{"id":"https://openalex.org/W4283791586","doi":"https://doi.org/10.1016/j.neucom.2022.06.111","title":"Activation functions in deep learning: A comprehensive survey and benchmark","display_name":"Activation functions in deep learning: A comprehensive survey and benchmark","publication_year":2022,"publication_date":"2022-07-03","ids":{"openalex":"https://openalex.org/W4283791586","doi":"https://doi.org/10.1016/j.neucom.2022.06.111","mag":"3202774390"},"language":"en","primary_location":{"id":"doi:10.1016/j.neucom.2022.06.111","doi":"https://doi.org/10.1016/j.neucom.2022.06.111","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.neucom.2022.06.111","pdf_url":null,"source":{"id":"https://openalex.org/S45693802","display_name":"Neurocomputing","issn_l":"0925-2312","issn":["0925-2312","1872-8286"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","doyens","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neurocomputing","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2109.14545","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048082929","display_name":"Shiv Ram Dubey","orcid":"https://orcid.org/0000-0002-4532-8996","observed_orcids":["https://orcid.org/0000-0002-4532-8996"]},"institutions":[{"id":"https://openalex.org/I26072440","display_name":"Indian Institute of Information Technology Allahabad","ror":"https://ror.org/03rgjt374","country_code":"IN","type":"education","lineage":["https://openalex.org/I26072440"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shiv Ram Dubey","raw_affiliation_strings":["Computer Vision and Biometrics Laboratory, Indian Institute of Information Technology, Allahabad, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Vision and Biometrics Laboratory, Indian Institute of Information Technology, Allahabad, India","institution_ids":["https://openalex.org/I26072440"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071107603","display_name":"Satish Kumar Singh","orcid":"https://orcid.org/0000-0002-8536-4991","observed_orcids":["https://orcid.org/0000-0002-8536-4991"]},"institutions":[{"id":"https://openalex.org/I26072440","display_name":"Indian Institute of Information Technology Allahabad","ror":"https://ror.org/03rgjt374","country_code":"IN","type":"education","lineage":["https://openalex.org/I26072440"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Satish Kumar Singh","raw_affiliation_strings":["Computer Vision and Biometrics Laboratory, Indian Institute of Information Technology, Allahabad, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Vision and Biometrics Laboratory, Indian Institute of Information Technology, Allahabad, India","institution_ids":["https://openalex.org/I26072440"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025093894","display_name":"B.B. Chaudhuri","orcid":"https://orcid.org/0000-0003-0297-8929","observed_orcids":["https://orcid.org/0000-0003-0297-8929"]},"institutions":[{"id":"https://openalex.org/I1288043984","display_name":"Techno India University","ror":"https://ror.org/00v1y6t69","country_code":"IN","type":"education","lineage":["https://openalex.org/I1288043984"]},{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bidyut Baran Chaudhuri","raw_affiliation_strings":["Techno India University, Kolkata, India and Indian Statistical Institute, Kolkata, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Techno India University, Kolkata, India and Indian Statistical Institute, Kolkata, India","institution_ids":["https://openalex.org/I1288043984","https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048082929"],"corresponding_institution_ids":["https://openalex.org/I26072440"],"apc_list":{"value":2470,"currency":"USD","value_usd":2470},"apc_paid":null,"fwci":77.5561,"has_fulltext":true,"cited_by_count":1529,"citation_normalized_percentile":{"value":0.99974988,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"503","issue":null,"first_page":"92","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.98580002784729,"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":0.98580002784729,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.00430000014603138,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12676","display_name":"Machine Learning and ELM","score":0.0034000000450760126,"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/activation-functions","display_name":"activation functions","score":0.9959999918937683},{"id":"https://openalex.org/keywords/deep-neural-network","display_name":"deep neural network","score":0.796999990940094},{"id":"https://openalex.org/keywords/relu","display_name":"ReLU","score":0.7170000076293945},{"id":"https://openalex.org/keywords/elu","display_name":"ELU","score":0.9779999852180481},{"id":"https://openalex.org/keywords/swish","display_name":"Swish","score":0.9589999914169312},{"id":"https://openalex.org/keywords/hyperbolic-tangent","display_name":"hyperbolic tangent function","score":0.8679999709129333},{"id":"https://openalex.org/keywords/monotonicity","display_name":"monotonicity","score":0.7179999947547913},{"id":"https://openalex.org/keywords/smoothness","display_name":"smoothness","score":0.968999981880188},{"id":"https://openalex.org/keywords/benchmark","display_name":"benchmark","score":0.42100000381469727},{"id":"https://openalex.org/keywords/activation-function-selection","display_name":"activation