{"id":"https://openalex.org/W3044794971","doi":"https://doi.org/10.1109/tetc.2021.3050989","title":"The Effects of Approximate Multiplication on Convolutional Neural Networks","display_name":"The Effects of Approximate Multiplication on Convolutional Neural Networks","publication_year":2021,"publication_date":"2021-01-13","ids":{"openalex":"https://openalex.org/W3044794971","doi":"https://doi.org/10.1109/tetc.2021.3050989","mag":"3044794971"},"language":"en","primary_location":{"id":"doi:10.1109/tetc.2021.3050989","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetc.2021.3050989","pdf_url":null,"source":{"id":"https://openalex.org/S2496326734","display_name":"IEEE Transactions on Emerging Topics in Computing","issn_l":"2168-6750","issn":["2168-6750","2376-4562"],"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 Emerging Topics in Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.10500","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Min Soo Kim","orcid":"https://orcid.org/0000-0001-8838-8246"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Min Soo Kim","raw_affiliation_strings":["NGD Systems, Irvine, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-8838-8246","affiliations":[{"raw_affiliation_string":"NGD Systems, Irvine, CA, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Alberto A. Del Barrio","orcid":"https://orcid.org/0000-0002-6769-1200"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alberto A. Del Barrio","raw_affiliation_strings":["Department of Computer Architecture and Automation, Complutense University of Madrid, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-6769-1200","affiliations":[{"raw_affiliation_string":"Department of Computer Architecture and Automation, Complutense University of Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"middle","author":{"id":null,"display_name":"HyunJin Kim","orcid":"https://orcid.org/0000-0001-5017-3995"},"institutions":[{"id":"https://openalex.org/I89015989","display_name":"Dankook University","ror":"https://ror.org/058pdbn81","country_code":"KR","type":"education","lineage":["https://openalex.org/I89015989"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"HyunJin Kim","raw_affiliation_strings":["School of Electronics and Electrical Engineering, Dankook University, Yongin-si, Gyeonggi-do, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0001-5017-3995","affiliations":[{"raw_affiliation_string":"School of Electronics and Electrical Engineering, Dankook University, Yongin-si, Gyeonggi-do, Republic of Korea","institution_ids":["https://openalex.org/I89015989"]}]},{"author_position":"last","author":{"id":null,"display_name":"Nader Bagherzadeh","orcid":"https://orcid.org/0000-0001-7216-0546"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nader Bagherzadeh","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of California, Irvine, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7216-0546","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7781,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.94143644,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"10","issue":"2","first_page":"904","last_page":"916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.26660001277923584,"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"}},"topics":[{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.26660001277923584,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.21089999377727509,"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"}},{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.1712000072002411,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.8398000001907349},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.6699000000953674},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.6471999883651733},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.483599990606308},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4471000134944916},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4122999906539917},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.38749998807907104},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.37389999628067017}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.8398000001907349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7764999866485596},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.6699000000953674},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6471999883651733},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5145999789237976},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.483599990606308},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4779999852180481},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4122999906539917},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.38749998807907104},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.37389999628067017},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.3714999854564667},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.2800000011920929},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.273499995470047},{"id":"https://openalex.org/C2944601119","wikidata":"https://www.wikidata.org/wiki/Q43744058","display_name":"Residual