{"id":"https://openalex.org/W4402159576","doi":"https://doi.org/10.1109/tcsi.2024.3443270","title":"Hardware-Efficient SoftMax Architecture With Bit-Wise Exponentiation and Reciprocal Calculation","display_name":"Hardware-Efficient SoftMax Architecture With Bit-Wise Exponentiation and Reciprocal Calculation","publication_year":2024,"publication_date":"2024-08-20","ids":{"openalex":"https://openalex.org/W4402159576","doi":"https://doi.org/10.1109/tcsi.2024.3443270"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2024.3443270","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2024.3443270","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/A5100706198","display_name":"Jeongmin Kim","orcid":"https://orcid.org/0009-0003-1704-9871"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jeongmin Kim","raw_affiliation_strings":["School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0009-0003-1704-9871","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090216943","display_name":"Sungho Kim","orcid":"https://orcid.org/0009-0008-3916-720X"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sungho Kim","raw_affiliation_strings":["School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0009-0008-3916-720X","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050328398","display_name":"Kangjoon Choi","orcid":"https://orcid.org/0009-0004-4137-7688"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kangjoon Choi","raw_affiliation_strings":["School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0009-0004-4137-7688","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087977408","display_name":"In\u2010Cheol Park","orcid":"https://orcid.org/0000-0003-3524-2838"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"In-Cheol Park","raw_affiliation_strings":["School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0000-0003-3524-2838","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8728,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.96361153,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"71","issue":"10","first_page":"4574","last_page":"4585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9940999746322632,"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":0.9940999746322632,"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":0.9839000105857849,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9684000015258789,"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/exponentiation","display_name":"Exponentiation","score":0.7899908423423767},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.685202419757843},{"id":"https://openalex.org/keywords/softmax-function","display_name":"Softmax function","score":0.6027066707611084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.602043092250824},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5707309246063232},{"id":"https://openalex.org/keywords/modular-exponentiation","display_name":"Modular exponentiation","score":0.5161217451095581},{"id":"https://openalex.org/keywords/bit","display_name":"Bit (key)","score":0.5063952207565308},{"id":"https://openalex.org/keywords/architecture","display_name":"Architecture","score":0.45598509907722473},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.4209054708480835},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.4083385169506073},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.32352787256240845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2845061123371124},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2180805802345276},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12792173027992249},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.12026768922805786},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.11273279786109924},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.098915696144104}],"concepts":[{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.7899908423423767},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.685202419757843},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.6027066707611084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.602043092250824},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5707309246063232},{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.5161217451095581},{"id":"https://openalex.org/C117011727","wikidata":"https://www.wikidata.org/wiki/Q1278488","display_name":"Bit (key)","level":2,"score":0.5063952207565308},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.45598509907722473},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.4209054708480835},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.4083385169506073},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.32352787256240845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2845061123371124},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2180805802345276},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12792173027992249},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.12026768922805786},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.11273279786109924},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.098915696144104},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/tcsi.2024.3443270","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2024.3443270","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":[{"id":"https://metadata.un.org/sdg/7","score":0.4099999964237213,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1587217691","https://openalex.org/W2052860758","https://openalex.org/W2608093348","https://openalex.org/W2701059868","https://openalex.org/W2896457183","https://openalex.org/W2903640996","https://openalex.org/W2906917284","https://openalex.org/W2910396952","https://openalex.org/W2914968962","https://openalex.org/W2921952613","https://openalex.org/W2937064326","https://openalex.org/W2946480111","https://openalex.org/W2951045917","https://openalex.org/W2964110616","https://openalex.org/W3023331847","https://openalex.org/W3034999214","https://openalex.org/W3036061420","https://openalex.org/W3090555870","https://openalex.org/W3094502228","https://openalex.org/W3126895102","https://openalex.org/W3159727696","https://openalex.org/W3160618415","https://openalex.org/W3176578160","https://openalex.org/W3183327882","https://openalex.org/W3196923642","https://openalex.org/W3207366647","https://openalex.org/W4233267564","https://openalex.org/W4293768835","https://openalex.org/W4312554056","https://openalex.org/W4312847929","https://openalex.org/W4313467238","https://openalex.org/W4378364815","https://openalex.org/W4385080022","https://openalex.org/W4385245566","https://openalex.org/W4386859272","https://openalex.org/W4388853572","https://openalex.org/W4394625669","https://openalex.org/W6744013678","https://openalex.org/W6755207826","https://openalex.org/W6769311223","https://openalex.org/W6778883912"],"related_works":["https://openalex.org/W4235485585","https://openalex.org/W670148","https://openalex.org/W1507420113","https://openalex.org/W4242613270","https://openalex.org/W28274153","https://openalex.org/W2107014706","https://openalex.org/W2736837562","https://openalex.org/W2020808628","https://openalex.org/W2113040119","https://openalex.org/W2767903583"],"abstract_inverted_index":{"The":[0],"SoftMax":[1,35,57,192],"function":[2],"is":[3,105,123,164,227],"one":[4,148],"of":[5,22,27,45,72,159,199,205],"the":[6,20,25,31,41,101,109,117,120,131,157,160,172,176,182,189],"activation":[7],"functions":[8],"used":[9,152],"in":[10,53,70,139],"deep":[11],"neural":[12],"networks":[13],"(DNN)":[14],"to":[15,19,82,93,112,129,166,181,236],"normalize":[16],"input":[17,103,110],"values":[18,111],"range":[21],"(0,1).":[23],"With":[24],"advent":[26],"DNN":[28],"models":[29],"including":[30],"Transformer,":[32],"operations":[33,47],"utilizing":[34],"have":[36,79],"gained":[37],"significant":[38,68],"attention,":[39],"and":[40,61,75,86,156,201,213],"efficient":[42],"hardware":[43,54,73,132],"implementation":[44],"such":[46],"has":[48],"become":[49],"a":[50,67,90,126,187,195,202],"prominent":[51],"issue":[52],"realization.":[55],"Implementing":[56],"often":[58],"involves":[59],"exponential":[60,140,162],"division":[62,168],"operations,":[63,141],"which":[64],"can":[65],"be":[66],"bottleneck":[69],"terms":[71],"cost":[74],"performance.":[76],"Various":[77],"efforts":[78],"been":[80],"made":[81],"address":[83],"this":[84,87],"challenge,":[85],"paper":[88],"introduces":[89],"novel":[91],"approach":[92],"efficiently":[94],"implement":[95],"SoftMax.":[96],"In":[97,116],"most":[98],"previous":[99,183,237],"works,":[100],"maximum":[102,121],"value":[104,122,128],"subtracted":[106],"from":[107],"all":[108],"ensure":[113],"numerical":[114,136],"stability.":[115,137],"proposed":[118,173,190],"approach,":[119],"replaced":[124],"with":[125,134,146,169,229],"different":[127],"reduce":[130],"complexity":[133,178],"ensuring":[135],"Additionally,":[138],"simple":[142],"Look-Up":[143],"Tables":[144],"(LUTs)":[145],"only":[147],"entry":[149],"each":[150],"are":[151],"for":[153],"bit-wise":[154],"calculations,":[155],"reciprocal":[158],"total":[161],"sum":[163],"computed":[165],"replace":[167],"multiplication.":[170],"Applying":[171],"methods":[174],"reduces":[175],"computational":[177],"significantly":[179],"compared":[180,235],"log-sum-exp":[184],"approach.":[185],"As":[186],"result,":[188],"8-bit":[191],"accelerator":[193],"achieves":[194],"high":[196,203],"operating":[197],"frequency":[198],"3.12GHz":[200],"throughput":[204],"25G":[206],"inputs/s.":[207],"It":[208],"also":[209],"improves":[210],"area":[211],"efficiency":[212],"power":[214],"consumption":[215],"by":[216],"at":[217],"least":[218],"2":[219],"times.":[220],"From":[221],"an":[222],"accuracy":[223,234],"perspective,":[224],"furthermore,":[225],"it":[226],"associated":[228],"similar":[230],"or":[231],"even":[232],"better":[233],"works.":[238]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}