{"id":"https://openalex.org/W1964288235","doi":"https://doi.org/10.1109/tnnls.2014.2383395","title":"Memristor-Based Multilayer Neural Networks With Online Gradient Descent Training","display_name":"Memristor-Based Multilayer Neural Networks With Online Gradient Descent Training","publication_year":2015,"publication_date":"2015-01-14","ids":{"openalex":"https://openalex.org/W1964288235","doi":"https://doi.org/10.1109/tnnls.2014.2383395","mag":"1964288235","pmid":"https://pubmed.ncbi.nlm.nih.gov/25594981"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2014.2383395","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2014.2383395","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5025123281","display_name":"Daniel Soudry","orcid":"https://orcid.org/0000-0001-9368-6352"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Soudry","raw_affiliation_strings":["Center for Theoretical Neuroscience, and the Grossman Center for the Statistics of Mind, Columbia University, New York, NY, USA","Department of StatisticsCenter for Theoretical Neuroscience, and the Grossman Center for the Statistics of Mind, Columbia University, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Theoretical Neuroscience, and the Grossman Center for the Statistics of Mind, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of StatisticsCenter for Theoretical Neuroscience, and the Grossman Center for the Statistics of Mind, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032709945","display_name":"Dotan Di Castro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dotan Di Castro","raw_affiliation_strings":["Yahoo! Labs, Haifa, Israel","Yahoo! Labs., Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yahoo! Labs, Haifa, Israel","institution_ids":[]},{"raw_affiliation_string":"Yahoo! Labs., Haifa, Israel","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001611795","display_name":"A. Gal","orcid":"https://orcid.org/0000-0003-0834-2649"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Asaf Gal","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","Department of Electrical EngineeringBiological Networks Research Laboratories, Technion-Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Electrical EngineeringBiological Networks Research Laboratories, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051888366","display_name":"Avinoam Kolodny","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Avinoam Kolodny","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","Department of Electrical Engineering, Technion??Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Electrical Engineering, Technion??Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014138496","display_name":"Shahar Kvatinsky","orcid":"https://orcid.org/0000-0001-7277-7271"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shahar Kvatinsky","raw_affiliation_strings":["Department of Computer Science, Stanford University, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.1088,"has_fulltext":false,"cited_by_count":267,"citation_normalized_percentile":{"value":0.9920137,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"26","issue":"10","first_page":"2408","last_page":"2421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":1.0,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":1.0,"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/T11992","display_name":"CCD and CMOS Imaging Sensors","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/T11601","display_name":"Neuroscience and Neural Engineering","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/memristor","display_name":"Memristor","score":0.9199966192245483},{"id":"https://openalex.org/keywords/memistor","display_name":"Memistor","score":0.7153797149658203},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.704225480556488},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6505847573280334},{"id":"https://openalex.org/keywords/cmos","display_name":"CMOS","score":0.6338948607444763},{"id":"https://openalex.org/keywords/backpropagation","display_name":"Backpropagation","score":0.6306480169296265},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.548134982585907},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.545257568359375},{"id":"https://openalex.org/keywords/neuromorphic-engineering","display_name":"Neuromorphic engineering","score":0.5074369311332703},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5040165781974792},{"id":"https://openalex.org/keywords/synaptic-weight","display_name":"Synaptic weight","score":0.49309393763542175},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.40862080454826355},{"id":"https://openalex.org/keywords/resistive-random-access-memory","display_name":"Resistive