{"id":"https://openalex.org/W7166194053","doi":"https://doi.org/10.48550/arxiv.2606.26424","title":"Rethinking Training & Inference for Forecasting: Linking Winner-Take-All back to GMMs","display_name":"Rethinking Training & Inference for Forecasting: Linking Winner-Take-All back to GMMs","publication_year":2026,"publication_date":"2026-06-24","ids":{"openalex":"https://openalex.org/W7166194053","doi":"https://doi.org/10.48550/arxiv.2606.26424"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.26424","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26424","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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.26424","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043687189","display_name":"Qiyuan Wu","orcid":"https://orcid.org/0000-0002-8751-2003"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Qiyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139428998","display_name":"Katie Z Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Katie Z","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139437481","display_name":"Bharath Hariharan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hariharan, Bharath","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139391280","display_name":"Wei-Lun Chao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chao, Wei-Lun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108155319","display_name":"M Campbell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Campbell, Mark","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/T11099","display_name":"Autonomous Vehicle Technology and Safety","score":0.7860000133514404,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11099","display_name":"Autonomous Vehicle Technology and Safety","score":0.7860000133514404,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.06430000066757202,"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":0.027300000190734863,"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/inference","display_name":"Inference","score":0.6722999811172485},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6557999849319458},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.6324999928474426},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.6098999977111816},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.5048999786376953},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4871000051498413},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.4781000018119812},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4474000036716461},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4189000129699707}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6729999780654907},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6722999811172485},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6557999849319458},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6324999928474426},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.6098999977111816},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5062999725341797},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.505299985408783},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.4781000018119812},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4474000036716461},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4189000129699707},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.3686999976634979},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3564000129699707},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27129998803138733},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.2648000121116638},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.26424","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26424","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":"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":"doi:10.48550/arxiv.2606.26424","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26424","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":"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"},"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":{"Trajectory":[0],"forecasting":[1],"for":[2,20],"autonomous":[3],"driving":[4],"has":[5],"advanced":[6],"rapidly,":[7],"yet":[8],"representative":[9],"models":[10,38],"often":[11],"produce":[12,136],"uninformative":[13,71],"posteriors":[14,142],"over":[15],"forecast":[16],"modes,":[17,83],"causing":[18],"problems":[19],"mode":[21,65,72,141],"pruning.":[22],"We":[23,55],"trace":[24],"this":[25,58,93],"to":[26,51],"a":[27,43,111,161],"modeling-training":[28],"mismatch:":[29],"forecasters":[30],"are":[31],"typically":[32],"modeled":[33],"as":[34],"conditional":[35],"Gaussian":[36],"mixture":[37],"(GMMs)":[39],"but":[40],"trained":[41],"with":[42,120,174],"winner-take-all":[44],"(WTA)":[45],"loss":[46],"that":[47,57,104,116,169],"assigns":[48],"each":[49],"sample":[50],"its":[52],"nearest":[53],"mode.":[54],"argue":[56],"K-means-like":[59],"hard":[60,118],"assignment":[61,86],"(one-hot),":[62],"while":[63],"preventing":[64],"collapse,":[66],"is":[67],"the":[68,76],"source":[69],"of":[70],"probabilities:":[73],"it":[74],"over-segments":[75],"trajectory":[77],"space,":[78],"ignores":[79],"relatedness":[80],"among":[81],"nearby":[82,106],"and":[84,109,143,164],"yields":[85],"instability":[87],"under":[88],"small":[89],"perturbations.":[90],"Guided":[91],"by":[92],"lens,":[94],"we":[95],"introduce":[96],"two":[97],"post-hoc":[98],"treatments:":[99],"(1)":[100],"test-time":[101],"posterior-weighted":[102],"merging":[103],"aggregates":[105],"candidate":[107],"trajectories;":[108],"(2)":[110],"one-step":[112],"expectation-maximization":[113],"(EM)":[114],"update":[115],"replaces":[117],"labels":[119],"soft":[121],"responsibilities,":[122],"sharing":[123],"probability":[124],"mass":[125],"across":[126],"neighboring":[127],"modes.":[128],"Across":[129],"several":[130],"WTA-trained":[131],"architectures,":[132],"these":[133],"lightweight":[134],"steps":[135],"more":[137],"informative,":[138],"faithfully":[139],"ranked":[140],"strengthen":[144],"final":[145],"forecasts":[146],"on":[147],"popular":[148],"displacement":[149],"metrics":[150],"--":[151],"without":[152],"retraining.":[153],"Our":[154],"analysis":[155],"unifies":[156],"recent":[157],"design":[158],"choices":[159],"through":[160],"GMM-vs-K-means":[162],"perspective":[163],"offers":[165],"principled,":[166],"practical":[167],"corrections":[168],"better":[170],"align":[171],"training":[172],"objectives":[173],"inference.":[175]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-27T00:00:00"}