{"id":"https://openalex.org/W4405209743","doi":"https://doi.org/10.1137/24m1636617","title":"Early Stopping of Untrained Convolutional Neural Networks","display_name":"Early Stopping of Untrained Convolutional Neural Networks","publication_year":2024,"publication_date":"2024-12-10","ids":{"openalex":"https://openalex.org/W4405209743","doi":"https://doi.org/10.1137/24m1636617"},"language":"en","primary_location":{"id":"doi:10.1137/24m1636617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1636617","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","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/A5022550099","display_name":"Tim Jahn","orcid":"https://orcid.org/0000-0002-7633-8265"},"institutions":[{"id":"https://openalex.org/I2800345347","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800345347"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tim Jahn","raw_affiliation_strings":["Institut f\u00fcr Mathematik, TU Berlin, Berlin, 10623 Germany"],"raw_orcid":"https://orcid.org/0000-0002-7633-8265","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, TU Berlin, Berlin, 10623 Germany","institution_ids":["https://openalex.org/I2800345347","https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039605463","display_name":"Bangti Jin","orcid":"https://orcid.org/0000-0002-3775-9155"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Bangti Jin","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China"],"raw_orcid":"https://orcid.org/0000-0002-3775-9155","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9891,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86636378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"17","issue":"4","first_page":"2331","last_page":"2361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9969000220298767,"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":0.9944000244140625,"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/convolutional-neural-network","display_name":"Convolutional neural network","score":0.701571524143219},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5817582011222839},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.473550945520401},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3542836308479309}],"concepts":[{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.701571524143219},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5817582011222839},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.473550945520401},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3542836308479309}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1636617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1636617","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1521016025","display_name":"EXC 2047: Hausdorff Center for Mathematics (HCM)","funder_award_id":"390685813","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7725451807","display_name":"EXC 2046: MATH+: Berlin Mathematics Research Center","funder_award_id":"390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W354722939","https://openalex.org/W1564864701","https://openalex.org/W1570089119","https://openalex.org/W2014963263","https://openalex.org/W2024829682","https://openalex.org/W2904608878","https://openalex.org/W2906587342","https://openalex.org/W3002289736","https://openalex.org/W3011771465","https://openalex.org/W3040793855","https://openalex.org/W3101558399","https://openalex.org/W3163954017","https://openalex.org/W4296001753","https://openalex.org/W4313316206","https://openalex.org/W4313526320","https://openalex.org/W4323660577","https://openalex.org/W4399321906","https://openalex.org/W4400839799"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2033914206","https://openalex.org/W2042327336"],"abstract_inverted_index":{"Abstract.":[0],"In":[1,46],"recent":[2],"years,":[3],"new":[4],"regularization":[5,90],"methods":[6,40],"based":[7],"on":[8,97],"(deep)":[9],"neural":[10,37,63,73,102,113,144],"networks":[11,64,74,145],"have":[12],"shown":[13],"very":[14],"promising":[15],"empirical":[16],"performance":[17],"for":[18,78,120,137],"the":[19,34,52,93,98,101,107,111,121,124,129,168],"numerical":[20],"solution":[21],"of":[22,36,54,92,100,110,123,140],"ill-posed":[23,70],"problems,":[24],"e.g.,":[25],"in":[26],"medical":[27],"imaging":[28,30],"and":[29,150],"science.":[31],"Due":[32,105],"to":[33,65,68,106,166],"nonlinearity":[35],"networks,":[38],"these":[39],"often":[41],"lack":[42],"satisfactory":[43],"theoretical":[44,169],"justification.":[45],"this":[47],"work,":[48],"we":[49],"rigorously":[50],"discuss":[51],"convergence":[53,159],"a":[55],"successful":[56],"unsupervised":[57],"approach":[58,94],"that":[59,128],"utilizes":[60],"untrained":[61,142],"convolutional":[62,143],"represent":[66],"solutions":[67],"linear":[69],"problems.":[71],"Untrained":[72],"are":[75,163],"particularly":[76],"appealing":[77],"many":[79],"applications":[80],"because":[81],"they":[82],"do":[83],"not":[84],"require":[85],"paired":[86],"training":[87],"data.":[88],"The":[89],"property":[91],"relies":[95],"solely":[96],"architecture":[99],"network":[103],"instead.":[104],"vast":[108],"overparameterization":[109],"employed":[112],"network,":[114],"suitable":[115],"early":[116,138],"stopping":[117,139],"is":[118,133],"essential":[119],"success":[122],"method.":[125],"We":[126],"establish":[127],"classical":[130],"discrepancy":[131],"principle":[132],"an":[134,154],"adequate":[135],"method":[136],"two-layer":[141],"learned":[146],"by":[147],"gradient":[148],"descent,":[149],"furthermore,":[151],"it":[152],"yields":[153],"approximation":[155],"with":[156],"minimax":[157],"optimal":[158],"rates.":[160],"Numerical":[161],"results":[162],"also":[164],"presented":[165],"illustrate":[167],"findings.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}