{"id":"https://openalex.org/W3197566623","doi":"https://doi.org/10.1109/tnnls.2022.3185375","title":"Neural Network Gaussian Processes by Increasing Depth","display_name":"Neural Network Gaussian Processes by Increasing Depth","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W3197566623","doi":"https://doi.org/10.1109/tnnls.2022.3185375","mag":"3197566623","pmid":"https://pubmed.ncbi.nlm.nih.gov/35786562"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2022.3185375","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3185375","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/A5073419905","display_name":"Shao-Qun Zhang","orcid":"https://orcid.org/0000-0002-0614-8984"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shao-Qun Zhang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100455768","display_name":"Fei Wang","orcid":"https://orcid.org/0000-0001-9459-9461"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fei Wang","raw_affiliation_strings":["Department of Population Health Sciences, Weill Cornell Medicine, Cornell University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Population Health Sciences, Weill Cornell Medicine, Cornell University, New York, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018677035","display_name":"Fenglei Fan","orcid":"https://orcid.org/0000-0003-3691-5141"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feng-Lei Fan","raw_affiliation_strings":["Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073419905"],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":null,"apc_paid":null,"fwci":1.1034,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80489183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"35","issue":"2","first_page":"2881","last_page":"2886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9995999932289124,"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/T10977","display_name":"Optical Imaging and Spectroscopy Techniques","score":0.963100016117096,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9592999815940857,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.7202016711235046},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6965824961662292},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6939760446548462},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.6579879522323608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5802006125450134},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5484495759010315},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.542829692363739},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5393277406692505},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.5091890692710876},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.47306978702545166},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.4309088885784149},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4217897653579712},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.41054049134254456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4102988839149475},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38120606541633606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.324659526348114},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.13110148906707764},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11429193615913391}],"concepts":[{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.7202016711235046},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6965824961662292},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6939760446548462},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.6579879522323608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5802006125450134},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5484495759010315},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.542829692363739},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5393277406692505},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.5091890692710876},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.47306978702545166},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.4309088885784149},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4217897653579712},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.41054049134254456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4102988839149475},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38120606541633606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.324659526348114},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.13110148906707764},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11429193615913391},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2022.3185375","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3185375","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:35786562","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35786562","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W579617791","https://openalex.org/W1460189015","https://openalex.org/W1482196458","https://openalex.org/W1487444668","https://openalex.org/W1523471994","https://openalex.org/W1537220347","https://openalex.org/W1544131626","https://openalex.org/W1647616909","https://openalex.org/W2056099894","https://openalex.org/W2076066837","https://openalex.org/W2137983211","https://openalex.org/W2167608136","https://openalex.org/W2507039649","https://openalex.org/W2802739963","https://openalex.org/W2811199191","https://openalex.org/W2910655610","https://openalex.org/W2963097630","https://openalex.org/W2963323437","https://openalex.org/W2964052793","https://openalex.org/W2970889419","https://openalex.org/W2995072672","https://openalex.org/W3034979923","https://openalex.org/W3037003270","https://openalex.org/W3037333676","https://openalex.org/W3087545942","https://openalex.org/W3092342941","https://openalex.org/W3098291775","https://openalex.org/W3106295246","https://openalex.org/W3121758917","https://openalex.org/W3131795773","https://openalex.org/W3146803896","https://openalex.org/W3169353662","https://openalex.org/W3213093647","https://openalex.org/W3213816148","https://openalex.org/W4301621763","https://openalex.org/W6684918892","https://openalex.org/W6743923790","https://openalex.org/W6745256532","https://openalex.org/W6753275298","https://openalex.org/W6758352740","https://openalex.org/W6767295766","https://openalex.org/W6768529065","https://openalex.org/W6774449618","https://openalex.org/W6780105080","https://openalex.org/W6783283440","https://openalex.org/W6784287845","https://openalex.org/W6785630404","https://openalex.org/W6790773018","https://openalex.org/W6803560560"],"related_works":["https://openalex.org/W1992356684","https://openalex.org/W4211052589","https://openalex.org/W4230188731","https://openalex.org/W2101272603","https://openalex.org/W2963637926","https://openalex.org/W2036620345","https://openalex.org/W4388336565","https://openalex.org/W2178986460","https://openalex.org/W4200022986","https://openalex.org/W1977123013"],"abstract_inverted_index":{"Recent":[0],"years":[1],"have":[2],"witnessed":[3],"an":[4],"increasing":[5,47,92],"interest":[6],"in":[7,50],"the":[8,18,23,31,37,51,73,93,113,120,127,141,145,158,166,174,177],"correspondence":[9],"between":[10],"infinitely":[11],"wide":[12],"networks":[13],"and":[14,20,116,140],"Gaussian":[15,27,40,105,129,146,161,179],"processes.":[16],"Despite":[17],"effectiveness":[19],"elegance":[21],"of":[22,33,53,75,95,123,144,157,176],"current":[24],"neural":[25,38,62,97],"network":[26,39,63,88,98],"process":[28,130,147,162,180],"theory,":[29],"to":[30,89,103,112,118],"best":[32],"our":[34,155],"knowledge,":[35],"all":[36],"processes":[41],"(NNGPs)":[42],"are":[43],"essentially":[44],"induced":[45],"by":[46,79,131,181],"width.":[48],"However,":[49],"era":[52],"deep":[54,124],"learning,":[55],"what":[56],"concerns":[57],"us":[58],"more":[59],"regarding":[60],"a":[61,76,80,86,96,104,109],"is":[64,108],"its":[65,136],"depth":[66,71,94],"as":[67,69],"well":[68],"how":[70],"impacts":[72],"behaviors":[74],"network.":[77],"Inspired":[78],"width-depth":[81],"symmetry":[82],"consideration,":[83],"we":[84,133,172],"use":[85],"shortcut":[87],"show":[90],"that":[91],"can":[99,151],"also":[100,164],"give":[101],"rise":[102],"process,":[106],"which":[107],"valuable":[110],"addition":[111],"existing":[114],"theory":[115],"contributes":[117],"revealing":[119],"true":[121],"picture":[122],"learning.":[125],"Beyond":[126],"proposed":[128,159,178],"depth,":[132],"theoretically":[134],"characterize":[135],"uniform":[137],"tightness":[138],"property":[139],"smallest":[142],"eigenvalue":[143],"kernel.":[148],"These":[149],"characterizations":[150],"not":[152],"only":[153],"enhance":[154],"understanding":[156],"depth-induced":[160],"but":[163],"pave":[165],"way":[167],"for":[168],"future":[169],"applications.":[170],"Lastly,":[171],"examine":[173],"performance":[175],"regression":[182],"experiments":[183],"on":[184],"two":[185],"benchmark":[186],"datasets.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}