{"id":"https://openalex.org/W2910396952","doi":"https://doi.org/10.1109/apccas.2018.8605654","title":"A High-Speed and Low-Complexity Architecture for Softmax Function in Deep Learning","display_name":"A High-Speed and Low-Complexity Architecture for Softmax Function in Deep Learning","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2910396952","doi":"https://doi.org/10.1109/apccas.2018.8605654","mag":"2910396952"},"language":"en","primary_location":{"id":"doi:10.1109/apccas.2018.8605654","is_oa":false,"landing_page_url":"https://doi.org/10.1109/apccas.2018.8605654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)","raw_type":"proceedings-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/A5100785858","display_name":"Meiqi Wang","orcid":"https://orcid.org/0000-0001-9553-3640"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Meiqi Wang","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084117570","display_name":"Siyuan Lu","orcid":"https://orcid.org/0000-0002-8639-3081"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siyuan Lu","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090345723","display_name":"Danyang Zhu","orcid":"https://orcid.org/0000-0001-9213-5399"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Danyang Zhu","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019940239","display_name":"Jun Lin","orcid":"https://orcid.org/0000-0003-2760-4333"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Lin","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100696999","display_name":"Zhongfeng Wang","orcid":"https://orcid.org/0000-0002-7227-4786"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongfeng Wang","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100785858"],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":null,"apc_paid":null,"fwci":4.1436,"has_fulltext":false,"cited_by_count":192,"citation_normalized_percentile":{"value":0.95813547,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"223","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9987999796867371,"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":0.9987999796867371,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/softmax-function","display_name":"Softmax function","score":0.9521108865737915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6735207438468933},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.5586851239204407},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5089905261993408},{"id":"https://openalex.org/keywords/cmos","display_name":"CMOS","score":0.4708758592605591},{"id":"https://openalex.org/keywords/hardware-architecture","display_name":"Hardware architecture","score":0.4669331908226013},{"id":"https://openalex.org/keywords/throughput","display_name":"Throughput","score":0.46176260709762573},{"id":"https://openalex.org/keywords/architecture","display_name":"Architecture","score":0.4598231613636017},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.45087525248527527},{"id":"https://openalex.org/keywords/computer-architecture","display_name":"Computer architecture","score":0.43788453936576843},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.4010695815086365},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.38791200518608093},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3600964844226837},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.3510555326938629},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3480193018913269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16432610154151917},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.16104906797409058},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.1289188265800476},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10243606567382812},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.091787189245224},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0800970196723938}],"concepts":[{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.9521108865737915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6735207438468933},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.5586851239204407},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5089905261993408},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.4708758592605591},{"id":"https://openalex.org/C65232700","wikidata":"https://www.wikidata.org/wiki/Q5656403","display_name":"Hardware architecture","level":3,"score":0.4669331908226013},{"id":"https://openalex.org/C157764524","wikidata":"https://www.wikidata.org/wiki/Q1383412","display_name":"Throughput","level":3,"score":0.46176260709762573},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.4598231613636017},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.45087525248527527},{"id":"https://openalex.org/C118524514","wikidata":"https://www.wikidata.org/wiki/Q173212","display_name":"Computer architecture","level":1,"score":0.43788453936576843},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.4010695815086365},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.38791200518608093},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3600964844226837},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.3510555326938629},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3480193018913269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16432610154151917},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.16104906797409058},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.1289188265800476},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10243606567382812},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.091787189245224},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0800970196723938},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"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},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","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":[],"locations_count":1,"locations":[{"id":"doi:10.1109/apccas.2018.8605654","is_oa":false,"landing_page_url":"https://doi.org/10.1109/apccas.2018.8605654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1971467632","https://openalex.org/W1976039195","https://openalex.org/W1993589577","https://openalex.org/W2094665651","https://openalex.org/W2102113734","https://openalex.org/W2112796928","https://openalex.org/W2136922672","https://openalex.org/W2585720638","https://openalex.org/W2608093348","https://openalex.org/W2613119772","https://openalex.org/W2621285457","https://openalex.org/W2730834423","https://openalex.org/W2787895998","https://openalex.org/W2914968962","https://openalex.org/W2962820060","https://openalex.org/W2962826786","https://openalex.org/W4230442731","https://openalex.org/W4297699616","https://openalex.org/W6648556970","https://openalex.org/W6675365184","https://openalex.org/W6736797231","https://openalex.org/W6737910693","https://openalex.org/W6738743430","https://openalex.org/W6747972019"],"related_works":["https://openalex.org/W3107204728","https://openalex.org/W4287591324","https://openalex.org/W3108503355","https://openalex.org/W3090555870","https://openalex.org/W4226420367","https://openalex.org/W2962876041","https://openalex.org/W3022820045","https://openalex.org/W2801655600","https://openalex.org/W3176578160","https://openalex.org/W3128424724"],"abstract_inverted_index":{"Recently,":[0],"significant":[1],"improvement":[2],"has":[3,27],"been":[4,29],"achieved":[5,145],"for":[6,129,171],"hardware":[7,17,44,105,169],"architecture":[8,122],"design":[9,101],"of":[10,19,46,126,136,159],"deep":[11],"neural":[12],"networks":[13],"(DNNs).":[14],"However,":[15],"the":[16,73,87,94,112,121,157,164],"implementation":[18,45,170],"one":[20],"widely":[21],"used":[22,55],"softmax":[23,47,172],"function":[24],"in":[25,173],"DNNs":[26],"not":[28],"much":[30],"investigated,":[31],"which":[32],"involves":[33],"expensive":[34],"division":[35],"and":[36,51,65,86,109,146],"exponentiation":[37],"units.":[38],"This":[39],"paper":[40],"performs":[41],"an":[42],"efficient":[43,168],"function.":[48,59],"Mathematical":[49],"transformations":[50],"linear":[52],"fitting":[53],"are":[54,69,84],"to":[56,71],"simplify":[57],"this":[58,162],"Multiple":[60],"algorithmic":[61],"strength":[62],"reduction":[63],"strategies":[64],"fast":[66],"addition":[67],"methods":[68],"employed":[70],"optimize":[72],"architecture.":[74],"By":[75],"using":[76,104],"these":[77],"techniques,":[78],"complicated":[79],"logic":[80],"units":[81],"like":[82],"multipliers":[83],"eliminated":[85],"memory":[88],"consumption":[89],"is":[90,97,102,144,163],"largely":[91],"reduced":[92],"while":[93],"accuracy":[95],"loss":[96],"negligible.":[98],"The":[99,133],"proposed":[100],"coded":[103],"description":[106],"language":[107],"(HDL)":[108],"synthesized":[110],"under":[111],"TSMC":[113],"28-nm":[114],"CMOS":[115],"technology.":[116],"Synthesis":[117],"results":[118],"show":[119],"that":[120],"achieves":[123],"a":[124],"throughput":[125],"6.976":[127],"G/s":[128],"8-bit":[130],"input":[131],"data.":[132],"power":[134],"efficiency":[135],"463.04":[137],"Gb/(mm":[138],"<sup":[139,151],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[140,152],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[141,153],"\u00b7":[142],"mW)":[143],"it":[147],"costs":[148],"only":[149],"0.015mm":[150],"area":[154],"resources.":[155],"To":[156],"best":[158],"our":[160],"knowledge,":[161],"first":[165],"work":[166],"on":[167],"open":[174],"literature.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":41},{"year":2024,"cited_by_count":46},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":32},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":5}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
