{"id":"https://openalex.org/W4288064556","doi":"https://doi.org/10.1109/tai.2022.3194132","title":"Residual Tensor Train: A Quantum-Inspired Approach for Learning Multiple Multilinear Correlations","display_name":"Residual Tensor Train: A Quantum-Inspired Approach for Learning Multiple Multilinear Correlations","publication_year":2022,"publication_date":"2022-07-27","ids":{"openalex":"https://openalex.org/W4288064556","doi":"https://doi.org/10.1109/tai.2022.3194132"},"language":"en","primary_location":{"id":"doi:10.1109/tai.2022.3194132","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tai.2022.3194132","pdf_url":null,"source":{"id":"https://openalex.org/S4210169448","display_name":"IEEE Transactions on Artificial Intelligence","issn_l":"2691-4581","issn":["2691-4581"],"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 Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2108.08659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100432872","display_name":"Yiwei Chen","orcid":"https://orcid.org/0000-0001-5739-2429"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yiwei Chen","raw_affiliation_strings":["Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-5739-2429","affiliations":[{"raw_affiliation_string":"Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102769004","display_name":"Yu Pan","orcid":"https://orcid.org/0000-0001-6900-4016"},"institutions":[{"id":"https://openalex.org/I4391767838","display_name":"State Key Laboratory of Industrial Control Technology","ror":"https://ror.org/03a33a786","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767838","https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Pan","raw_affiliation_strings":["State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-6900-4016","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I4391767838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000582423","display_name":"Daoyi Dong","orcid":"https://orcid.org/0000-0002-7425-3559"},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]},{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Daoyi Dong","raw_affiliation_strings":["School of Engineering and Information Technology, University of New South Wales, Canberra, Australia"],"raw_orcid":"https://orcid.org/0000-0002-7425-3559","affiliations":[{"raw_affiliation_string":"School of Engineering and Information Technology, University of New South Wales, Canberra, Australia","institution_ids":["https://openalex.org/I188329596","https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100432872"],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":1.3662,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79376499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":"5","first_page":"1101","last_page":"1113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.8809256553649902},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.7446251511573792},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7445393800735474},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6198052763938904},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.609904944896698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5599387288093567},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5303044319152832},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5206941366195679},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.5124066472053528},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4578991234302521},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4296434223651886},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4156220555305481},{"id":"https://openalex.org/keywords/decision-boundary","display_name":"Decision boundary","score":0.4154895544052124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4073539078235626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33498895168304443},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3218728303909302},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.3162556290626526},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.19220700860023499},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.11608362197875977},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11452817916870117}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.8809256553649902},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.7446251511573792},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7445393800735474},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6198052763938904},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.609904944896698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5599387288093567},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5303044319152832},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5206941366195679},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.5124066472053528},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4578991234302521},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4296434223651886},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4156220555305481},{"id":"https://openalex.org/C42023084","wikidata":"https://www.wikidata.org/wiki/Q5249231","display_name":"Decision boundary","level":3,"score":0.4154895544052124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4073539078235626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33498895168304443},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3218728303909302},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3162556290626526},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.19220700860023499},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.11608362197875977},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11452817916870117},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tai.2022.3194132","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tai.2022.3194132","pdf_url":null,"source":{"id":"https://openalex.org/S4210169448","display_name":"IEEE Transactions on Artificial