random-access memory","score":0.40295296907424927},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3629171848297119},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.34717410802841187},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.32320863008499146},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.21203091740608215},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11470925807952881}],"concepts":[{"id":"https://openalex.org/C150072547","wikidata":"https://www.wikidata.org/wiki/Q212923","display_name":"Memristor","level":2,"score":0.9199966192245483},{"id":"https://openalex.org/C1895703","wikidata":"https://www.wikidata.org/wiki/Q6034938","display_name":"Memistor","level":4,"score":0.7153797149658203},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.704225480556488},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6505847573280334},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.6338948607444763},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.6306480169296265},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.548134982585907},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.545257568359375},{"id":"https://openalex.org/C151927369","wikidata":"https://www.wikidata.org/wiki/Q1981312","display_name":"Neuromorphic engineering","level":3,"score":0.5074369311332703},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5040165781974792},{"id":"https://openalex.org/C66949984","wikidata":"https://www.wikidata.org/wiki/Q7662043","display_name":"Synaptic weight","level":3,"score":0.49309393763542175},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.40862080454826355},{"id":"https://openalex.org/C182019814","wikidata":"https://www.wikidata.org/wiki/Q1143830","display_name":"Resistive random-access memory","level":3,"score":0.40295296907424927},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3629171848297119},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.34717410802841187},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.32320863008499146},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.21203091740608215},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11470925807952881},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009862","descriptor_name":"Online Systems","qualifier_ui":"Q000295","qualifier_name":"instrumentation","is_major_topic":false},{"descriptor_ui":"D009862","descriptor_name":"Online Systems","qualifier_ui":"Q000295","qualifier_name":"instrumentation","is_major_topic":false},{"descriptor_ui":"D009862","descriptor_name":"Online Systems","qualifier_ui":"Q000295","qualifier_name":"instrumentation","is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":"Q000295","qualifier_name":"instrumentation","is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":"Q000295","qualifier_name":"instrumentation","is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":"Q000295","qualifier_name":"instrumentation","is_major_topic":false},{"descriptor_ui":"D013569","descriptor_name":"Synapses","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013569","descriptor_name":"Synapses","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013569","descriptor_name":"Synapses","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2014.2383395","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2014.2383395","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:25594981","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25594981","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320326823","display_name":"Intel Collaboration Research Institute for Computational Intelligence","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":82,"referenced_works":["https://openalex.org/W21556541","https://openalex.org/W1535810436","https://openalex.org/W1554663460","https://openalex.org/W1663973292","https://openalex.org/W1967602196","https://openalex.org/W1968020335","https://openalex.org/W1973352490","https://openalex.org/W1973433558","https://openalex.org/W1982580897","https://openalex.org/W1986273360","https://openalex.org/W1989866912","https://openalex.org/W1990404128","https://openalex.org/W1995676447","https://openalex.org/W1997078229","https://openalex.org/W2007898123","https://openalex.org/W2008901850","https://openalex.org/W2024168688","https://openalex.org/W2025357764","https://openalex.org/W2026122895","https://openalex.org/W2028166238","https://openalex.org/W2028528153","https://openalex.org/W2030568691","https://openalex.org/W2031605963","https://openalex.org/W2040354407","https://openalex.org/W2040870580","https://openalex.org/W2044493455","https://openalex.org/W2045009304","https://openalex.org/W2045614943","https