{"id":"https://openalex.org/W4383957700","doi":"https://doi.org/10.1162/neco_a_01597","title":"Attention in a Family of Boltzmann Machines Emerging From Modern Hopfield Networks","display_name":"Attention in a Family of Boltzmann Machines Emerging From Modern Hopfield Networks","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W4383957700","doi":"https://doi.org/10.1162/neco_a_01597","pmid":"https://pubmed.ncbi.nlm.nih.gov/37432863"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01597","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01597","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","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/A5047076115","display_name":"Toshihiro Ota","orcid":"https://orcid.org/0000-0002-7303-5648"},"institutions":[{"id":"https://openalex.org/I4210089607","display_name":"CyberAgent (Japan)","ror":"https://ror.org/0060jg679","country_code":"JP","type":"company","lineage":["https://openalex.org/I4210089607"]},{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I4210136457","display_name":"Shibuya (Japan)","ror":"https://ror.org/03t1ztz45","country_code":"JP","type":"company","lineage":["https://openalex.org/I4210136457"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Toshihiro Ota","raw_affiliation_strings":["CyberAgent, Shibuya, Tokyo, 150-6121, Japan","RIKEN, Wako, Saitama, 351-0198, Japan ota_toshihiro@cyberagent.co.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CyberAgent, Shibuya, Tokyo, 150-6121, Japan","institution_ids":["https://openalex.org/I4210089607","https://openalex.org/I4210136457"]},{"raw_affiliation_string":"RIKEN, Wako, Saitama, 351-0198, Japan ota_toshihiro@cyberagent.co.jp","institution_ids":["https://openalex.org/I4210089607","https://openalex.org/I4210110652"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037944527","display_name":"Ryo Karakida","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ryo Karakida","raw_affiliation_strings":["AIST, Aomi, Tokyo, 135-0064, Japan karakida.ryo@aist.go.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AIST, Aomi, Tokyo, 135-0064, Japan karakida.ryo@aist.go.jp","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037944527","https://openalex.org/A5047076115"],"corresponding_institution_ids":["https://openalex.org/I4210089607","https://openalex.org/I4210110652","https://openalex.org/I4210136457"],"apc_list":null,"apc_paid":null,"fwci":0.4749,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59016993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"35","issue":"8","first_page":"1463","last_page":"1480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","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/T10320","display_name":"Neural Networks and Applications","score":0.9991999864578247,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9922000169754028,"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/hopfield-network","display_name":"Hopfield network","score":0.8590615391731262},{"id":"https://openalex.org/keywords/boltzmann-machine","display_name":"Boltzmann machine","score":0.767745316028595},{"id":"https://openalex.org/keywords/restricted-boltzmann-machine","display_name":"Restricted Boltzmann machine","score":0.7547063827514648},{"id":"https://openalex.org/keywords/softmax-function","display_name":"Softmax function","score":0.7285003662109375},{"id":"https://openalex.org/keywords/autoencoder","display_name":"Autoencoder","score":0.7181645035743713},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.634882926940918},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5972321629524231},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.519053041934967},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5156689882278442},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.49184346199035645},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4511682987213135},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44102734327316284},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4323245882987976},{"id":"https://openalex.org/keywords/bidirectional-associative-memory","display_name":"Bidirectional associative memory","score":0.4142149090766907},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34392082691192627},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.335606187582016},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3186110258102417},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11595150828361511},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10280176997184753}],"concepts":[{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.8590615391731262},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.767745316028595},{"id":"https://openalex.org/C199354608","wikidata":"https://www.wikidata.org/wiki/Q7316287","display_name":"Restricted Boltzmann