{"id":"https://openalex.org/W4400411159","doi":"https://doi.org/10.1109/tac.2024.3424628","title":"A Uniform Framework of Yau\u2013Yau Algorithm Based on Deep Learning With the Capability of Overcoming the Curse of Dimensionality","display_name":"A Uniform Framework of Yau\u2013Yau Algorithm Based on Deep Learning With the Capability of Overcoming the Curse of Dimensionality","publication_year":2024,"publication_date":"2024-07-08","ids":{"openalex":"https://openalex.org/W4400411159","doi":"https://doi.org/10.1109/tac.2024.3424628"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2024.3424628","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3424628","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","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/A5061898071","display_name":"Xiuqiong Chen","orcid":"https://orcid.org/0000-0003-3844-7177"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiuqiong Chen","raw_affiliation_strings":["School of Mathematics, Renmin University of China, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008394333","display_name":"Zeju Sun","orcid":"https://orcid.org/0009-0008-9348-1988"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeju Sun","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048234832","display_name":"Yangtianze Tao","orcid":"https://orcid.org/0000-0002-3775-6712"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yangtianze Tao","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019752361","display_name":"Stephen S.\u2010T. Yau","orcid":"https://orcid.org/0000-0001-7634-7981"},"institutions":[{"id":"https://openalex.org/I4403928416","display_name":"Beijing Institute of Mathematical Sciences and Applications","ror":"https://ror.org/05t6hvr95","country_code":null,"type":"education","lineage":["https://openalex.org/I4403928416","https://openalex.org/I99065089"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Stephen S.-T. Yau","raw_affiliation_strings":["Beijing Institute of Mathematical Sciences and Applications, Beijing, China","Department of Mathematical Sciences, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beijing Institute of Mathematical Sciences and Applications, Beijing, China","institution_ids":["https://openalex.org/I4403928416"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061898071"],"corresponding_institution_ids":["https://openalex.org/I78988378"],"apc_list":null,"apc_paid":null,"fwci":0.6457,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6777032,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"70","issue":"1","first_page":"339","last_page":"354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13717","display_name":"Advanced Algorithms and Applications","score":0.3264000117778778,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T13717","display_name":"Advanced Algorithms and Applications","score":0.3264000117778778,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10320","display_name":"Neural Networks and Applications","score":0.29089999198913574,"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/T10057","display_name":"Face and Expression Recognition","score":0.2712000012397766,"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/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.8932814598083496},{"id":"https://openalex.org/keywords/curse","display_name":"Curse","score":0.7099838256835938},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48773226141929626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45966872572898865},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44507795572280884},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.41770702600479126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35144102573394775},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07977443933486938},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.07193189859390259}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.8932814598083496},{"id":"https://openalex.org/C2780273121","wikidata":"https://www.wikidata.org/wiki/Q109411","display_name":"Curse","level":2,"score":0.7099838256835938},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48773226141929626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45966872572898865},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44507795572280884},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41770702600479126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35144102573394775},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07977443933486938},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.07193189859390259},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2024.3424628","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3424628","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1799712014","display_name":null,"funder_award_id":"12201631","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G960385224","display_name":null,"funder_award_id":"123B2020","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":36,"referenced_works":["https://openalex.org/W226131373","https://openalex.org/W1540262613","https://openalex.org/W1573874356","https://openalex.org/W1604264128","https://openalex.org/W1964846093","https://openalex.org/W1976787988","https://openalex.org/W1986892149","https://openalex.org/W2003318329","https://openalex.org/W2007046555","https://openalex.org/W2009104157","https://openalex.org/W2018028661","https://openalex.org/W2041380796","https://openalex.org/W2080273507","https://openalex.org/W2083402998","https://openalex.org/W2098422935","https://openalex.org/W2098613108","https://openalex.org/W2101764833","https://openalex.org/W2121990344","https://openalex.org/W2123487311","https://openalex.org/W2125188192","https://openalex.org/W2137345842","https://openalex.org/W2141394518","https://openalex.org/W2145317976","https://openalex.org/W2157098139","https://openalex.org/W2162733643","https://openalex.org/W2264432461","https://openalex.org/W2321824591","https://openalex.org/W2748456849","https://openalex.org/W2803629276","https://openalex.org/W2959389853","https://openalex.org/W2965485141","https://openalex.org/W3036151507","https://openalex.org/W6677422266","https://openalex.org/W6680173660","https://openalex.org/W6796070361","https://openalex.org/W6838298536"],"related_works":["https://openalex.org/W4386146136","https://openalex.org/W1561349031","https://openalex.org/W4251206704","https://openalex.org/W3206079743","https://openalex.org/W2039478586","https://openalex.org/W2528559906","https://openalex.org/W2561617217","https://openalex.org/W3088621770","https://openalex.org/W408992594","https://openalex.org/W2115449043"],"abstract_inverted_index":{"In":[0,45],"numerous":[1],"application":[2],"areas,":[3],"high-dimensional":[4,133],"nonlinear":[5,67],"filtering":[6],"is":[7,42,126],"still":[8,43],"a":[9,36,60],"challenging":[10],"problem.":[11],"The":[12],"introduction":[13],"of":[14,24,39,53,85,117],"deep":[15],"learning":[16],"and":[17,27,58,63,75],"neural":[18,55,87],"networks":[19,56],"has":[20,110],"improved":[21],"the":[22,50,72,83,86,104,111,115],"efficiency":[23],"classical":[25,130],"algorithms":[26,131],"they":[28],"perform":[29],"well":[30],"in":[31,90],"many":[32],"practical":[33],"tasks.":[34],"However,":[35],"theoretical":[37],"interpretation":[38],"their":[40],"feasibility":[41],"lacking.":[44],"this":[46,91],"article,":[47],"we":[48],"exploit":[49],"representational":[51],"ability":[52,112],"recurrent":[54],"(RNNs)":[57],"provide":[59],"computationally":[61],"efficient":[62],"optimal":[64],"framework":[65],"for":[66,132],"filter":[68],"design":[69],"based":[70,107],"on":[71,108],"Yau\u2013Yau":[73,105],"algorithm":[74,92,106],"RNNs.":[76],"Theoretically,":[77],"it":[78],"can":[79],"be":[80],"proved":[81],"that":[82,103,123],"size":[84],"network":[88],"required":[89],"increases":[93],"only":[94],"polynomially":[95],"rather":[96],"than":[97,129],"exponentially":[98],"with":[99],"dimension,":[100],"which":[101],"implies":[102],"RNNs":[109],"to":[113],"overcome":[114],"curse":[116],"dimensionality.":[118],"Numerical":[119],"results":[120],"also":[121],"show":[122],"our":[124],"method":[125],"more":[127],"competitive":[128],"problems.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
