{"id":"https://openalex.org/W4400230406","doi":"https://doi.org/10.1109/iscas58744.2024.10558086","title":"A Hardware-Friendly Alternative to Softmax Function and Its Efficient VLSI Implementation for Deep Learning Applications","display_name":"A Hardware-Friendly Alternative to Softmax Function and Its Efficient VLSI Implementation for Deep Learning Applications","publication_year":2024,"publication_date":"2024-05-19","ids":{"openalex":"https://openalex.org/W4400230406","doi":"https://doi.org/10.1109/iscas58744.2024.10558086"},"language":"en","primary_location":{"id":"doi:10.1109/iscas58744.2024.10558086","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/iscas58744.2024.10558086","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Circuits and Systems (ISCAS)","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/A5111710452","display_name":"Meng-Hsun Hsieh","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Meng-Hsun Hsieh","raw_affiliation_strings":["National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan"],"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109741288","display_name":"Xuan-Hong Li","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Xuan-Hong Li","raw_affiliation_strings":["National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan"],"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103008781","display_name":"Yu-Hsiang Huang","orcid":"https://orcid.org/0000-0003-4013-0865"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu-Hsiang Huang","raw_affiliation_strings":["National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan"],"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036029066","display_name":"Pei-Hsuan Kuo","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Pei-Hsuan Kuo","raw_affiliation_strings":["National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan"],"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107969989","display_name":"Juinn-Dar Huang","orcid":"https://orcid.org/0000-0001-5961-7863"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Juinn-Dar Huang","raw_affiliation_strings":["National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan"],"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University,Department of Electronics and Electrical Engineering &amp; Institute of Electronics,Hsinchu,Taiwan","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5111710452"],"corresponding_institution_ids":["https://openalex.org/I148366613"],"apc_list":null,"apc_paid":null,"fwci":0.5319,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60466328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9703999757766724,"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"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9703999757766724,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9488999843597412,"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/T11992","display_name":"CCD and CMOS Imaging Sensors","score":0.9101999998092651,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/softmax-function","display_name":"Softmax function","score":0.7758972644805908},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.7609516382217407},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7084609866142273},{"id":"https://openalex.org/keywords/computer-architecture","display_name":"Computer architecture","score":0.6894360780715942},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5318009257316589},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.4248659014701843},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.40652531385421753},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.36774134635925293},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2916603684425354}],"concepts":[{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.7758972644805908},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.7609516382217407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7084609866142273},{"id":"https://openalex.org/C118524514","wikidata":"https://www.wikidata.org/wiki/Q173212","display_name":"Computer architecture","level":1,"score":0.6894360780715942},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5318009257316589},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.4248659014701843},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.40652531385421753},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.36774134635925293},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2916603684425354},{"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":1,"locations":[{"id":"doi:10.1109/iscas58744.2024.10558086","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/iscas58744.2024.10558086","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Circuits and Systems (ISCAS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W2560674852","https://openalex.org/W2608093348","https://openalex.org/W2903640996","https://openalex.org/W2910396952","https://openalex.org/W2946480111","https://openalex.org/W3021972173","https://openalex.org/W3036061420","https://openalex.org/W3082834449","https://openalex.org/W3107894966","https://openalex.org/W3138516171","https://openalex.org/W3183327882","https://openalex.org/W3207366647","https://openalex.org/W3211525823","https://openalex.org/W4292779060","https://openalex.org/W4293768835","https://openalex.org/W4385080022","https://openalex.org/W6778883912","https://openalex.org/W6788135285"],"related_works":["https://openalex.org/W3107204728","https://openalex.org/W4287591324","https://openalex.org/W3108503355","https://openalex.org/W4226420367","https://openalex.org/W2962876041","https://openalex.org/W4323060069","https://openalex.org/W2134640991","https://openalex.org/W3027318491","https://openalex.org/W101478184","https://openalex.org/W1986774039"],"abstract_inverted_index":{"The":[0,47],"Softmax":[1,15,171],"function":[2,48],"holds":[3],"an":[4,84],"essential":[5],"role":[6],"in":[7,27,59,135,157,172,196],"most":[8],"machine":[9],"learning":[10,179],"algorithms.":[11],"Conventional":[12],"realization":[13],"of":[14,43,89,149],"necessitates":[16],"computationally":[17],"intensive":[18],"exponential":[19,45,97],"operations":[20],"and":[21,53,62,98,101,138,146,154,175,181,187,199],"divisions,":[22],"thereby":[23],"posing":[24],"formidable":[25],"challenges":[26],"developing":[28],"low-cost":[29],"hardware":[30,86,176,184],"implementations.":[31],"This":[32],"paper":[33,81],"presents":[34],"a":[35,110,158,165,193],"promising":[36,167],"hardware-friendly":[37,162],"alternative,":[38],"Squaremax,":[39],"which":[40,124],"gets":[41],"rid":[42],"complex":[44,170],"operations.":[46],"definition":[49],"is":[50,102,164],"extremely":[51],"simple":[52],"can":[54],"thus":[55],"be":[56],"efficiently":[57],"implemented":[58],"both":[60,173],"software":[61,174],"hardware.":[63],"Experimental":[64],"results":[65],"show":[66],"that":[67],"Squaremax":[68,163],"consistently":[69],"attains":[70],"comparable":[71],"or":[72],"superior":[73],"accuracy":[74],"over":[75],"several":[76],"popular":[77],"models.":[78],"Besides,":[79],"this":[80],"also":[82],"proposes":[83],"efficient":[85,188],"architecture":[87,185],"design":[88,186],"Squaremax.":[90],"It":[91,108],"requires":[92],"no":[93],"functional":[94],"units":[95],"for":[96,116,177],"logarithmic":[99],"operations,":[100],"even":[103],"lookup":[104],"table":[105],"(LUT)":[106],"free.":[107],"adopts":[109],"flexible":[111],"16-bit":[112],"fixed-point":[113],"Q":[114],"format":[115],"I/O":[117],"to":[118,126,169],"better":[119],"preserve":[120],"the":[121,182],"output":[122],"precision,":[123],"leads":[125],"higher":[127],"model":[128],"accuracy.":[129],"Moreover,":[130],"it":[131],"yields":[132],"substantial":[133],"improvements":[134],"speed,":[136,197],"area,":[137,198],"power,":[139],"as":[140,142],"well":[141],"achieves":[143],"remarkable":[144],"area":[145],"power":[147],"efficiency":[148],"664":[150],"G/mm<sup":[151],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[152],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[153],"1396":[155],"G/W":[156],"40nm":[159],"process.":[160],"Therefore,":[161],"very":[166],"alternative":[168],"deep":[178],"applications,":[180],"proposed":[183],"LUT-free":[189],"implementation":[190],"do":[191],"achieve":[192],"notable":[194],"improvement":[195],"power.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-21T23:12:01.093139","created_date":"2025-10-10T00:00:00"}