Intelligence","issn_l":"2691-4581","issn":["2691-4581"],"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 Artificial Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2108.08659","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.08659","pdf_url":"https://arxiv.org/pdf/2108.08659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:2108.08659","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.08659","pdf_url":"https://arxiv.org/pdf/2108.08659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[{"score":0.7300000190734863,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G6868492047","display_name":null,"funder_award_id":"62173296","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G994192881","display_name":null,"funder_award_id":"61703364","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W1522301498","https://openalex.org/W1836465849","https://openalex.org/W1964357740","https://openalex.org/W2002485180","https://openalex.org/W2029469881","https://openalex.org/W2081855772","https://openalex.org/W2103537693","https://openalex.org/W2104657103","https://openalex.org/W2125930537","https://openalex.org/W2127426251","https://openalex.org/W2141200867","https://openalex.org/W2147800946","https://openalex.org/W2160068178","https://openalex.org/W2160416736","https://openalex.org/W2167453047","https://openalex.org/W2170653751","https://openalex.org/W2194775991","https://openalex.org/W2291880741","https://openalex.org/W2293506269","https://openalex.org/W2302255633","https://openalex.org/W2311523351","https://openalex.org/W2378988337","https://openalex.org/W2470457291","https://openalex.org/W2492294785","https://openalex.org/W2541674938","https://openalex.org/W2551156993","https://openalex.org/W2590822257","https://openalex.org/W2750384547","https://openalex.org/W2753545915","https://openalex.org/W2766980496","https://openalex.org/W2794602324","https://openalex.org/W2808455355","https://openalex.org/W2919115771","https://openalex.org/W2940740645","https://openalex.org/W2951542569","https://openalex.org/W2952505042","https://openalex.org/W2963066927","https://openalex.org/W2963407932","https://openalex.org/W2963521811","https://openalex.org/W2981694290","https://openalex.org/W2997011911","https://openalex.org/W3006217815","https://openalex.org/W3081468433","https://openalex.org/W3100492273","https://openalex.org/W3100993774","https://openalex.org/W3103289362","https://openalex.org/W3103841689","https://openalex.org/W4242841269","https://openalex.org/W4286908223","https://openalex.org/W4295151193","https://openalex.org/W4295312788","https://openalex.org/W4388317959","https://openalex.org/W6631190155","https://openalex.org/W6638667902","https://openalex.org/W6678818196","https://openalex.org/W6678846912","https://openalex.org/W6696852441","https://openalex.org/W6698183232","https://openalex.org/W6713960836","https://openalex.org/W6720612731","https://openalex.org/W6729059855","https://openalex.org/W6729942461","https://openalex.org/W6730172645","https://openalex.org/W6743676628","https://openalex.org/W6743688258","https://openalex.org/W6745820876","https://openalex.org/W6752310137","https://openalex.org/W6764213378","https://openalex.org/W6766978945","https://openalex.org/W6802888284"],"related_works":["https://openalex.org/W2950475743","https://openalex.org/W4386603768","https://openalex.org/W2886711096","https://openalex.org/W2987302549","https://openalex.org/W2999408031","https://openalex.org/W2952270521","https://openalex.org/W1934446750","https://openalex.org/W2297581032","https://openalex.org/W4384296820","https://openalex.org/W4308235762"],"abstract_inverted_index":{"States":[0],"of":[1,55,104,118,137],"quantum":[2],"many-body":[3],"systems":[4],"are":[5,198],"defined":[6],"in":[7,75,156],"a":[8,40,63,71,76,122,129],"high-dimensional":[9,77],"Hilbert":[10],"space,":[11],"where":[12],"rich":[13],"and":[14,82,94,150,171,178],"complex":[15,25,202],"interactions":[16],"among":[17],"subsystems":[18],"can":[19,98,145],"be":[20,99],"modeled.":[21],"In":[22,35,85],"machine":[23],"learning,":[24],"multiple":[26,52],"multilinear":[27,42,53],"correlations":[28,54],"may":[29],"also":[30],"exist":[31],"within":[32,62],"input":[33],"features.":[34],"this":[36],"article,":[37],"we":[38,87,107],"present":[39],"quantum-inspired":[41],"model,":[43],"named":[44],"residual":[45],"tensor":[46,138,169],"train":[47,139],"(ResTT),":[48],"to":[49,59,69,200],"capture":[50],"the":[51,90,95,109,116,148,157,167],"features,":[56],"from":[57],"low":[58],"high":[60],"orders,":[61],"single":[64],"model.":[65],"ResTT":[66,119,144,165,182],"is":[67,131],"able":[68],"build":[70],"robust":[72],"decision":[73],"boundary":[74],"space":[78],"for":[79,111],"solving":[80],"fitting":[81],"classification":[83],"tasks.":[84],"particular,":[86],"prove":[88,126],"that":[89,114,127,136,143,154,164],"fully":[91],"connected":[92],"layer":[93],"Volterra":[96],"series":[97],"taken":[100],"as":[101],"special":[102],"cases":[103],"ResTT.":[105],"Furthermore,":[106],"derive":[108],"rule":[110,130],"weight":[112],"initialization":[113],"stabilizes":[115],"training":[117],"based":[120],"on":[121,176,190],"mean-field":[123],"analysis.":[124],"We":[125],"such":[128],"much":[132],"more":[133],"relaxed":[134],"than":[135,186],"(TT),":[140],"which":[141,197],"means":[142],"easily":[146],"address":[147],"vanishing":[149],"exploding":[151],"gradient":[152],"problem":[153],"exists":[155],"existing":[158],"TT":[159],"models.":[160],"Numerical":[161],"experiments":[162],"demonstrate":[163],"outperforms":[166],"state-of-the-art":[168],"network":[170],"benchmark":[172],"deep":[173],"learning":[174],"models":[175],"MNIST":[177],"Fashion-MNIST":[179],"datasets.":[180],"Moreover,":[181],"achieves":[183],"better":[184],"performance":[185],"other":[187],"statistical":[188],"methods":[189],"two":[191],"practical":[192],"examples":[193],"with":[194],"limited":[195],"data,":[196],"known":[199],"have":[201],"feature":[203],"interactions.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2022-07-28T00:00:00"}
