{"id":"https://openalex.org/W4200336303","doi":"https://doi.org/10.3390/info12120513","title":"Learnable Leaky ReLU (LeLeLU): An Alternative Accuracy-Optimized Activation Function","display_name":"Learnable Leaky ReLU (LeLeLU): An Alternative Accuracy-Optimized Activation Function","publication_year":2021,"publication_date":"2021-12-09","ids":{"openalex":"https://openalex.org/W4200336303","doi":"https://doi.org/10.3390/info12120513"},"language":"en","primary_location":{"id":"doi:10.3390/info12120513","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info12120513","pdf_url":"https://www.mdpi.com/2078-2489/12/12/513/pdf?version=1639041221","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2078-2489/12/12/513/pdf?version=1639041221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028486652","display_name":"Andreas Maniatopoulos","orcid":null},"institutions":[{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Andreas Maniatopoulos","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Democritus University of Greece, 67100 Xanthi, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Democritus University of Greece, 67100 Xanthi, Greece","institution_ids":["https://openalex.org/I147962203"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064706177","display_name":"Nikolaos Mitianoudis","orcid":"https://orcid.org/0000-0003-0898-6102"},"institutions":[{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Nikolaos Mitianoudis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Democritus University of Greece, 67100 Xanthi, Greece"],"raw_orcid":"https://orcid.org/0000-0003-0898-6102","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Democritus University of Greece, 67100 Xanthi, Greece","institution_ids":["https://openalex.org/I147962203"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064706177"],"corresponding_institution_ids":["https://openalex.org/I147962203"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.8792,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.94954891,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"12","issue":"12","first_page":"513","last_page":"513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9994999766349792,"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/T10320","display_name":"Neural Networks and Applications","score":0.9987000226974487,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9987000226974487,"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-function","display_name":"Activation function","score":0.9427087903022766},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6413300037384033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6394080519676208},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.579076886177063},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5472254157066345},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5054707527160645},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4997072219848633},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4528922438621521},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4330149292945862},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.43193304538726807},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0876929759979248}],"concepts":[{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.9427087903022766},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6413300037384033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6394080519676208},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.579076886177063},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5472254157066345},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5054707527160645},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4997072219848633},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4528922438621521},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4330149292945862},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.43193304538726807},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0876929759979248},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/info12120513","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info12120513","pdf_url":"https://www.mdpi.com/2078-2489/12/12/513/pdf?version=1639041221","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ae0c5be334034ddca897deae4b0b14a2","is_oa":true,"landing_page_url":"https://doaj.org/article/ae0c5be334034ddca897deae4b0b14a2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information, Vol 12, Iss 12, p 513 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2078-2489/12/12/513/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/info12120513","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information; Volume 12; Issue 12; Pages: 513","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/info12120513","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info12120513","pdf_url":"https://www.mdpi.com/2078-2489/12/12/513/pdf?version=1639041221","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200336303.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1665214252","https://openalex.org/W1677182931","https://openalex.org/W1902934009","https://openalex.org/W2095705004","https://openalex.org/W2141062232","https://openalex.org/W2168148636","https://openalex.org/W2170282759","https://openalex.org/W3089733125","https://openalex.org/W3141520081","https://openalex.org/W4205694016","https://openalex.org/W6674330103","https://openalex.org/W6682889407","https://openalex.org/W6739879593"],"related_works":["https://openalex.org/W3110577345","https://openalex.org/W2946235959","https://openalex.org/W2902935192","https://openalex.org/W3134817226","https://openalex.org/W4318066384","https://openalex.org/W3215912596","https://openalex.org/W3034021666","https://openalex.org/W2898900925","https://openalex.org/W3170224572","https://openalex.org/W4393036827"],"abstract_inverted_index":{"In":[0,71],"neural":[1],"networks,":[2],"a":[3,36,76,97],"vital":[4],"component":[5],"in":[6,66,96],"the":[7,13,49,54,92],"learning":[8,65],"and":[9,41],"inference":[10],"process":[11],"is":[12],"activation":[14,24,43,58,78,85],"function.":[15],"There":[16],"are":[17,45],"many":[18,81],"different":[19],"approaches,":[20],"but":[21],"only":[22,35],"nonlinear":[23],"functions":[25,44,59],"allow":[26],"such":[27,42],"networks":[28],"to":[29],"compute":[30],"non-trivial":[31],"problems":[32],"by":[33],"using":[34],"small":[37],"number":[38],"of":[39,51,83,99],"nodes,":[40],"called":[46],"nonlinearities.":[47],"With":[48],"emergence":[50],"deep":[52],"learning,":[53],"need":[55],"for":[56],"competent":[57],"that":[60],"can":[61],"enable":[62],"or":[63],"expedite":[64],"deeper":[67],"layers":[68],"has":[69],"emerged.":[70],"this":[72],"paper,":[73],"we":[74],"propose":[75],"novel":[77],"function,":[79],"combining":[80],"features":[82],"successful":[84],"functions,":[86],"achieving":[87],"2.53%":[88],"higher":[89],"accuracy":[90],"than":[91],"industry":[93],"standard":[94],"ReLU":[95],"variety":[98],"test":[100],"cases.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":6}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2021-12-31T00:00:00"}