function selection","score":0.5490000247955322}],"concepts":[{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.9067218899726868},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.7090854048728943},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6936812996864319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6750564575195312},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6301045417785645},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6134041547775269},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6129341125488281},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5827586650848389},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.558883786201477},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4982459545135498},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.49788618087768555},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.44384855031967163},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.417688250541687},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.39487597346305847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2364950180053711},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.neucom.2022.06.111","doi":"https://doi.org/10.1016/j.neucom.2022.06.111","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.neucom.2022.06.111","pdf_url":null,"source":{"id":"https://openalex.org/S45693802","display_name":"Neurocomputing","issn_l":"0925-2312","issn":["0925-2312","1872-8286"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","doyens","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neurocomputing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2109.14545","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.14545","pdf_url":"https://arxiv.org/pdf/2109.14545","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3202774390","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2109.14545.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2109.14545","doi":"https://doi.org/10.48550/arxiv.2109.14545","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2109.14545","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2109.14545","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.14545","pdf_url":"https://arxiv.org/pdf/2109.14545","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283791586.pdf","grobid_xml":"https://content.openalex.org/works/W4283791586.grobid-xml"},"referenced_works_count":198,"referenced_works":["https://openalex.org/W150571132","https://openalex.org/W1593271688","https://openalex.org/W1602740539","https://openalex.org/W1665214252","https://openalex.org/W1667249920","https://openalex.org/W1677182931","https://openalex.org/W1686810756","https://openalex.org/W1921523184","https://openalex.org/W2045101371","https://openalex.org/W2097117768","https://openalex.org/W2101105183","https://openalex.org/W2112796928","https://openalex.org/W2119169819","https://openalex.org/W2143612262","https://openalex.org/W2156387975","https://openalex.org/W2158798595","https://openalex.org/W2163605009","https://openalex.org/W2168148636","https://openalex.org/W2176412452","https://openalex.org/W2194775991","https://openalex.org/W2201305792","https://openalex.org/W2265678348","https://openalex.org/W2270144854","https://openalex.org/W2279639021","https://openalex.org/W2292877769","https://openalex.org/W2300805302","https://openalex.org/W2339741109","https://openalex.org/W2397642239","https://openalex.org/W2415288898","https://openalex.org/W2462831000","https://openalex.org/W2512630954","https://openalex.org/W2526044239","https://openalex.org/W2528305538","https://openalex.org/W2555745781","https://openalex.org/W2573798946","https://openalex.org/W2601530120","https://openalex.org/W2605620767","https://openalex.org/W2607735137","https://openalex.org/W2612445135","https://openalex.org/W2624413595","https://openalex.org/W2624901902","https://openalex.org/W2695935728","https://openalex.org/W2730411900","https://openalex.org/W2734664495","https://openalex.org/W2735225686","https://openalex.org/W2751261182","https://openalex.org/W2751432555","https://openalex.org/W2752782242","https://openalex.org/W2752965212","https://openalex.org/W2754580451","https://openalex.org/W2755110721","https://openalex.org/W2760217853","https://openalex.org/W2762260865","https://openalex.org/W2765421612","https://openalex.org/W2766609943","https://openalex.org/W2767058041","https://openalex.org/W2767286248","https://openalex.org/W2769852551","https://openalex.org/W2784978858","https://openalex.org/W2786462089","https://openalex.org/W2786627679","https://openalex.org/W2788991260","https://openalex.org/W2792268997","https://openalex.org/W2796065044","https://openalex.org/W2796199633","https://openalex.org/W2796384729","https://openalex.org/W2800423036","https://openalex.org/W2802862615","https://openalex.org/W2803957979","https://openalex.org/W2884