{"id":"https://openalex.org/W1991635091","doi":"https://doi.org/10.1142/s0129065709002130","title":"FASTER TRAINING USING FUSION OF ACTIVATION FUNCTIONS FOR FEED FORWARD NEURAL NETWORKS","display_name":"FASTER TRAINING USING FUSION OF ACTIVATION FUNCTIONS FOR FEED FORWARD NEURAL NETWORKS","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W1991635091","doi":"https://doi.org/10.1142/s0129065709002130","mag":"1991635091","pmid":"https://pubmed.ncbi.nlm.nih.gov/20039466"},"language":"en","primary_location":{"id":"doi:10.1142/s0129065709002130","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129065709002130","pdf_url":null,"source":{"id":"https://openalex.org/S197665576","display_name":"International Journal of Neural Systems","issn_l":"0129-0657","issn":["0129-0657","1793-6462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Neural Systems","raw_type":"journal-article"},"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/A5100781881","display_name":"Md. Asaduzzaman","orcid":"https://orcid.org/0000-0001-8853-0708"},"institutions":[{"id":"https://openalex.org/I1307585291","display_name":"Khulna University of Engineering and Technology","ror":"https://ror.org/04y58d606","country_code":"BD","type":"education","lineage":["https://openalex.org/I1307585291"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"MD. ASADUZZAMAN","raw_affiliation_strings":["Khulna University of Engineering & Technology (KUET), Department of Electrical & Electronic Engineering, Khulna-9203, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khulna University of Engineering & Technology (KUET), Department of Electrical & Electronic Engineering, Khulna-9203, Bangladesh","institution_ids":["https://openalex.org/I1307585291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101908972","display_name":"Md. Shahjahan","orcid":"https://orcid.org/0000-0001-9019-5400"},"institutions":[{"id":"https://openalex.org/I1307585291","display_name":"Khulna University of Engineering and Technology","ror":"https://ror.org/04y58d606","country_code":"BD","type":"education","lineage":["https://openalex.org/I1307585291"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"MD. SHAHJAHAN","raw_affiliation_strings":["Khulna University of Engineering & Technology (KUET), Department of Electrical & Electronic Engineering, Khulna-9203, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khulna University of Engineering & Technology (KUET), Department of Electrical & Electronic Engineering, Khulna-9203, Bangladesh","institution_ids":["https://openalex.org/I1307585291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018767527","display_name":"Kazuyuki Murase","orcid":"https://orcid.org/0000-0002-2358-995X"},"institutions":[{"id":"https://openalex.org/I111966504","display_name":"University of Fukui","ror":"https://ror.org/00msqp585","country_code":"JP","type":"education","lineage":["https://openalex.org/I111966504"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"KAZUYUKI MURASE","raw_affiliation_strings":["University of Fukui, Department of Human & Artificial Intelligence Systems, Bunkyo 3-9-1, Fukui-910-8705, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Fukui, Department of Human & Artificial Intelligence Systems, Bunkyo 3-9-1, Fukui-910-8705, Japan","institution_ids":["https://openalex.org/I111966504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.0595,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9781098,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"19","issue":"06","first_page":"437","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9919999837875366,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/activation-function","display_name":"Activation function","score":0.6984105706214905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6648038625717163},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6612058281898499},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5894221067428589},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.5771851539611816},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5304825901985168},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.46496158838272095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45740512013435364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41809725761413574},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.41026657819747925},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2290259301662445}],"concepts":[{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6984105706214905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6648038625717163},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6612058281898499},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5894221067428589},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.5771851539611816},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5304825901985168},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.46496158838272095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45740512013435364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41809725761413574},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.41026657819747925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2290259301662445},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"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":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001330","descriptor_name":"Electronic