{"id":"https://openalex.org/W3036061420","doi":"https://doi.org/10.1109/tcsii.2020.3002564","title":"Efficient Precision-Adjustable Architecture for Softmax Function in Deep Learning","display_name":"Efficient Precision-Adjustable Architecture for Softmax Function in Deep Learning","publication_year":2020,"publication_date":"2020-06-16","ids":{"openalex":"https://openalex.org/W3036061420","doi":"https://doi.org/10.1109/tcsii.2020.3002564","mag":"3036061420"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2020.3002564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2020.3002564","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 II: Express Briefs","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/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"],"raw_orcid":null,"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"],"raw_orcid":"https://orcid.org/0000-0002-8639-3081","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/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":false,"raw_author_name":"Meiqi Wang","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-9553-3640","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"],"raw_orcid":null,"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"],"raw_orcid":"https://orcid.org/0000-0002-7227-4786","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":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":null,"apc_paid":null,"fwci":4.3318,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.95426861,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"67","issue":"12","first_page":"3382","last_page":"3386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9994000196456909,"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":0.9994000196456909,"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/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"}},{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9947999715805054,"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/softmax-function","display_name":"Softmax function","score":0.988853931427002},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.6820505261421204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6712315082550049},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.6276878118515015},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5423551201820374},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5387389063835144},{"id":"https://openalex.org/keywords/architecture","display_name":"Architecture","score":0.5070669651031494},{"id":"https://openalex.org/keywords/computer-architecture","display_name":"Computer architecture","score":0.48109978437423706},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.46074309945106506},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.4311956465244293},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.3970574736595154},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3733660578727722},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.34592974185943604},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09954231977462769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.09060117602348328}],"concepts":[{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.988853931427002},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.6820505261421204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6712315082550049},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.6276878118515015},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5423551201820374},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5387389063835144},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.5070669651031494},{"id":"https://openalex.org/C118524514","wikidata":"https://www.wikidata.org/wiki/Q173212","display_name":"Computer architecture","level":1,"score":0.48109978437423706},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.46074309945106506},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.4311956465244293},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.3970574736595154},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3733660578727722},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.34592974185943604},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09954231977462769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.09060117602348328},{"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},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":1,"locations":[{"id":"doi:10.1109/tcsii.2020.3002564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2020.3002564","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.5199999809265137}],"awards":[{"id":"https://openalex.org/G1941337620","display_name":null,"funder_award_id":"021014380065","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4112626697","display_name":null,"funder_award_id":"61774082","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4988504959","display_name":null,"funder_award_id":"61604068","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W2094665651","https://openalex.org/W2102113734","https://openalex.org/W2405226465","https://openalex.org/W2608093348","https://openalex.org/W2903640996","https://openalex.org/W2914968962","https://openalex.org/W2920950200","https://openalex.org/W2937064326","https://openalex.org/W2944322787","https://openalex.org/W2946480111","https://openalex.org/W2963088785","https://openalex.org/W2963403868","https://openalex.org/W2963703618","https://openalex.org/W2964110616","https://openalex.org/W4385245566","https://openalex.org/W6675365184","https://openalex.org/W6736797231","https://openalex.org/W6739901393","https://openalex.org/W6743446608"],"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/W3005627584","https://openalex.org/W4303493643"],"abstract_inverted_index":{"The":[0,118],"softmax":[1,36,51,69,93],"function":[2,52],"has":[3],"been":[4],"widely":[5],"used":[6],"in":[7,45,78,155],"deep":[8,80],"neural":[9],"networks":[10],"(DNNs),":[11],"and":[12,42,64,105,128,138,157,159],"studies":[13],"on":[14,85,130],"efficient":[15,32,90],"hardware":[16,33,124,173],"accelerators":[17],"for":[18,35,68,92],"DNN":[19],"have":[20],"also":[21],"attracted":[22],"tremendous":[23],"attention.":[24],"However,":[25],"it":[26],"is":[27,53,70,94,121],"very":[28],"challenging":[29],"to":[30,111],"design":[31,120],"architectures":[34],"because":[37],"of":[38],"the":[39,50,86,98,102,165],"expensive":[40],"exponentiation":[41],"division":[43],"calculations":[44],"it.":[46],"In":[47],"this":[48],"brief,":[49],"firstly":[54],"simplified":[55],"by":[56,161],"exploring":[57],"algorithmic":[58],"strength":[59],"reductions.":[60],"Afterwards,":[61],"a":[62,113],"hardware-friendly":[63],"precision-adjustable":[65],"calculation":[66],"method":[67],"proposed,":[71],"which":[72],"can":[73,107,167],"meet":[74],"different":[75],"precision":[76],"requirements":[77],"various":[79],"learning":[81],"(DL)":[82],"tasks.":[83],"Based":[84],"above":[87],"innovations,":[88],"an":[89],"architecture":[91,150],"presented.":[95],"By":[96],"tuning":[97],"parameter":[99],"P":[100,163],",":[101,164],"system":[103],"accuracy":[104,166],"complexity":[106],"be":[108,168],"adjusted":[109],"dynamically":[110],"achieve":[112],"good":[114],"tradeoff":[115],"between":[116],"them.":[117],"proposed":[119],"coded":[122],"using":[123],"description":[125],"language":[126],"(HDL)":[127],"evaluated":[129],"two":[131],"platforms,":[132],"Xilinx":[133],"Zynq-7000":[134],"ZC706":[135],"development":[136],"board":[137],"TSMC":[139],"28-nm":[140],"CMOS":[141],"technology,":[142],"respectively.":[143],"Hardware":[144],"implementation":[145],"results":[146],"show":[147],"that":[148,160],"our":[149],"significantly":[151],"outperforms":[152],"other":[153],"works":[154],"speed":[156],"area,":[158],"adjusting":[162],"further":[169],"increased":[170],"with":[171],"little":[172],"overhead.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":31},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}