{"id":"https://openalex.org/W3206494906","doi":"https://doi.org/10.48550/arxiv.2104.11734","title":"Exact marginal prior distributions of finite Bayesian neural networks","display_name":"Exact marginal prior distributions of finite Bayesian neural networks","publication_year":2021,"publication_date":"2021-04-23","ids":{"openalex":"https://openalex.org/W3206494906","doi":"https://doi.org/10.48550/arxiv.2104.11734","mag":"3206494906"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2104.11734","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.11734","pdf_url":"https://arxiv.org/pdf/2104.11734","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.11734","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063822685","display_name":"Jacob A. Zavatone-Veth","orcid":"https://orcid.org/0000-0002-4060-1738","observed_orcids":["https://orcid.org/0000-0002-4060-1738"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zavatone-Veth, Jacob A.","raw_affiliation_strings":["Department of Physics Harvard University Cambridge , MA 02138","Harvard University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics Harvard University Cambridge , MA 02138","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Harvard University ,","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023195984","display_name":"Cengiz Pehlevan","orcid":"https://orcid.org/0000-0001-9767-6063","observed_orcids":["https://orcid.org/0000-0001-9767-6063"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pehlevan, Cengiz","raw_affiliation_strings":["School of Engineering and Applied Sciences Harvard University Cambridge , MA 02138","Harvard University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Sciences Harvard University Cambridge , MA 02138","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Harvard University ,","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9437999725341797,"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":0.9437999725341797,"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/T10320","display_name":"Neural Networks and Applications","score":0.04439999908208847,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.0017999999690800905,"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/bayesian-neural-networks","display_name":"Bayesian neural networks","score":0.9210000038146973},{"id":"https://openalex.org/keywords/marginal-distributions","display_name":"marginal distributions","score":0.6150000095367432},{"id":"https://openalex.org/keywords/deep-linear-networks","display_name":"deep linear networks","score":0.7799999713897705},{"id":"https://openalex.org/keywords/relu-neural-networks","display_name":"ReLU networks","score":0.953000009059906},{"id":"https://openalex.org/keywords/meijer-g-function","display_name":"Meijer G-function","score":0.9700000286102295},{"id":"https://openalex.org/keywords/non-gaussian-priors","display_name":"non-Gaussian priors","score":0.7599999904632568},{"id":"https://openalex.org/keywords/tail-decay","display_name":"tail decay","score":0.7889999747276306},{"id":"https://openalex.org/keywords/feedforward-neural-networks","display_name":"feedforward neural networks","score":0.718999981880188}],"concepts":[{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.9323284029960632},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6483069658279419},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5655267238616943},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5564849972724915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5184061527252197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4627167582511902},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45253923535346985},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4473169445991516},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.420576810836792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3703741729259491},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3688667118549347},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3643052577972412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14231404662132263},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13370636105537415},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2104.11734","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.11734","pdf_url":"https://arxiv.org/pdf/2104.11734","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.2104.11734","doi":"https://doi.org/10.48550/arxiv.2104.11734","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.11734","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":"article-journal"},{"id":"mag:3214638589","doi":null,"is_oa":false,"landing_page_url":"https://papers.nips.cc/paper/2021/hash/1baff70e2669e8376347efd3a874a341-Abstract.html","pdf_url":null,"source":{"id":"https://openalex.org/S4363606243","display_name":"neural information processing systems","issn_l":"1049-5258","issn":["1049-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Neural Information Processing Systems","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2104.11734","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.11734","pdf_url":"https://arxiv.org/pdf/2104.11734","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309622","display_name":"Harvard University","ror":"https://ror.org/03vek6s52"},{"id":"https://openalex.org/F4320334227","display_name":"Harvard Data Science Initiative, Harvard University","ror":null},{"id":"https://openalex.org/F4320338027","display_name":"FAS Division of Science, Harvard University","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W568726942","https://openalex.org/W1489991626","https://openalex.org/W1530042113","https://openalex.org/W2004216344","https://openalex.org/W2080059175","https://openalex.org/W2081299583","https://openalex.org/W2111051539","https://openalex.org/W2154087390","https://openalex.org/W2157005274","https://openalex.org/W2320321016","https://openalex.org/W2550524953","https://openalex.org/W2557283755","https://openalex.org/W2765572925","https://openalex.org/W2766678531","https://openalex.org/W2911504931","https://openalex.org/W2913473169","https://openalex.org/W2943838153","https://openalex.org/W2962685794","https://openalex.org/W2970289029","https://openalex.org/W2978199389","https://openalex.org/W2994922086","https://openalex.org/W3006861283","https://openalex.org/W3014864774","https://openalex.org/W3034669169","https://openalex.org/W3035216170","https://openalex.org/W3035679810","https://openalex.org/W3037003270","https://openalex.org/W3060669478","https://openalex.org/W3086778125","https://openalex.org/W3090487863","https://openalex.org/W3101069636","https://openalex.org/W3110116503","https://openalex.org/W3113190353","https://openalex.org/W3123387470","https://openalex.org/W3130833330","https://openalex.org/W3159054876","https://openalex.org/W3166609963","https://openalex.org/W3167954842","https://openalex.org/W3178741258","https://openalex.org/W3202780401"],"related_works":["https://openalex.org/W3157538235","https://openalex.org/W3167954842","https://openalex.org/W3202217159","https://openalex.org/W3036525728","https://openalex.org/W2943838153","https://openalex.org/W3172130470","https://openalex.org/W3014605228","https://openalex.org/W2072555316","https://openalex.org/W3130833330","https://openalex.org/W4385428903"],"abstract_inverted_index":{"Bayesian":[0,29,70],"neural":[1,71],"networks":[2,30,104],"are":[3],"theoretically":[4],"well-understood":[5],"only":[6,45],"in":[7,83,115,127],"the":[8,55,77,86,100],"infinite-width":[9],"limit,":[10],"where":[11],"Gaussian":[12,18],"priors":[13,19,41,58,101,126],"over":[14,20],"network":[15,21,95,125],"weights":[16],"yield":[17],"outputs.":[22],"Recent":[23],"work":[24],"has":[25,79],"suggested":[26],"that":[27],"finite":[28,67,93,124],"may":[31],"outperform":[32],"their":[33,37,130],"infinite":[34],"counterparts,":[35],"but":[36],"non-Gaussian":[38],"function":[39,56],"space":[40,57],"have":[42],"been":[43],"characterized":[44],"though":[46],"perturbative":[47],"approaches.":[48],"Here,":[49],"we":[50],"derive":[51],"exact":[52],"solutions":[53],"for":[54,59],"individual":[60],"input":[61],"examples":[62],"of":[63,66,85,91,99,102,105,112,123,129],"a":[64,80,92,97],"class":[65],"fully-connected":[68],"feedforward":[69],"networks.":[72],"For":[73],"deep":[74],"linear":[75,103],"networks,":[76],"prior":[78,90],"simple":[81],"expression":[82],"terms":[84,128],"Meijer":[87],"$G$-function.":[88],"The":[89],"ReLU":[94],"is":[96],"mixture":[98],"smaller":[106],"widths,":[107],"corresponding":[108],"to":[109],"different":[110],"numbers":[111],"active":[113],"units":[114],"each":[116],"layer.":[117],"Our":[118],"results":[119],"unify":[120],"previous":[121],"descriptions":[122],"tail":[131],"decay":[132],"and":[133],"large-width":[134],"behavior.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2021-10-25T00:00:00"}