machine","level":3,"score":0.7547063827514648},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.7285003662109375},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.7181645035743713},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.634882926940918},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5972321629524231},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.519053041934967},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5156689882278442},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.49184346199035645},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4511682987213135},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44102734327316284},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4323245882987976},{"id":"https://openalex.org/C120620853","wikidata":"https://www.wikidata.org/wiki/Q506355","display_name":"Bidirectional associative memory","level":4,"score":0.4142149090766907},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34392082691192627},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.335606187582016},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3186110258102417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11595150828361511},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10280176997184753},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_a_01597","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01597","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:37432863","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37432863","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":"Neural computation","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8999999761581421}],"awards":[{"id":"https://openalex.org/G6904737600","display_name":"\u7dda\u5f62\u6027\u3068\u975e\u7dda\u5f62\u6027\u306e\u5354\u540c\u306b\u3088\u308b\u53ef\u89e3\u306a\u30e9\u30f3\u30c0\u30e0\u795e\u7d4c\u56de\u8def\u306e\u6df1\u5316","funder_award_id":"23K16965","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W2013035813","https://openalex.org/W2112246162","https://openalex.org/W2128084896","https://openalex.org/W2136922672","https://openalex.org/W2142773971","https://openalex.org/W2337702836","https://openalex.org/W2509617460","https://openalex.org/W2559655401","https://openalex.org/W2587333550","https://openalex.org/W2612690371","https://openalex.org/W2612972698","https://openalex.org/W2902186035","https://openalex.org/W3102889924","https://openalex.org/W3103855458","https://openalex.org/W3157506437","https://openalex.org/W4307007921","https://openalex.org/W6677919164","https://openalex.org/W6678801095","https://openalex.org/W6687311570","https://openalex.org/W6715433548","https://openalex.org/W6725220630","https://openalex.org/W6739901393","https://openalex.org/W6756683548","https://openalex.org/W6781636266","https://openalex.org/W6782102740","https://openalex.org/W6795140394"],"related_works":["https://openalex.org/W1675968628","https://openalex.org/W3044458868","https://openalex.org/W2125150881","https://openalex.org/W3216432081","https://openalex.org/W2392741316","https://openalex.org/W3173236029","https://openalex.org/W2368008317","https://openalex.org/W2607300641","https://openalex.org/W4383957700","https://openalex.org/W4311250006"],"abstract_inverted_index":{"Hopfield":[0,16,33,49],"networks":[1,17,50],"and":[2,25,56,98,104,117,126,147],"Boltzmann":[3],"machines":[4],"(BMs)":[5],"are":[6],"fundamental":[7],"energy-based":[8],"neural":[9],"network":[10],"models.":[11],"Recent":[12],"studies":[13],"on":[14,31],"modern":[15,48],"have":[18],"broadened":[19],"the":[20,44,52,67,72,85,112,122,127,150],"class":[21],"of":[22,47,153],"energy":[23,54,68,145,151],"functions":[24,55,146],"led":[26],"to":[27,71,83,107,161],"a":[28,62,77,94],"unified":[29],"perspective":[30],"general":[32],"networks,":[34],"including":[35],"an":[36],"attention":[37,73],"module.":[38],"In":[39,65],"this":[40],"letter,":[41],"we":[42,81,110],"consider":[43],"BM":[45,87,125],"counterparts":[46],"using":[51],"associated":[53],"study":[57],"their":[58],"salient":[59],"properties":[60],"from":[61,134],"trainability":[63],"perspective.":[64],"particular,":[66],"function":[69,97,152],"corresponding":[70],"module":[74],"naturally":[75],"introduces":[76],"novel":[78],"BM,":[79],"which":[80],"refer":[82],"as":[84],"attentional":[86],"(AttnBM).":[88],"We":[89,138],"verify":[90],"that":[91,149],"AttnBM":[92,116],"has":[93],"tractable":[95],"likelihood":[96],"gradient":[99],"for":[100],"certain":[101],"special":[102],"cases":[103],"is":[105],"easy":[106],"train.":[108],"Moreover,":[109],"reveal":[111],"hidden":[113],"connections":[114],"between":[115],"some":[118],"single-layer":[119],"models,":[120],"namely":[121],"gaussian-Bernoulli":[123],"restricted":[124],"denoising":[128,135],"autoencoder":[129],"with":[130],"softmax":[131],"units":[132],"coming":[133],"score":[136],"matching.":[137],"also":[139],"investigate":[140],"BMs":[141,159],"introduced":[142],"by":[143],"other":[144],"show":[148],"dense":[154],"associative":[155],"memory":[156],"models":[157],"gives":[158],"belonging":[160],"exponential":[162],"family":[163],"harmoniums.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
