"w.r.t.":[101],"close":[104],"supremum":[107],"all":[110],"members":[111],"F.":[113],"This":[114],"Expectation":[115],"Maximization":[116],"(EMX)":[117],"problem":[118],"captures":[119],"many":[120],"well":[121],"studied":[122],"Surprisingly,":[125],"show":[127],"EMX":[130,166],"simple":[134],"classes":[135],"depends":[136],"on":[137],"cardinality":[139],"continuum":[142],"therefore":[145],"independent":[146],"ZFC":[151],"axioms.":[152],"Our":[153],"results":[154],"imply":[155],"there":[158],"exist":[159],"no":[160],"\"finitary\"":[161],"parameter":[163],"characterizes":[165],"way":[170],"VC-dimension":[174]},"counts_by_year":[],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
