{"id":"https://openalex.org/W4297899337","doi":"https://doi.org/10.48550/arxiv.2209.10091","title":"Variational Inference for Infinitely Deep Neural Networks","display_name":"Variational Inference for Infinitely Deep Neural Networks","publication_year":2022,"publication_date":"2022-09-21","ids":{"openalex":"https://openalex.org/W4297899337","doi":"https://doi.org/10.48550/arxiv.2209.10091"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2209.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.10091","pdf_url":"https://arxiv.org/pdf/2209.10091","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2209.10091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028389447","display_name":"Achille Nazaret","orcid":"https://orcid.org/0000-0002-5428-9810"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nazaret, Achille","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5070920982","display_name":"David M. Blei","orcid":"https://orcid.org/0000-0002-5588-4611"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blei, David","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":true,"cited_by_count":1,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9918000102043152,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9918000102043152,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9898999929428101,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9864000082015991,"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/truncation","display_name":"Truncation (statistics)","score":0.7778675556182861},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7257847189903259},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5963369607925415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5739419460296631},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5579556226730347},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5184283256530762},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4687243700027466},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.46781206130981445},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.4669528901576996},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.41186007857322693},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3746859133243561},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3656657040119171},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34188371896743774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1909697949886322},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.15688136219978333},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.08067381381988525}],"concepts":[{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.7778675556182861},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7257847189903259},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5963369607925415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5739419460296631},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5579556226730347},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5184283256530762},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4687243700027466},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46781206130981445},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4669528901576996},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.41186007857322693},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3746859133243561},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3656657040119171},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34188371896743774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1909697949886322},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.15688136219978333},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.08067381381988525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2209.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.10091","pdf_url":"https://arxiv.org/pdf/2209.10091","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.48550/arxiv.2209.10091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2209.10091","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":"pmh:oai:arXiv.org:2209.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.10091","pdf_url":"https://arxiv.org/pdf/2209.10091","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1007321806","display_name":null,"funder_award_id":"N00014-17-1-2131)","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4353487559","display_name":null,"funder_award_id":"ONR-N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4504108201","display_name":null,"funder_award_id":"N00014-17-1","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4621806789","display_name":"RI: Small: New Directions in Probabilistic Deep Learning: Exponential Families, Bayesian Nonparametrics and Empirical Bayes","funder_award_id":"2127869","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7106078634","display_name":null,"funder_award_id":"17-1-2131","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8929337198","display_name":null,"funder_award_id":"N00014-17","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320315389","display_name":"Open Philanthropy Project","ror":"https://ror.org/004d1k391"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W2536422707","https://openalex.org/W24145419","https://openalex.org/W2036329708","https://openalex.org/W2073514592","https://openalex.org/W138907054"],"abstract_inverted_index":{"We":[0,71,158,167],"introduce":[1],"the":[2,18,39,52,61,64,86,92,106,134,154,160,170,177],"unbounded":[3,33],"depth":[4,94,175],"neural":[5,66,87,115,183,196],"network":[6,67,88,116],"(UDN),":[7],"an":[8,24,32],"infinitely":[9],"deep":[10],"probabilistic":[11],"model":[12,142],"that":[13,150,169],"adapts":[14,172],"its":[15,45,69,131,173],"complexity":[16],"to":[17,78,141,176,194],"training":[19],"data.":[20,46,166],"The":[21],"UDN":[22,54,161,171],"contains":[23],"infinite":[25,65],"sequence":[26],"of":[27,50,59,63,85,91,118,133,156,185],"hidden":[28],"layers":[29],"and":[30,68,90,96,121,164,189],"places":[31],"prior":[34],"on":[35,101,162],"a":[36,48,56,73,83,110],"truncation":[37,93,135],"L,":[38,95],"layer":[40],"from":[41],"which":[42],"it":[43,113,122,144,180,190],"produces":[44],"Given":[47],"dataset":[49,178],"observations,":[51],"posterior":[53,174],"provides":[55],"conditional":[57],"distribution":[58,84,132],"both":[60],"parameters":[62,129],"truncation.":[70],"develop":[72],"novel":[74],"variational":[75,107,128],"inference":[76],"algorithm":[77,152],"approximate":[79],"this":[80,104,151],"posterior,":[81],"optimizing":[82],"weights":[89,117],"without":[97],"any":[98],"upper":[99],"limit":[100],"L.":[102],"To":[103],"end,":[105],"family":[108],"has":[109],"special":[111],"structure:":[112],"models":[114],"arbitrary":[119],"depth,":[120],"dynamically":[123],"creates":[124],"or":[125],"removes":[126],"free":[127],"as":[130],"is":[136,145],"optimized.":[137],"(Unlike":[138],"heuristic":[139],"approaches":[140,193],"search,":[143],"solely":[146],"through":[147],"gradient-based":[148],"optimization":[149],"explores":[153],"space":[155],"truncations.)":[157],"study":[159],"real":[163],"synthetic":[165],"find":[168],"complexity;":[179,188],"outperforms":[181,191],"standard":[182],"networks":[184],"similar":[186],"computational":[187],"other":[192],"infinite-depth":[195],"networks.":[197]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-09T07:27:16.801131","created_date":"2025-10-10T00:00:00"}
