{"id":"https://openalex.org/W7160950446","doi":"https://doi.org/10.48550/arxiv.2605.08344","title":"What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching","display_name":"What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160950446","doi":"https://doi.org/10.48550/arxiv.2605.08344"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.08344","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08344","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.2605.08344","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135994876","display_name":"Alec Helbling","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Helbling, Alec","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040385670","display_name":"S. Hern\u00e1ndez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hernandez, Sebastian Gutierrez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127843796","display_name":"Benjamin Hoover","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hoover, Benjamin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135951235","display_name":"Duen Horng Chau","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chau, Duen Horng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089095944","display_name":"Parikshit Ram","orcid":"https://orcid.org/0000-0002-9456-029X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ram, Parikshit","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.13019999861717224,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.13019999861717224,"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"}},{"id":"https://openalex.org/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.10840000212192535,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.08179999887943268,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/identifiability","display_name":"Identifiability","score":0.6360999941825867},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6326000094413757},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5898000001907349},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5688999891281128},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5364000201225281},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5005999803543091}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.6360999941825867},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6326000094413757},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5898000001907349},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5688999891281128},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5364000201225281},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5360999703407288},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4936999976634979},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4544999897480011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43160000443458557},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29170000553131104}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.08344","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08344","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.2605.08344","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08344","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":{"Recent":[0],"work":[1,36,101],"has":[2,205],"shown":[3],"that":[4,20,86,98,112,158,178,201,234],"models":[5,8,100],"flow":[6,42,229],"matching":[7,43,230],"can":[9,133],"be":[10,134],"trained":[11],"without":[12],"explicit":[13,245],"time":[14,23,119,132,217,246],"conditioning,":[15],"challenging":[16],"the":[17,21,40,71,76,96,113,137,147,179,187,203,235,240],"standard":[18],"view":[19],"interpolation":[22],"is":[24,75,89,182,239],"needed":[25],"to":[26,146,186],"disambiguate":[27],"velocity":[28,59],"targets.":[29],"But":[30],"why":[31,227],"should":[32],"a":[33,52,129,150,155,162,174,206],"time-blind":[34,41,87,99,228],"model":[35],"at":[37,166],"all?":[38],"Decomposing":[39],"loss,":[44],"we":[45,176],"identify":[46],"two":[47],"sources":[48],"of":[49,115,140,242],"irreducible":[50],"error:":[51],"coupling":[53,188,204],"variance,":[54],"which":[55,74],"arises":[56],"from":[57,122,136,161],"ambiguous":[58],"targets":[60],"induced":[61],"by":[62,80,110],"how":[63],"noise":[64],"and":[65,70,199,212,222,232],"data":[66,117,126,198],"points":[67],"are":[68],"paired,":[69],"time-blindness":[72,180],"gap,":[73],"additional":[77],"error":[78],"caused":[79],"ignoring":[81],"time.":[82],"This":[83],"gap":[84,181],"shows":[85],"training":[88],"strictly":[90],"harder":[91],"than":[92,215],"conventional":[93],"training,":[94],"reinforcing":[95],"puzzle":[97],"so":[102],"well":[103],"in":[104,143],"practice.":[105],"We":[106,190],"resolve":[107],"this":[108,153],"tension":[109],"showing":[111],"geometry":[114],"high-dimensional":[116],"makes":[118],"identifiable":[120],"directly":[121],"noisy":[123,141],"observations.":[124],"When":[125],"concentrates":[127],"near":[128],"$k$-dimensional":[130],"subspace,":[131],"recovered":[135],"statistical":[138],"structure":[139],"interpolants":[142],"directions":[144],"orthogonal":[145],"data;":[148],"under":[149],"spiked-covariance":[151],"model,":[152],"yields":[154],"closed-form":[156],"estimator":[157],"recovers":[159],"$t$":[160],"single":[163],"observation":[164],"$z$":[165],"rate":[167],"$O(1/\\sqrt{d-k})$":[168],"for":[169],"ambient":[170],"dimension":[171],"$d$.":[172],"As":[173],"consequence,":[175],"prove":[177],"asymptotically":[183],"negligible":[184],"relative":[185],"variance.":[189],"empirically":[191],"demonstrate":[192],"our":[193],"identifiability":[194],"result":[195],"on":[196,210],"real-world":[197],"show":[200,233],"changing":[202],"much":[207],"larger":[208],"effect":[209],"loss":[211],"sample":[213],"quality":[214],"removing":[216],"conditioning":[218],"across":[219],"CIFAR-10,":[220],"CelebA-HQ,":[221],"FFHQ.":[223],"These":[224],"results":[225],"explain":[226],"works":[231],"main":[236],"practical":[237],"lever":[238],"choice":[241],"coupling,":[243],"not":[244],"conditioning.":[247]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-13T00:00:00"}