{"id":"https://openalex.org/W2143687481","doi":"https://doi.org/10.1111/tops.12036","title":"Fractal Analysis Illuminates the Form of Connectionist Structural Gradualness","display_name":"Fractal Analysis Illuminates the Form of Connectionist Structural Gradualness","publication_year":2013,"publication_date":"2013-06-24","ids":{"openalex":"https://openalex.org/W2143687481","doi":"https://doi.org/10.1111/tops.12036","mag":"2143687481","pmid":"https://pubmed.ncbi.nlm.nih.gov/23798028"},"language":"en","primary_location":{"id":"doi:10.1111/tops.12036","doi":"https://doi.org/10.1111/tops.12036","is_oa":false,"landing_page_url":"https://doi.org/10.1111/tops.12036","pdf_url":null,"source":{"id":"https://openalex.org/S22283869","display_name":"Topics in Cognitive Science","issn_l":"1756-8757","issn":["1756-8757","1756-8765"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Topics in Cognitive Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"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/A5060057619","display_name":"Whitney Tabor","orcid":"https://orcid.org/0000-0002-6818-3283","observed_orcids":["https://orcid.org/0000-0002-6818-3283"]},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Whitney Tabor","raw_affiliation_strings":["Department of Psychology and Program in Cognitive Science University of Connecticut","University of Connecticut Department of Psychology and Program in Cognitive Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychology and Program in Cognitive Science University of Connecticut","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"University of Connecticut Department of Psychology and Program in Cognitive Science","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023223601","display_name":"Pyeong Whan Cho","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pyeong Whan Cho","raw_affiliation_strings":["Department of Psychology and Program in Cognitive Science University of Connecticut","University of Connecticut Department of Psychology and Program in Cognitive Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychology and Program in Cognitive Science University of Connecticut","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"University of Connecticut Department of Psychology and Program in Cognitive Science","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068820366","display_name":"Emily Szkudlarek","orcid":"https://orcid.org/0000-0002-8607-7302","observed_orcids":["https://orcid.org/0000-0002-8607-7302"]},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emily Szkudlarek","raw_affiliation_strings":["Department of Psychology and Program in Cognitive Science University of Connecticut","University of Connecticut Department of Psychology and Program in Cognitive Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychology and Program in Cognitive Science University of Connecticut","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"University of Connecticut Department of Psychology and Program in Cognitive Science","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060057619"],"corresponding_institution_ids":["https://openalex.org/I140172145"],"apc_list":{"value":3470,"currency":"USD","value_usd":3470},"apc_paid":null,"fwci":2.208,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.88883701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"5","issue":"3","first_page":"634","last_page":"667"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.3662000000476837,"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/T10320","display_name":"Neural Networks and Applications","score":0.3662000000476837,"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/T10034","display_name":"Syntax, Semantics, Linguistic Variation","score":0.2639000117778778,"subfield":{"id":"https://openalex.org/subfields/1203","display_name":"Language and Linguistics"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.12150000035762787,"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/elman-neural-network","display_name":"Elman neural network","score":0.7749999761581421},{"id":"https://openalex.org/keywords/fractal-coding","display_name":"fractal coding","score":0.8640000224113464},{"id":"https://openalex.org/keywords/grammatical-structure","display_name":"grammatical structure","score":0.6370000243186951},{"id":"https://openalex.org/keywords/training-program","display_name":"training program","score":0.421999990940094},{"id":"https://openalex.org/keywords/natural-language-syntax","display_name":"natural language syntax","score":0.43700000643730164}],"concepts":[{"id":"https://openalex.org/C8521452","wikidata":"https://www.wikidata.org/wiki/Q203790","display_name":"Connectionism","level":3,"score":0.9087132811546326},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.7439188957214355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6725723743438721},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.5425044894218445},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5325798988342285},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5204920172691345},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.520195484161377},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4784986078739166},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46979984641075134},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45819932222366333},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.4314602017402649},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.415547251701355},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.3664143979549408},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.3548091650009155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2388806939125061},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21743068099021912},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.1761532425880432},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14900809526443481},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.11925530433654785},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005793","descriptor_name":"Generalization, Psychological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007802","descriptor_name":"Language","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017709","descriptor_name":"Fractals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1111/tops.12036","doi":"https://doi.org/10.1111/tops.12036","is_oa":false,"landing_page_url":"https://doi.org/10.1111/tops.12036","pdf_url":null,"source":{"id":"https://openalex.org/S22283869","display_name":"Topics in Cognitive Science","issn_l":"1756-8757","issn":["1756-8757","1756-8765"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Topics in Cognitive Science","raw_type":"journal-article"},{"id":"pmid:23798028","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23798028","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Topics in cognitive science","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.463.1553","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.463.1553","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://psychology.uconn.edu/labs/solab/papers/tabor2013faitfocsg.