Data Processing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D001330","descriptor_name":"Electronic Data Processing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D001330","descriptor_name":"Electronic Data Processing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","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":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013663","descriptor_name":"Teaching","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013663","descriptor_name":"Teaching","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013663","descriptor_name":"Teaching","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","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":"D016571","descriptor_name":"Neural Networks, Computer","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":"D055641","descriptor_name":"Mathematical Concepts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055641","descriptor_name":"Mathematical Concepts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055641","descriptor_name":"Mathematical Concepts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1142/s0129065709002130","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129065709002130","pdf_url":null,"source":{"id":"https://openalex.org/S197665576","display_name":"International Journal of Neural Systems","issn_l":"0129-0657","issn":["0129-0657","1793-6462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Neural Systems","raw_type":"journal-article"},{"id":"pmid:20039466","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20039466","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,"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":"International journal of neural systems","raw_type":null},{"id":"pmh:oai:crf.flib.u-fukui.ac.jp:10461/21791","is_oa":false,"landing_page_url":"http://hdl.handle.net/10098/2975","pdf_url":null,"source":{"id":"https://openalex.org/S4306402072","display_name":"University of Fukui Library (University of Fukui)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I111966504","host_organization_name":"University of Fukui","host_organization_lineage":["https://openalex.org/I111966504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W69026678","https://openalex.org/W1979164697","https://openalex.org/W2006560811","https://openalex.org/W2008183381","https://openalex.org/W2021914902","https://openalex.org/W2027407435","https://openalex.org/W2043677883","https://openalex.org/W2067755824","https://openalex.org/W2106688677","https://openalex.org/W2133170554","https://openalex.org/W2143908786","https://openalex.org/W2148991744","https://openalex.org/W2149736651","https://openalex.org/W2153335355","https://openalex.org/W2155482699","https://openalex.org/W2160456997","https://openalex.org/W2163232986","https://openalex.org/W2294658705","https://openalex.org/W4210925605"],"related_works":["https://openalex.org/W3024979424","https://openalex.org/W4283785902","https://openalex.org/W2895192346","https://openalex.org/W3032499992","https://openalex.org/W2041004593","https://openalex.org/W3134817226","https://openalex.org/W3110577345","https://openalex.org/W3136579697","https://openalex.org/W2811324119","https://openalex.org/W1504105233"],"abstract_inverted_index":{"Multilayer":[0],"feed-forward":[1],"neural":[2],"networks":[3,26],"are":[4,56],"widely":[5],"used":[6,22,165],"based":[7],"on":[8,108],"minimization":[9],"of":[10,34,45,70,74,82,99],"an":[11],"error":[12],"function.":[13],"Back":[14],"propagation":[15],"(BP)":[16],"is":[17,77,103,145,157],"a":[18],"famous":[19],"training":[20],"method":[21,102],"in":[23,49,85,167],"the":[24,32,39,71,75,80,93,100,130],"multilayer":[25],"but":[27],"it":[28],"often":[29],"suffers":[30],"from":[31],"drawback":[33],"slow":[35],"convergence.":[36],"To":[37],"make":[38],"learning":[40,94],"faster,":[41],"we":[42],"propose":[43],"'Fusion":[44],"Activation":[46],"Functions'":[47],"(FAF)":[48],"which":[50],"different":[51],"conventional":[52],"activation":[53],"functions":[54],"(AFs)":[55],"combined":[57],"to":[58,78,95,124,159],"compute":[59],"final":[60],"activation.":[61],"This":[62],"has":[63,121],"not":[64],"been":[65,122],"studied":[66],"extensively":[67],"yet.":[68],"One":[69],"sub":[72],"goals":[73],"paper":[76],"check":[79],"role":[81],"linear":[83],"AFs":[84,164],"combination.":[86],"We":[87],"investigate":[88],"whether":[89],"FAF":[90,120],"can":[91],"enable":[92],"be":[96],"faster.":[97],"Validity":[98],"proposed":[101],"examined":[104],"by":[105],"performing":[106],"simulations":[107],"challenging":[109],"nine":[110],"real":[111],"benchmark":[112],"classification":[113,141],"and":[114,127,139],"time":[115,151],"series":[116,152],"prediction":[117,153],"problems.":[118,142],"The":[119,143,155],"applied":[123],"2-bit,":[125],"3-bit":[126],"4-bit":[128],"parity,":[129],"breast":[131],"cancer,":[132],"Diabetes,":[133],"Heart":[134],"disease,":[135],"Iris,":[136],"wine,":[137],"Glass":[138],"Soybean":[140],"algorithm":[144,156],"also":[146],"tested":[147],"with":[148],"Mackey-Glass":[149],"chaotic":[150],"problem.":[154],"shown":[158],"work":[160],"better":[161],"than":[162],"other":[163],"independently":[166],"BP":[168],"such":[169],"as":[170],"sigmoid":[171],"(SIG),":[172],"arctangent":[173],"(ATAN),":[174],"logarithmic":[175],"(LOG).":[176]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}