{"id":"https://openalex.org/W7214806221","doi":"https://doi.org/10.48550/arxiv.2609.33087","title":"Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Design","display_name":"Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Design","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214806221","doi":"https://doi.org/10.48550/arxiv.2609.33087"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33087","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33087","pdf_url":"https://arxiv.org/pdf/2609.33087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.33087","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153414720","display_name":"Henry Pritchard","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pritchard, Henry","raw_affiliation_strings":["Computer Engineering , University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Engineering , University of California , San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039057672","display_name":"Rahul Parhi","orcid":"https://orcid.org/0000-0002-1971-7699","observed_orcids":["https://orcid.org/0000-0002-1971-7699"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Parhi, Rahul","raw_affiliation_strings":["Computer Engineering , University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Engineering , University of California , San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9740999937057495,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9740999937057495,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.010200000368058681,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.00570000009611249,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/plug-and-play-methods","display_name":"plug-and-play methods","score":0.9129999876022339},{"id":"https://openalex.org/keywords/convergence-guarantees","display_name":"convergence guarantees","score":0.7670000195503235},{"id":"https://openalex.org/keywords/proximal-operator","display_name":"proximal operator","score":0.8510000109672546},{"id":"https://openalex.org/keywords/activation-functions","display_name":"activation functions","score":0.6340000033378601},{"id":"https://openalex.org/keywords/image-reconstruction","display_name":"image reconstruction","score":0.49300000071525574}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7583000063896179},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6699000000953674},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6179999709129333},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6029999852180481},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.579200029373169},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5662999749183655},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49129998683929443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4887999892234802},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44269999861717224},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44209998846054077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37880000472068787},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2888000011444092},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2766999900341034},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C193415008","wikidata":"https://www.wikidata.org/wiki/Q639681","display_name":"Network architecture","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.25850000977516174},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33087","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33087","pdf_url":"https://arxiv.org/pdf/2609.33087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2609.33087","doi":"https://doi.org/10.48550/arxiv.2609.33087","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33087","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.33087","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33087","pdf_url":"https://arxiv.org/pdf/2609.33087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214806221.pdf","grobid_xml":"https://content.openalex.org/works/W7214806221.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2626376214","https://openalex.org/W2754296883","https://openalex.org/W3202187012","https://openalex.org/W4249513058","https://openalex.org/W4384263560","https://openalex.org/W4393435350","https://openalex.org/W7127432832","https://openalex.org/W7202172764"],"related_works":["https://openalex.org/W2945291039","https://openalex.org/W4225499846","https://openalex.org/W3159379662","https://openalex.org/W3138006921","https://openalex.org/W3197693870","https://openalex.org/W4319044279","https://openalex.org/W4387878454","https://openalex.org/W4387447990","https://openalex.org/W7124464191","https://openalex.org/W3095914024"],"abstract_inverted_index":{"Plug-and-Play":[0],"(PnP)":[1],"methods":[2],"replace":[3],"proximal":[4,23,43,103,123],"operators":[5],"with":[6,84],"learned":[7,78],"denoisers,":[8],"which":[9],"produce":[10],"state-of-the-art":[11],"reconstruction":[12],"quality,":[13],"but":[14],"sacrifice":[15],"the":[16,34,42,53,60,77,82,85,97,102,109,121],"variational":[17],"interpretation":[18],"and":[19,58,93,114],"convergence":[20],"guarantees":[21],"of":[22,45,56,66],"methods.":[24],"Learned":[25],"Proximal":[26],"Networks":[27],"(LPNs)":[28],"address":[29],"this":[30,49],"problem":[31],"by":[32,101,112],"designing":[33],"denoiser":[35],"architecture":[36],"so":[37],"that":[38],"it":[39],"is":[40],"exactly":[41],"operator":[44],"a":[46,63,87,116],"regularizer.":[47],"In":[48,105],"work,":[50],"we":[51,107],"clarify":[52],"theoretical":[54],"foundations":[55],"LPNs":[57],"extend":[59],"framework":[61],"to":[62],"broader":[64],"class":[65],"activation":[67],"functions.":[68],"We":[69],"then":[70],"study":[71],"two":[72],"practical":[73],"mechanisms":[74],"for":[75,119],"controlling":[76],"prior:":[79],"(i)":[80],"averaging":[81,113],"LPN":[83],"identity,":[86],"common":[88],"heuristic":[89],"in":[90],"PnP":[91],"methods,":[92],"(ii)":[94],"directly":[95],"scaling":[96],"implicit":[98],"regularizer":[99,110],"induced":[100,111],"operator.":[104,124],"particular,":[106],"characterize":[108],"develop":[115],"convergent":[117],"method":[118],"evaluating":[120],"scaled":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
