{"id":"https://openalex.org/W7214041111","doi":"https://doi.org/10.48550/arxiv.2609.24328","title":"A Distributional Optimisation Perspective on Combining Models in Deep Learning","display_name":"A Distributional Optimisation Perspective on Combining Models in Deep Learning","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214041111","doi":"https://doi.org/10.48550/arxiv.2609.24328"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24328","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24328","pdf_url":"https://arxiv.org/pdf/2609.24328","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.24328","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033850912","display_name":"Congye Wang","orcid":"https://orcid.org/0009-0001-0167-1362","observed_orcids":["https://orcid.org/0009-0001-0167-1362"]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wang, Congye","raw_affiliation_strings":["Newcastle University , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Newcastle University , UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132653696","display_name":"Yan Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lin, Yan","raw_affiliation_strings":["Newcastle University , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Newcastle University , UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072864244","display_name":"Zheyang Shen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Shen, Zheyang","raw_affiliation_strings":["Newcastle University , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Newcastle University , UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101955793","display_name":"Matthew A. Fisher","orcid":"https://orcid.org/0000-0003-0344-235X","observed_orcids":["https://orcid.org/0000-0003-0344-235X"]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Fisher, Matthew A.","raw_affiliation_strings":["Newcastle University , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Newcastle University , UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135791642","display_name":"Chris. J. Oates","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oates, Chris. J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.6571999788284302,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.6571999788284302,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.15219999849796295,"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":0.04729999974370003,"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/model-combination","display_name":"model combination","score":0.7580000162124634},{"id":"https://openalex.org/keywords/ensemble-learning","display_name":"ensemble learning","score":0.7409999966621399},{"id":"https://openalex.org/keywords/llm-fine-tuning","display_name":"LLM fine-tuning","score":0.7950000166893005},{"id":"https://openalex.org/keywords/commonsense-reasoning","display_name":"commonsense reasoning","score":0.9259999990463257}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.7217000126838684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6922000050544739},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.6141999959945679},{"id":"https://openalex.org/C150899416","wikidata":"https://www.wikidata.org/wiki/Q1820378","display_name":"Transfer of learning","level":2,"score":0.5022000074386597},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C45942800","wikidata":"https://www.wikidata.org/wiki/Q245652","display_name":"Ensemble learning","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4066999852657318},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.398499995470047},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.39559999108314514},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C193221554","wikidata":"https://www.wikidata.org/wiki/Q5153664","display_name":"Commonsense reasoning","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C2780004032","wikidata":"https://www.wikidata.org/wiki/Q6485978","display_name":"Langevin dynamics","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24328","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24328","pdf_url":"https://arxiv.org/pdf/2609.24328","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.24328","doi":"https://doi.org/10.48550/arxiv.2609.24328","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24328","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.24328","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24328","pdf_url":"https://arxiv.org/pdf/2609.24328","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214041111.pdf","grobid_xml":"https://content.openalex.org/works/W7214041111.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1593114658","https://openalex.org/W2771061327","https://openalex.org/W2794325560","https://openalex.org/W2964121744","https://openalex.org/W4297631950","https://openalex.org/W4389524317","https://openalex.org/W4401306886","https://openalex.org/W4412889977","https://openalex.org/W4414597041","https://openalex.org/W6959850551","https://openalex.org/W7117108127","https://openalex.org/W7162529784"],"related_works":["https://openalex.org/W4287997757","https://openalex.org/W7133229373","https://openalex.org/W3183487613","https://openalex.org/W4415795422","https://openalex.org/W3161663089","https://openalex.org/W3159490446","https://openalex.org/W3201854402","https://openalex.org/W7152034199","https://openalex.org/W4378465302","https://openalex.org/W4416047526"],"abstract_inverted_index":{"Combining":[0],"predictions":[1],"from":[2],"different":[3],"models":[4,18,62,168],"can":[5],"improve":[6],"performance":[7],"at":[8],"machine":[9],"learning":[10],"tasks,":[11],"but":[12,74,115],"the":[13,16,20,42,46,59,75,106,112,118,134],"training":[14],"of":[15,48,61,77,149,165],"individual":[17],"and":[19,30,95,139,153,163],"rule":[21],"used":[22],"to":[23,71,133],"combine":[24],"them":[25],"are":[26,70],"typically":[27],"chosen":[28],"separately,":[29],"by":[31],"ad":[32],"hoc":[33],"means.":[34],"Recent":[35],"advances":[36],"in":[37,111,117],"distributional":[38,102],"optimisation":[39,43],"(i.e.":[40],"where":[41],"occurs":[44],"over":[45],"set":[47],"probability":[49],"distributions)":[50],"offer":[51],"an":[52,156],"opportunity":[53],"for":[54,126,142],"principled":[55],"joint":[56],"training,":[57],"viewing":[58],"collection":[60],"as":[63,100],"a":[64,146,170],"discrete":[65],"distribution":[66],"whose":[67],"support":[68],"points":[69],"be":[72],"optimised,":[73],"potential":[76],"these":[78],"methods":[79],"is":[80,109],"not":[81,116],"well-understood.":[82],"In":[83],"this":[84,143],"paper":[85],"we":[86],"(1)":[87],"cast":[88],"two":[89],"standard":[90],"combination":[91],"strategies":[92],"-":[93,99],"ensembles":[94],"low-rank":[96],"adapter":[97],"averaging":[98],"entropy-regularised":[101],"optimisation,":[103],"observing":[104],"that":[105,122],"resulting":[107],"objective":[108],"convex":[110],"ensemble":[113],"case":[114],"adapter-averaging":[119],"case,":[120],"so":[121],"existing":[123,138],"convergence":[124],"guarantees":[125],"mean":[127],"field":[128],"Langevin":[129],"dynamics":[130],"transfer":[131],"only":[132],"former;":[135],"(2)":[136],"assess":[137],"novel":[140],"algorithms":[141],"task,":[144],"including":[145],"functional":[147],"variant":[148],"variational":[150],"gradient":[151],"descent;":[152],"(3)":[154],"report":[155],"empirical":[157],"study":[158],"spanning":[159],"synthetic":[160],"classification":[161],"tasks":[162],"fine-tuning":[164],"large":[166],"language":[167],"on":[169],"commonsense":[171],"reasoning":[172],"benchmark.":[173]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}