{"id":"https://openalex.org/W1620637521","doi":"https://doi.org/10.3233/fi-2010-344","title":"A Note on a priori Estimations of Classification Circuit Complexity","display_name":"A Note on a priori Estimations of Classification Circuit Complexity","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1620637521","doi":"https://doi.org/10.3233/fi-2010-344","mag":"1620637521"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2010-344","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-344","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"type":"article","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/A5029149047","display_name":"Andreas Albrecht","orcid":"https://orcid.org/0000-0002-9813-4319"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andreas A. Albrecht","raw_affiliation_strings":["CCRCB, Queen's University Belfast, Belfast, Northern Ireland, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CCRCB, Queen's University Belfast, Belfast, Northern Ireland, UK","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111468969","display_name":"Alexander V. Chashkin","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander V. Chashkin","raw_affiliation_strings":["Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058155947","display_name":"Costas S. Iliopoulos","orcid":"https://orcid.org/0000-0003-3909-0077"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Costas S. Iliopoulos","raw_affiliation_strings":["Department of Computer Science, King's College London, London, England, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, King's College London, London, England, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046346935","display_name":"O. M. Kasim-Zade","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Oktay M. Kasim-Zade","raw_affiliation_strings":["Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065636977","display_name":"Georgios Lappas","orcid":"https://orcid.org/0000-0001-8428-2954"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georgios Lappas","raw_affiliation_strings":["T.E.I. of Western Macedonia, Kastoria, Greece","T.E.I. of Western Macedonia, Kastoria, Greece#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"T.E.I. of Western Macedonia, Kastoria, Greece","institution_ids":[]},{"raw_affiliation_string":"T.E.I. of Western Macedonia, Kastoria, Greece#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042428919","display_name":"Kathleen Steinh\u00f6fel","orcid":"https://orcid.org/0000-0002-9533-4649"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kathleen K. Steinh\u00f6fel","raw_affiliation_strings":["Department of Computer Science, King's College London, London, England, UK","(Correspd.) Department of Computer Science, King's College London, London, England, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, King's College London, London, England, UK","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"(Correspd.) Department of Computer Science, King's College London, London, England, UK#TAB#","institution_ids":["https://openalex.org/I183935753"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.06345018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"104","issue":"3","first_page":"201","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.998199999332428,"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":0.998199999332428,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5545865893363953},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.4596753418445587},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45657089352607727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4560719132423401},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.417240172624588},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.35476329922676086},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28245997428894043},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.1623009443283081},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.08516323566436768},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07588797807693481}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5545865893363953},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.4596753418445587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45657089352607727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4560719132423401},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.417240172624588},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.35476329922676086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28245997428894043},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.1623009443283081},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.08516323566436768},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07588797807693481},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3233/fi-2010-344","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-344","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},{"id":"pmh:oai:eprints.mdx.ac.uk:12394","is_oa":false,"landing_page_url":"https://eprints.mdx.ac.uk/12394/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400025","display_name":"Middlesex University Research Repository (Middlesex University Of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60488453","host_organization_name":"Middlesex University","host_organization_lineage":["https://openalex.org/I60488453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/46d008c0-65f6-44cc-a231-c6e28b2e0d42","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/46d008c0-65f6-44cc-a231-c6e28b2e0d42","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Albrecht , A A , Chashkin , A V , Iliopoulos , C S , Kasim-Zade , O M , Lappas , G &amp; Steinhofel , K 2010 , ' A Note on A Priori Estimations of Classification Circuit Complexity ' , FUNDAMENTA INFORMATICAE , vol. 104 , no. 3 , pp. 201 - 217 . https://doi.org/10.3233/FI-2010-344","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W89972798","https://openalex.org/W1541778944","https://openalex.org/W1649899421","https://openalex.org/W1800056794","https://openalex.org/W1969557815","https://openalex.org/W1989789052","https://openalex.org/W2001619934","https://openalex.org/W2011956661","https://openalex.org/W2023577742","https://openalex.org/W2033500239","https://openalex.org/W2041334099","https://openalex.org/W2066915075","https://openalex.org/W2090398894","https://openalex.org/W2099579348","https://openalex.org/W2103000160","https://openalex.org/W2129178713","https://openalex.org/W2141630781","https://openalex.org/W2150588589","https://openalex.org/W2155482699","https://openalex.org/W2156222099","https://openalex.org/W2156260858","https://openalex.org/W2165025072","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298"],"abstract_inverted_index":{"The":[0,28],"paper":[1],"aims":[2],"at":[3],"tight":[4],"upper":[5,29,126,149],"bounds":[6,30,127,150],"on":[7,131,170],"the":[8,32,49,125,132,148,164,182],"size":[9,34,166],"of":[10,51,135,173,206],"pattern":[11,174],"classification":[12,175,208],"circuits":[13,64],"that":[14,58,124,153,163,184],"can":[15],"be":[16],"used":[17],"for":[18,79,107,156],"a":[19,24,171,178,202],"priori":[20],"parameter":[21],"settings":[22],"in":[23,112,144],"machine":[25],"learning":[26],"context.":[27],"relate":[31],"circuit":[33,165],"S(C)":[35],"to":[36,200],"n":[37,74,90,95,102,134,140,143],"L":[38,43,47,75,84,91,96,103,117,141,194],":=":[39,72,86],"[log":[40],"2":[41,101,105],"m":[42,46,116],"],":[44],"where":[45,111],"is":[48],"number":[50,172],"training":[52],"samples.":[53],"In":[54],"particular,":[55],"we":[56,180],"show":[57],"there":[59],"exist":[60],"unbounded":[61,80],"fan-in":[62],"threshold":[63],"with":[65],"less":[66],"than":[67],"(a)":[68],"S":[69,83,187,193],"R":[70,188],"cc":[71,85,189,195],"2\u00b7\u221a2":[73],"+":[76,92,104],"3":[77],"gates":[78,106,197],"depth,":[81,110],"(b)":[82],"34.8":[87],"\u00b7":[88,94,99,186,192],"\u221a2":[89],"14":[93],"\u2212":[97],"11":[98],"log":[100],"small":[108],"bounded":[109],"both":[113],"cases":[114],"all":[115],"samples":[118],"are":[119,154,198],"classified":[120],"correctly.":[121],"We":[122,159],"note":[123],"do":[128],"not":[129],"depend":[130],"length":[133],"input":[136],"(sample)":[137],"vectors.":[138],"Since":[139],"&lt;&lt;":[142],"real-world":[145],"problem":[146],"settings,":[147],"return":[151],"values":[152],"suitable":[155],"practical":[157],"applications.":[158],"provide":[160],"experimental":[161],"evidence":[162],"estimations":[167],"work":[168],"well":[169],"tasks.":[176],"As":[177],"result,":[179],"formulate":[181],"conjecture":[183],"[1.25":[185],"or":[190],"[0.07":[191],"]":[196],"sufficient":[199],"achieve":[201],"high":[203],"generalization":[204],"rate":[205],"bounded-depth":[207],"circuits.":[209]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
