{"id":"https://openalex.org/W4399938916","doi":"https://doi.org/10.1109/tcsi.2024.3413570","title":"A Fully Probabilistic Model for Sigmoid Approximation and Its Hardware- Efficient Implementation","display_name":"A Fully Probabilistic Model for Sigmoid Approximation and Its Hardware- Efficient Implementation","publication_year":2024,"publication_date":"2024-06-24","ids":{"openalex":"https://openalex.org/W4399938916","doi":"https://doi.org/10.1109/tcsi.2024.3413570"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2024.3413570","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2024.3413570","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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/A5030366997","display_name":"Wenhao Lu","orcid":"https://orcid.org/0000-0002-4842-2400"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wenhao Lu","raw_affiliation_strings":["Department of Electrical Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0002-4842-2400","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021479396","display_name":"Minshan Lu","orcid":"https://orcid.org/0000-0002-2448-0067"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Minshan Lu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065311088","display_name":"Xiangfen Zhang","orcid":"https://orcid.org/0000-0002-5332-3175"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangfen Zhang","raw_affiliation_strings":["College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-5332-3175","affiliations":[{"raw_affiliation_string":"College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042081078","display_name":"Zhongzhiguang Lu","orcid":"https://orcid.org/0009-0004-6755-2800"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhongzhiguang Lu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008871630","display_name":"Miao Sun","orcid":"https://orcid.org/0000-0002-4537-6998"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Miao Sun","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-4537-6998","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043713240","display_name":"Boyi Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Boyi Dong","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100703571","display_name":"Shu Zhou","orcid":"https://orcid.org/0000-0002-8493-4526"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhou Shu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Cluny Road, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-8493-4526","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Cluny Road, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5764,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68032104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"71","issue":"8","first_page":"3775","last_page":"3786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.8585000038146973,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.8585000038146973,"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/sigmoid-function","display_name":"Sigmoid function","score":0.7894319295883179},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6967082619667053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6134113669395447},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4367663264274597},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3094845414161682},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.20663896203041077}],"concepts":[{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.7894319295883179},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6967082619667053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6134113669395447},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4367663264274597},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3094845414161682},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.20663896203041077},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2024.3413570","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2024.3413570","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1973695593","https://openalex.org/W1998379075","https://openalex.org/W2109530046","https://openalex.org/W2167425979","https://openalex.org/W2750384547","https://openalex.org/W2889228961","https://openalex.org/W2952284650","https://openalex.org/W2966456821","https://openalex.org/W2971697187","https://openalex.org/W2974644665","https://openalex.org/W2975672665","https://openalex.org/W3003134479","https://openalex.org/W3011253169","https://openalex.org/W3030801383","https://openalex.org/W3032892975","https://openalex.org/W3116122527","https://openalex.org/W3160664745","https://openalex.org/W3192384093","https://openalex.org/W4206087890","https://openalex.org/W4210722876","https://openalex.org/W4224440775","https://openalex.org/W4246448119","https://openalex.org/W4282926144","https://openalex.org/W4312467304","https://openalex.org/W4313316261","https://openalex.org/W6636070404","https://openalex.org/W6743688258"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W4385957115","https://openalex.org/W2061372042","https://openalex.org/W3047779762","https://openalex.org/W1520030019","https://openalex.org/W2071654592","https://openalex.org/W3104477175","https://openalex.org/W2088157920","https://openalex.org/W4283785902"],"abstract_inverted_index":{"The":[0],"sigmoid":[1,32,89,189],"function":[2,7,33,90],"is":[3,15,108,132,140,157],"a":[4,68,82,88,104,193],"representative":[5],"activation":[6],"in":[8],"shallow":[9],"neural":[10,178],"networks.":[11],"Its":[12],"hardware":[13,60,147,165],"realization":[14],"challenging":[16],"due":[17],"to":[18,30,42,113,142],"the":[19,47,73,85,95,98,116,124,129,150,187],"complex":[20],"exponential":[21],"and":[22,34,62,103,164,172,174],"reciprocal":[23],"operations.":[24],"Existing":[25],"studies":[26],"applied":[27],"piecewise":[28,122],"models":[29],"approximate":[31],"employed":[35],"numerical":[36],"methods":[37],"or":[38,111],"non-uniform":[39],"input":[40,102],"segmentations":[41],"mitigate":[43],"fitting":[44,56],"inaccuracies.":[45],"However,":[46],"breakpoints":[48],"introduce":[49],"inevitable":[50],"approximation":[51,71,162],"precision":[52,125],"loss.":[53,197],"Besides,":[54],"additional":[55],"processes":[57],"greatly":[58],"increase":[59],"complexity":[61],"power":[63],"consumption.":[64],"This":[65],"paper":[66],"presents":[67],"hardware-friendly":[69],"sigmoidal":[70],"from":[72],"perspective":[74],"of":[75,87,100],"probability":[76,96],"theory.":[77],"We":[78],"find":[79],"that":[80,97,183],"for":[81,146],"given":[83],"input,":[84],"output":[86],"can":[91],"be":[92],"approximated":[93],"by":[94,128],"sum":[99],"this":[101],"Gaussian":[105],"random":[106],"variable":[107],"greater":[109],"than":[110],"equal":[112],"zero.":[114],"As":[115],"derived":[117],"theorem":[118,145],"does":[119],"not":[120],"involve":[121],"expressions,":[123],"loss":[126],"caused":[127],"breakpoint":[130],"issue":[131],"avoided.":[133],"A":[134],"low-complexity":[135],"binary-search-based":[136],"address":[137],"localization":[138],"method":[139],"proposed":[141,188],"optimize":[143],"our":[144],"implementation.":[148],"For":[149],"optimized":[151],"scheme,":[152],"an":[153],"efficient":[154],"implemented":[155],"circuit":[156],"also":[158],"presented.":[159],"Our":[160],"scheme\u2019s":[161],"ability":[163],"efficiency":[166],"are":[167],"validated":[168],"through":[169],"software":[170],"modeling":[171],"FPGA-":[173],"ASIC-based":[175],"experiments.":[176],"Feedforward":[177],"network-based":[179],"classification":[180],"applications":[181],"demonstrate":[182],"building":[184],"networks":[185],"with":[186],"approximator":[190],"has":[191],"only":[192],"tiny":[194],"recognition":[195],"rate":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}