522222","https://openalex.org/W2884552531","https://openalex.org/W2885304260","https://openalex.org/W2886690537","https://openalex.org/W2887286714","https://openalex.org/W2887666845","https://openalex.org/W2891455536","https://openalex.org/W2893539081","https://openalex.org/W2899663614","https://openalex.org/W2899675781","https://openalex.org/W2902393871","https://openalex.org/W2902777869","https://openalex.org/W2902935192","https://openalex.org/W2905485203","https://openalex.org/W2907593512","https://openalex.org/W2909136751","https://openalex.org/W2909554346","https://openalex.org/W2910114055","https://openalex.org/W2910121883","https://openalex.org/W2910415896","https://openalex.org/W2911843975","https://openalex.org/W2912413295","https://openalex.org/W2912776959","https://openalex.org/W2913189305","https://openalex.org/W2913292019","https://openalex.org/W2914242365","https://openalex.org/W2916909342","https://openalex.org/W2919115771","https://openalex.org/W2920039561","https://openalex.org/W2922301133","https://openalex.org/W2936783136","https://openalex.org/W2938101602","https://openalex.org/W2943971163","https://openalex.org/W2943971614","https://openalex.org/W2944869944","https://openalex.org/W2947207002","https://openalex.org/W2948551291","https://openalex.org/W2951375073","https://openalex.org/W2952720005","https://openalex.org/W2957705111","https://openalex.org/W2962834855","https://openalex.org/W2962847207","https://openalex.org/W2963009098","https://openalex.org/W2963420686","https://openalex.org/W2963446712","https://openalex.org/W2963570896","https://openalex.org/W2963606507","https://openalex.org/W2963872878","https://openalex.org/W2963920515","https://openalex.org/W2964055987","https://openalex.org/W2964625253","https://openalex.org/W2966217148","https://openalex.org/W2969937244","https://openalex.org/W2970031466","https://openalex.org/W2970375336","https://openalex.org/W2972760919","https://openalex.org/W2972999963","https://openalex.org/W2975209795","https://openalex.org/W2981052729","https://openalex.org/W2981381608","https://openalex.org/W2984776000","https://openalex.org/W2986351524","https://openalex.org/W2989588881","https://openalex.org/W2993587506","https://openalex.org/W2993843842","https://openalex.org/W2996221596","https://openalex.org/W2997275874","https://openalex.org/W2998088892","https://openalex.org/W2998348840","https://openalex.org/W3006793970","https://openalex.org/W3008371590","https://openalex.org/W3008480154","https://openalex.org/W3010400125","https://openalex.org/W3012334084","https://openalex.org/W3013965793","https://openalex.org/W3014573765","https://openalex.org/W3015219745","https://openalex.org/W3016986506","https://openalex.org/W3017300133","https://openalex.org/W3018757597","https://openalex.org/W3023212902","https://openalex.org/W3028519758","https://openalex.org/W3036154885","https://openalex.org/W3039655629","https://openalex.org/W3045233820","https://openalex.org/W3048593389","https://openalex.org/W3081361466","https://openalex.org/W3084521418","https://openalex.org/W3091064178","https://openalex.org/W3105654374","https://openalex.org/W3108274592","https://openalex.org/W3118608800","https://openalex.org/W3125923133","https://openalex.org/W3127062143","https://openalex.org/W3134811368","https://openalex.org/W3164816634","https://openalex.org/W3173369353","https://openalex.org/W3196308418","https://openalex.org/W3197438232","https://openalex.org/W4205388843","https://openalex.org/W4206573688","https://openalex.org/W4210618466","https://openalex.org/W4210844520","https://openalex.org/W4236965008","https://openalex.org/W4247924304","https://openalex.org/W4298417552","https://openalex.org/W4394669837","https://openalex.org/W4400898765","https://openalex.org/W6600002382","https://openalex.org/W6600011842","https://openalex.org/W6600291067","https://openalex.org/W6600756316","https://openalex.org/W6600763685","https://openalex.org/W6600938150","https://openalex.org/W6601266828","https://openalex.org/W6601430172","https://openalex.org/W6601651114","https://openalex.org/W6601700763","https://openalex.org/W6602646459","https://openalex.org/W6604344240","https://openalex.org/W6607167723","https://openalex.org/W6608849408","https://openalex.org/W6609214603","https://openalex.org/W6820111552","https://openalex.org/W6824754410","https://openalex.org/W6827496332","https://openalex.org/W6833262898","https://openalex.org/W6898505805","https://openalex.org/W7099244549"],"related_works":["https://openalex.org/W3202774390","https://openalex.org/W4400813227","https://openalex.org/W4396642253","https://openalex.org/W4391835903","https://openalex.org/W4401660979","https://openalex.org/W4401504310","https://openalex.org/W7139972063","https://openalex.org/W4385451479","https://openalex.org/W3045233820","https://openalex.org/W3123432941"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":358},{"year":2025,"cited_by_count":526},{"year":2024,"cited_by_count":405},{"year":2023,"cited_by_count":206},{"year":2022,"cited_by_count":34}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2022-07-05T00:00:00"}