neural network","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2621999979019165},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26179999113082886},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tetc.2021.3050989","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetc.2021.3050989","pdf_url":null,"source":{"id":"https://openalex.org/S2496326734","display_name":"IEEE Transactions on Emerging Topics in Computing","issn_l":"2168-6750","issn":["2168-6750","2376-4562"],"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 Emerging Topics in Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2007.10500","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.10500","pdf_url":"https://arxiv.org/pdf/2007.10500","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.10500","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.10500","pdf_url":"https://arxiv.org/pdf/2007.10500","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3484674056","display_name":null,"funder_award_id":"PR2003 20/01","funder_id":"https://openalex.org/F4320309764","funder_display_name":"Fundaci\u00f3n BBVA"},{"id":"https://openalex.org/G822310507","display_name":null,"funder_award_id":"S2018/TCS-4423","funder_id":"https://openalex.org/F4320313831","funder_display_name":"Comunidad de Madrid"}],"funders":[{"id":"https://openalex.org/F4320309764","display_name":"Fundaci\u00f3n BBVA","ror":"https://ror.org/01jzs3b90"},{"id":"https://openalex.org/F4320313831","display_name":"Comunidad de Madrid","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1669276382","https://openalex.org/W2010069327","https://openalex.org/W2051831389","https://openalex.org/W2111013824","https://openalex.org/W2155893237","https://openalex.org/W2156425544","https://openalex.org/W2170140732","https://openalex.org/W2194775991","https://openalex.org/W2276486856","https://openalex.org/W2300242332","https://openalex.org/W2400523863","https://openalex.org/W2531409750","https://openalex.org/W2533121491","https://openalex.org/W2549139847","https://openalex.org/W2590016403","https://openalex.org/W2694935213","https://openalex.org/W2790285612","https://openalex.org/W2897362884","https://openalex.org/W2897792138","https://openalex.org/W2900613774","https://openalex.org/W2913405856","https://openalex.org/W2920582597","https://openalex.org/W2958306322","https://openalex.org/W2963122961","https://openalex.org/W2963163009","https://openalex.org/W2980235527","https://openalex.org/W2981433297","https://openalex.org/W2981980078","https://openalex.org/W2983464374","https://openalex.org/W3023146441","https://openalex.org/W4233443202","https://openalex.org/W4235436861","https://openalex.org/W4236363946","https://openalex.org/W4246193833","https://openalex.org/W4246550359","https://openalex.org/W4247198796","https://openalex.org/W4249697915","https://openalex.org/W6696004547","https://openalex.org/W6696152683","https://openalex.org/W6696798448","https://openalex.org/W6734868079","https://openalex.org/W6745375725","https://openalex.org/W6776052016"],"related_works":[],"abstract_inverted_index":{"This":[0],"article":[1,166],"analyzes":[2],"the":[3,22,25,43,47,61,93,105,113,131,157,168],"effects":[4],"of":[5,24,74,138,153,164],"approximate":[6,18,64,94],"multiplication":[7,19,77,120],"when":[8],"performing":[9],"inferences":[10,31],"on":[11,80],"deep":[12],"convolutional":[13],"neural":[14],"networks":[15],"(CNNs).":[16],"The":[17,40,66,82,160],"can":[20,32,96,173],"reduce":[21],"cost":[23,136],"underlying":[26],"circuits":[27],"so":[28],"that":[29,54,92,99,124,171],"CNN":[30,58,183],"be":[33,174,180],"performed":[34,85],"more":[35,56],"efficiently":[36],"in":[37,46,182],"hardware":[38],"accelerators.":[39],"study":[41],"identifies":[42],"critical":[44],"factors":[45,68],"convolution,":[48],"fully-connected,":[49],"and":[50,115],"batch":[51],"normalization":[52],"layers":[53],"allow":[55],"accurate":[57,103],"predictions":[59,98],"despite":[60],"errors":[62,123],"from":[63],"multiplication.":[65],"same":[67],"also":[69],"provide":[70],"an":[71],"arithmetic":[72],"explanation":[73],"why":[75],"bfloat16":[76,141,158],"performs":[78],"well":[79],"CNNs.":[81],"experiments":[83],"are":[84,100,125],"with":[86,118],"recognized":[87],"network":[88],"architectures":[89],"to":[90,130,150,156,179],"show":[91],"multipliers":[95],"produce":[97],"nearly":[101],"as":[102,104],"FP32":[106,132],"references,":[107],"without":[108],"additional":[109],"training.":[110],"For":[111],"example,":[112],"ResNet":[114],"Inception-v4":[116],"models":[117],"Mitch-$w$w6":[119,139],"produces":[121],"Top-5":[122],"within":[126],"0.2":[127],"percent":[128,152],"compared":[129,155],"references.":[133],"A":[134],"brief":[135],"comparison":[137],"against":[140],"is":[142,167],"presented":[143],"where":[144],"a":[145],"MAC":[146,184],"operation":[147],"saves":[148],"up":[149],"80":[151],"energy":[154],"arithmetic.":[159],"most":[161],"far-reaching":[162],"contribution":[163],"this":[165],"analytical":[169],"justification":[170],"multiplications":[172],"approximated":[175],"while":[176],"additions":[177],"need":[178],"exact":[181],"operations.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2020-07-29T00:00:00"}