{"id":"https://openalex.org/W7131435386","doi":"https://doi.org/10.48550/arxiv.2602.19964","title":"On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference","display_name":"On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference","publication_year":2026,"publication_date":"2026-02-23","ids":{"openalex":"https://openalex.org/W7131435386","doi":"https://doi.org/10.48550/arxiv.2602.19964"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.19964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19964","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,"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.2602.19964","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070632989","display_name":"Moritz A. Zanger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zanger, Moritz A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126740854","display_name":"Yijun Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Yijun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037802170","display_name":"Pascal Van Der Vaart","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Van der Vaart, Pascal R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033832179","display_name":"Wendelin B\u00f6hmer","orcid":"https://orcid.org/0000-0002-4398-6792"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B\u00f6hmer, Wendelin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Spaan, Matthijs T. J.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Spaan, Matthijs T. J.","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":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.7849000096321106,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.7849000096321106,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.05900000035762787,"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":0.030400000512599945,"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/posterior-probability","display_name":"Posterior probability","score":0.5526000261306763},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5128999948501587},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4778999984264374},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.43290001153945923},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.41339999437332153},{"id":"https://openalex.org/keywords/predictive-inference","display_name":"Predictive inference","score":0.4050000011920929},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.36890000104904175},{"id":"https://openalex.org/keywords/fiducial-inference","display_name":"Fiducial inference","score":0.36559998989105225},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.35199999809265137}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6039999723434448},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.5526000261306763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5281000137329102},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5084999799728394},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4778999984264374},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.41339999437332153},{"id":"https://openalex.org/C917703","wikidata":"https://www.wikidata.org/wiki/Q7239668","display_name":"Predictive inference","level":5,"score":0.4050000011920929},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C95167961","wikidata":"https://www.wikidata.org/wiki/Q4483495","display_name":"Fiducial inference","level":5,"score":0.36559998989105225},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.35199999809265137},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3384999930858612},{"id":"https://openalex.org/C101112237","wikidata":"https://www.wikidata.org/wiki/Q4874481","display_name":"Bayesian statistics","level":4,"score":0.33219999074935913},{"id":"https://openalex.org/C71983512","wikidata":"https://www.wikidata.org/wiki/Q7915687","display_name":"Variable-order Bayesian network","level":4,"score":0.3163999915122986},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.30970001220703125},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C37903108","wikidata":"https://www.wikidata.org/wiki/Q4874474","display_name":"Bayesian linear regression","level":4,"score":0.2888000011444092},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C99173435","wikidata":"https://www.wikidata.org/wiki/Q4874469","display_name":"Bayesian experimental design","level":5,"score":0.2840000092983246},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.2671999931335449}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.19964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19964","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,"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.2602.19964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19964","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,"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":{"Uncertainty":[0],"quantification":[1,212],"is":[2,27,111],"central":[3,94],"to":[4,58,113,139],"safe":[5],"and":[6,53,199,202],"efficient":[7,207],"deployments":[8],"of":[9,86,117,146,196],"deep":[10,65,119,197],"learning":[11],"models,":[12],"yet":[13,208],"many":[14],"computationally":[15],"practical":[16],"methods":[17],"lack":[18],"lacking":[19],"rigorous":[20],"theoretical":[21,72,187],"motivation.":[22],"Random":[23],"network":[24,88],"distillation":[25],"(RND)":[26],"a":[28,38,118,124,160,185],"lightweight":[29],"technique":[30],"that":[31,131,164,189],"measures":[32,52],"novelty":[33],"via":[34],"prediction":[35],"errors":[36],"against":[37],"fixed":[39],"random":[40],"target.":[41],"While":[42],"empirically":[43],"effective,":[44],"it":[45],"has":[46],"remained":[47],"unclear":[48],"what":[49],"uncertainties":[50],"RND":[51,76,104,126,133,191],"how":[54],"its":[55,106],"estimates":[56],"relate":[57],"other":[59],"approaches,":[60],"e.g.":[61],"Bayesian":[62,147,171,200],"inference":[63,148],"or":[64],"ensembles.":[66],"This":[67],"paper":[68],"establishes":[69],"these":[70],"missing":[71],"connections":[73],"by":[74],"analyzing":[75],"within":[77,192],"the":[78,84,114,132,141,193],"neural":[79,151],"tangent":[80],"kernel":[81],"framework":[82],"in":[83,96],"limit":[85],"infinite":[87],"width.":[89],"Our":[90],"analysis":[91],"reveals":[92],"two":[93],"findings":[95,183],"this":[97,155,176],"limit:":[98],"(1)":[99],"The":[100],"uncertainty":[101,211],"signal":[102],"from":[103,168],"--":[105,110],"squared":[107],"self-predictive":[108],"error":[109,134],"equivalent":[112],"predictive":[115,144,173],"variance":[116],"ensemble.":[120],"(2)":[121],"By":[122],"constructing":[123],"specific":[125],"target":[127],"function,":[128],"we":[129,157],"show":[130],"distribution":[135,145,174],"can":[136],"be":[137],"made":[138],"mirror":[140],"centered":[142],"posterior":[143,161,172],"with":[149],"wide":[150],"networks.":[152],"Based":[153],"on":[154],"equivalence,":[156],"moreover":[158],"devise":[159],"sampling":[162],"algorithm":[163],"generates":[165],"i.i.d.":[166],"samples":[167],"an":[169],"exact":[170],"using":[175],"modified":[177],"\\textit{Bayesian":[178],"RND}":[179],"model.":[180],"Collectively,":[181],"our":[182],"provide":[184],"unified":[186],"perspective":[188],"places":[190],"principled":[194],"frameworks":[195],"ensembles":[198],"inference,":[201],"offer":[203],"new":[204],"avenues":[205],"for":[206],"theoretically":[209],"grounded":[210],"methods.":[213]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-26T00:00:00"}