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":84,"referenced_works":["https://openalex.org/W51799866","https://openalex.org/W55412705","https://openalex.org/W179997301","https://openalex.org/W339674347","https://openalex.org/W421997344","https://openalex.org/W616878787","https://openalex.org/W1480259434","https://openalex.org/W1496937667","https://openalex.org/W1512098439","https://openalex.org/W1540037108","https://openalex.org/W1550331971","https://openalex.org/W1574049752","https://openalex.org/W1579696469","https://openalex.org/W1581242383","https://openalex.org/W1586246979","https://openalex.org/W1641813156","https://openalex.org/W1965511524","https://openalex.org/W1970278892","https://openalex.org/W1972085588","https://openalex.org/W1975081431","https://openalex.org/W1984588653","https://openalex.org/W1992205856","https://openalex.org/W2000412342","https://openalex.org/W2001616149","https://openalex.org/W2002089154","https://openalex.org/W2004575963","https://openalex.org/W2009643715","https://openalex.org/W2016429292","https://openalex.org/W2017125617","https://openalex.org/W2020755048","https://openalex.org/W2025032307","https://openalex.org/W2032234582","https://openalex.org/W2045183093","https://openalex.org/W2048374649","https://openalex.org/W2049093093","https://openalex.org/W2070221296","https://openalex.org/W2071846104","https://openalex.org/W2071906671","https://openalex.org/W2076332735","https://openalex.org/W2077439714","https://openalex.org/W2081825452","https://openalex.org/W2082814186","https://openalex.org/W2084728994","https://openalex.org/W2086789740","https://openalex.org/W2087347434","https://openalex.org/W2087946919","https://openalex.org/W2094149843","https://openalex.org/W2110485445","https://openalex.org/W2116253599","https://openalex.org/W2116723809","https://openalex.org/W2118049235","https://openalex.org/W2122988375","https://openalex.org/W2125001590","https://openalex.org/W2133113917","https://openalex.org/W2134795071","https://openalex.org/W2138723298","https://openalex.org/W2143005196","https://openalex.org/W2144836808","https://openalex.org/W2145811616","https://openalex.org/W2146051167","https://openalex.org/W2151834591","https://openalex.org/W2154346509","https://openalex.org/W2160946777","https://openalex.org/W2161658801","https://openalex.org/W2161739581","https://openalex.org/W2162108317","https://openalex.org/W2336049016","https://openalex.org/W2339378878","https://openalex.org/W2498463154","https://openalex.org/W2571532437","https://openalex.org/W2576961557","https://openalex.org/W2766736793","https://openalex.org/W2897894404","https://openalex.org/W3207342693","https://openalex.org/W4230514523","https://openalex.org/W4232428815","https://openalex.org/W4239510810","https://openalex.org/W4240079771","https://openalex.org/W4240720324","https://openalex.org/W4245451182","https://openalex.org/W4285719527","https://openalex.org/W4300402905","https://openalex.org/W4301168154","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W2183191610","https://openalex.org/W2492681819","https://openalex.org/W7099005048","https://openalex.org/W55412705","https://openalex.org/W7026820340","https://openalex.org/W602702850","https://openalex.org/W1532366611","https://openalex.org/W1507084099","https://openalex.org/W7100746154","https://openalex.org/W11695154"],"abstract_inverted_index":{"We":[0,109,120],"examine":[1],"two":[2,122],"connectionist":[3,28,88,139,158],"networks-a":[4],"fractal":[5,37,126],"learning":[6,89,132],"neural":[7],"network":[8],"(FLNN)":[9],"and":[10,84,141,160,182],"a":[11,75,94,111,148],"Simple":[12],"Recurrent":[13],"Network":[14],"(SRN)-that":[15],"are":[16,51],"trained":[17,30],"to":[18,35,54,81],"process":[19],"center-embedded":[20],"symbol":[21],"sequences.":[22],"Previous":[23],"work":[24,41,184],"provides":[25],"evidence":[26],"that":[27,79,86,98,188],"networks":[29,140,159],"on":[31,43,185],"infinite-state":[32],"languages":[33],"tend":[34],"form":[36],"encodings.":[38,108],"Most":[39],"such":[40],"focuses":[42],"simple":[44],"counting":[45],"recursion":[46],"cases":[47,70,92,133],"(e.g.,":[48],"anbn),":[49],"which":[50],"not":[52],"comparable":[53],"the":[55,87,125,135,153,163,173,176],"complex":[56,131],"recursive":[57],"patterns":[58],"seen":[59],"in":[60,147],"natural":[61],"language":[62],"syntax.":[63],"Here,":[64],"we":[65],"consider":[66],"exponential":[67],"state":[68],"growth":[69],"(including":[71],"mirror":[72],"recursion),":[73],"describe":[74],"new":[76],"training":[77],"scheme":[78],"seems":[80],"facilitate":[82],"learning,":[83],"note":[85],"of":[90,128,137,144,157,178],"these":[91,129,186],"has":[93],"continuous":[95],"metamorphosis":[96],"property":[97],"looks":[99],"very":[100],"different":[101,168],"from":[102,169],"what":[103],"is":[104,167,189],"achievable":[105],"with":[106],"symbolic":[107,142,170],"identify":[110],"property-ragged":[112],"progressive":[113],"generalization-which":[114],"helps":[115,151],"make":[116],"this":[117],"difference":[118],"clearer.":[119],"suggest":[121],"conclusions.":[123],"First,":[124],"analysis":[127],"more":[130,190],"reveals":[134],"possibility":[136],"comparing":[138],"models":[143],"grammatical":[145],"structure":[146],"principled":[149],"way-this":[150],"remove":[152],"black":[154],"box":[155],"character":[156],"indicates":[161],"how":[162],"theory":[164],"they":[165],"support":[166],"approaches.":[171],"Second,":[172],"findings":[174],"indicate":[175],"value":[177],"future,":[179],"linked":[180],"mathematical":[181],"empirical":[183],"models-something":[187],"possible":[191],"now":[192],"than":[193],"it":[194],"was":[195],"10":[196],"years":[197],"ago.":[198]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}