://openalex.org/W2057167762","https://openalex.org/W2059888459","https://openalex.org/W2066280488","https://openalex.org/W2069233440","https://openalex.org/W2071129817","https://openalex.org/W2080625874","https://openalex.org/W2082892213","https://openalex.org/W2090207505","https://openalex.org/W2091777687","https://openalex.org/W2101661863","https://openalex.org/W2103496339","https://openalex.org/W2106010231","https://openalex.org/W2112181056","https://openalex.org/W2113651538","https://openalex.org/W2120480077","https://openalex.org/W2122733133","https://openalex.org/W2125010820","https://openalex.org/W2125993116","https://openalex.org/W2129936377","https://openalex.org/W2132424367","https://openalex.org/W2135691525","https://openalex.org/W2141125852","https://openalex.org/W2141740078","https://openalex.org/W2145942961","https://openalex.org/W2148776451","https://openalex.org/W2149380925","https://openalex.org/W2154208623","https://openalex.org/W2155954834","https://openalex.org/W2156163116","https://openalex.org/W2156782156","https://openalex.org/W2161574926","https://openalex.org/W2161758346","https://openalex.org/W2161786772","https://openalex.org/W2161972632","https://openalex.org/W2162651880","https://openalex.org/W2162827630","https://openalex.org/W2168231600","https://openalex.org/W2253807446","https://openalex.org/W2432567885","https://openalex.org/W2895674046","https://openalex.org/W2914484425","https://openalex.org/W2919115771","https://openalex.org/W3042184340","https://openalex.org/W3099743262","https://openalex.org/W3120740533","https://openalex.org/W4212863985","https://openalex.org/W4243757115","https://openalex.org/W4255949318","https://openalex.org/W4388297464","https://openalex.org/W6678242812","https://openalex.org/W6678426860","https://openalex.org/W6683799086","https://openalex.org/W6684089856","https://openalex.org/W6684859321"],"related_works":["https://openalex.org/W3212508523","https://openalex.org/W1995352804","https://openalex.org/W3207218810","https://openalex.org/W2895545069","https://openalex.org/W1872623660","https://openalex.org/W2016922062","https://openalex.org/W1990306796","https://openalex.org/W1970974872","https://openalex.org/W2926332116","https://openalex.org/W4205344526"],"abstract_inverted_index":{"Learning":[0],"in":[1,30],"multilayer":[2],"neural":[3],"networks":[4],"(MNNs)":[5],"relies":[6],"on":[7,77,165,182],"continuous":[8],"updating":[9],"of":[10,13,88,117,121,141,147,175],"large":[11],"matrices":[12],"synaptic":[14,44,114],"weights":[15],"by":[16,99,161],"local":[17],"rules.":[18],"Such":[19,152],"locality":[20],"can":[21,155],"be":[22],"exploited":[23],"for":[24,42,59],"massive":[25],"parallelism":[26],"when":[27],"implementing":[28],"MNNs":[29,159],"hardware.":[31],"However,":[32],"these":[33,61],"update":[34,62],"rules":[35],"require":[36],"a":[37,57,83,89,113,118,153],"multiply":[38],"and":[39,127,139,144,173],"accumulate":[40],"operation":[41],"each":[43],"weight,":[45],"which":[46],"is":[47,71,75,106,133],"challenging":[48],"to":[49,94,135],"implement":[50,157],"compactly":[51,156],"using":[52,68],"CMOS.":[53],"In":[54],"this":[55],"paper,":[56],"method":[58,74,111],"performing":[60],"operations":[63],"simultaneously":[64],"(incremental":[65],"outer":[66],"products)":[67],"memristor-based":[69,178],"arrays":[70],"proposed.":[72],"The":[73,109,171],"based":[76,164],"the":[78,86,95,100,104,142,176],"fact":[79],"that,":[80],"approximately,":[81],"given":[82],"voltage":[84],"pulse,":[85],"conductivity":[87],"memristor":[90,126],"will":[91],"increment":[92,105],"proportionally":[93],"pulse":[96,101],"duration":[97],"multiplied":[98],"magnitude":[102],"if":[103],"sufficiently":[107],"small.":[108],"proposed":[110,177],"uses":[112],"circuit":[115,132,154,179],"composed":[116],"small":[119],"number":[120],"components":[122],"per":[123],"synapse:":[124],"one":[125],"two":[128],"CMOS":[129],"transistors.":[130],"This":[131],"expected":[134],"consume":[136],"between":[137],"2%":[138],"8%":[140],"area":[143],"static":[145],"power":[146],"previous":[148],"CMOS-only":[149],"hardware":[150,158],"alternatives.":[151],"trainable":[160],"scalable":[162],"algorithms":[163],"online":[166],"gradient":[167],"descent":[168],"(e.g.,":[169],"backpropagation).":[170],"utility":[172],"robustness":[174],"are":[180],"demonstrated":[181],"standard":[183],"supervised":[184],"learning":[185],"tasks.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":29},{"year":2020,"cited_by_count":30},{"year":2019,"cited_by_count":38},{"year":2018,"cited_by_count":43},{"year":2017,"cited_by_count":24},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":6}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}