{"id":"https://openalex.org/W4415961820","doi":"https://doi.org/10.48550/arxiv.2510.17063","title":"Mode Collapse of Mean-Field Variational Inference","display_name":"Mode Collapse of Mean-Field Variational Inference","publication_year":2025,"publication_date":"2025-10-20","ids":{"openalex":"https://openalex.org/W4415961820","doi":"https://doi.org/10.48550/arxiv.2510.17063"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2510.17063","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.17063","pdf_url":"https://arxiv.org/pdf/2510.17063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.17063","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114224634","display_name":"Shunan Sheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheng, Shunan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102469032","display_name":"Bo-Han Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Bohan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052743324","display_name":"Alberto Gonz\u00e1lez-Sanz","orcid":"https://orcid.org/0009-0006-6768-2730"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gonz\u00e1lez-Sanz, Alberto","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":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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.3878999948501587,"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":0.3878999948501587,"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/T12303","display_name":"Tensor decomposition and applications","score":0.10369999706745148,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.09939999878406525,"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/inference","display_name":"Inference","score":0.6956999897956848},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.6309999823570251},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.602400004863739},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5605999827384949},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4975000023841858},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.4968999922275543},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4950999915599823}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6956999897956848},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.6309999823570251},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.602400004863739},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5605999827384949},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4975000023841858},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.4968999922275543},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4950999915599823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48890000581741333},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.483599990606308},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44699999690055847},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3693999946117401},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.362199991941452},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33489999175071716},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3151000142097473},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2718999981880188},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.26080000400543213}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.17063","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.17063","pdf_url":"https://arxiv.org/pdf/2510.17063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.17063","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.17063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.17063","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.17063","pdf_url":"https://arxiv.org/pdf/2510.17063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4415961820.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Mean-field":[0],"variational":[1,146],"inference":[2,147],"(MFVI)":[3],"is":[4,36],"a":[5,37,58,153],"widely":[6],"used":[7],"method":[8],"for":[9,116],"approximating":[10],"high-dimensional":[11],"probability":[12],"distributions":[13],"by":[14],"product":[15],"measures.":[16],"It":[17],"has":[18],"been":[19],"empirically":[20],"observed":[21],"that":[22,102,123],"MFVI":[23,48,104,151],"optimizers":[24],"often":[25],"suffer":[26],"from":[27],"mode":[28,72,127],"collapse.":[29],"Specifically,":[30],"when":[31,110],"the":[32,47,62,67,78,82,85,98,124,132,136,144,165],"target":[33],"measure":[34],"$\u03c0$":[35],"mixture":[38,87],"$\u03c0=":[39],"w":[40],"P_0":[41],"+":[42],"(1":[43],"-":[44],"w)":[45],"P_1$,":[46],"optimizer":[49,105],"tends":[50],"to":[51,80,107],"place":[52],"most":[53],"of":[54,61,71,84,100,126,135,167],"its":[55],"mass":[56,101],"near":[57],"single":[59],"component":[60,109],"mixture.":[63],"This":[64],"work":[65],"provides":[66],"first":[68],"theoretical":[69,161],"explanation":[70],"collapse":[73,128],"in":[74],"MFVI.":[75],"We":[76],"introduce":[77],"notion":[79],"capture":[81],"separatedness":[83],"two":[86],"components":[88],"--":[89,92],"called":[90],"$\\varepsilon$-separateness":[91],"and":[93,112,163],"derive":[94],"explicit":[95],"bounds":[96],"on":[97,131],"fraction":[99],"any":[103],"assigns":[106],"each":[108],"$P_0$":[111],"$P_1$":[113],"are":[114],"$\\varepsilon$-separated":[115],"sufficiently":[117],"small":[118],"$\\varepsilon$.":[119],"Our":[120],"results":[121],"suggest":[122],"occurrence":[125],"crucially":[129],"depends":[130],"relative":[133],"position":[134],"components.":[137],"To":[138],"address":[139],"this":[140],"issue,":[141],"we":[142],"propose":[143],"rotational":[145],"(RoVI),":[148],"which":[149],"augments":[150],"with":[152],"rotation":[154],"matrix.":[155],"The":[156],"numerical":[157],"studies":[158],"support":[159],"our":[160],"findings":[162],"demonstrate":[164],"benefits":[166],"RoVI.":[168]},"counts_by_year":[],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-22T00:00:00"}