{"id":"https://openalex.org/W7103135323","doi":"https://doi.org/10.48550/arxiv.2510.26704","title":"How Regularization Terms Make Invertible Neural Networks Bayesian Point Estimators","display_name":"How Regularization Terms Make Invertible Neural Networks Bayesian Point Estimators","publication_year":2025,"publication_date":"2025-10-30","ids":{"openalex":"https://openalex.org/W7103135323","doi":"https://doi.org/10.48550/arxiv.2510.26704"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2510.26704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.26704","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2510.26704","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Heilenk\u00f6tter, Nick","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Heilenk\u00f6tter, Nick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":true,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.2379000037908554,"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":0.2379000037908554,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.12139999866485596,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.10409999638795853,"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/invertible-matrix","display_name":"Invertible matrix","score":0.7208999991416931},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.671500027179718},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5870000123977661},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5774999856948853},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5745000243186951},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5716999769210815},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4893999993801117},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.45089998841285706}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7208999991416931},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.671500027179718},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5870000123977661},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5745000243186951},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5716999769210815},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4893999993801117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4812000095844269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47269999980926514},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.45089998841285706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41260001063346863},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4097999930381775},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34200000762939453},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.3312999904155731},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.323199987411499},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3005000054836273},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C68022304","wikidata":"https://www.wikidata.org/wiki/Q842217","display_name":"Bayes estimator","level":3,"score":0.26989999413490295},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2510.26704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.26704","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2510.26704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.26704","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Can":[0],"regularization":[1,68],"terms":[2,69],"in":[3,16,134],"the":[4,46,71,78,88,94,97,100,112],"training":[5,73],"of":[6,77,82],"invertible":[7,36],"neural":[8,37],"networks":[9,19,38],"lead":[10],"to":[11,26,93],"known":[12],"Bayesian":[13,54,84],"point":[14,85],"estimators":[15],"reconstruction?":[17],"Invertible":[18],"are":[20],"attractive":[21],"for":[22,35,70],"inverse":[23,118],"problems":[24],"due":[25],"their":[27],"inherent":[28],"stability":[29],"and":[30,65,116,126,137],"interpretability.":[31],"Recently,":[32],"optimization":[33],"strategies":[34],"that":[39],"approximate":[40],"either":[41],"a":[42,53,135],"reconstruction":[43,119],"map":[44],"or":[45],"forward":[47,114],"operator":[48,115],"have":[49],"been":[50],"studied":[51],"from":[52],"perspective,":[55],"but":[56],"each":[57,108],"has":[58],"limitations.":[59],"To":[60],"address":[61],"this,":[62],"we":[63],"introduce":[64,132],"analyze":[66],"two":[67],"network":[72],"that,":[74],"upon":[75],"inversion":[76],"network,":[79],"recover":[80],"properties":[81],"classical":[83],"estimators:":[86],"while":[87],"first":[89],"can":[90],"be":[91],"connected":[92],"posterior":[95],"mean,":[96],"second":[98],"resembles":[99],"MAP":[101],"estimator.":[102],"Our":[103],"theoretical":[104],"analysis":[105],"characterizes":[106],"how":[107,128],"loss":[109],"shapes":[110],"both":[111],"learned":[113],"its":[117],"map.":[120],"Numerical":[121],"experiments":[122],"support":[123],"our":[124],"findings":[125],"demonstrate":[127],"these":[129],"loss-term":[130],"regularizers":[131],"data-dependence":[133],"stable":[136],"interpretable":[138],"way.":[139]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-11-01T00:00:00"}