{"id":"https://openalex.org/W4404346934","doi":"https://doi.org/10.48550/arxiv.2410.23594","title":"How Do Flow Matching Models Memorize and Generalize in Sample Data Subspaces?","display_name":"How Do Flow Matching Models Memorize and Generalize in Sample Data Subspaces?","publication_year":2024,"publication_date":"2024-10-31","ids":{"openalex":"https://openalex.org/W4404346934","doi":"https://doi.org/10.48550/arxiv.2410.23594"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2410.23594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.23594","pdf_url":"https://arxiv.org/pdf/2410.23594","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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2410.23594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033363297","display_name":"Weiguo Gao","orcid":"https://orcid.org/0000-0003-0043-8320"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Weiguo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100351375","display_name":"Ming Li","orcid":"https://orcid.org/0000-0002-0722-028X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ming","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/T11326","display_name":"Stock Market Forecasting Methods","score":0.838100016117096,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11326","display_name":"Stock Market Forecasting Methods","score":0.838100016117096,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.8080000281333923,"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"}},{"id":"https://openalex.org/T11344","display_name":"Traffic Prediction and Management Techniques","score":0.7937999963760376,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7172836661338806},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.7111102938652039},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.6344594955444336},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4950794279575348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45991742610931396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37341850996017456},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32402878999710083},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19120007753372192},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10572564601898193},{"id":"https://openalex.org/keywords/chromatography","display_name":"Chromatography","score":0.06037408113479614}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7172836661338806},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.7111102938652039},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.6344594955444336},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4950794279575348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45991742610931396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37341850996017456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32402878999710083},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19120007753372192},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10572564601898193},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.06037408113479614},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2410.23594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.23594","pdf_url":"https://arxiv.org/pdf/2410.23594","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2410.23594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2410.23594","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:2410.23594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.23594","pdf_url":"https://arxiv.org/pdf/2410.23594","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4404346934.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2949110394","https://openalex.org/W2896134808","https://openalex.org/W4289378085","https://openalex.org/W2071055957","https://openalex.org/W4211228991","https://openalex.org/W2353790329","https://openalex.org/W3103861421","https://openalex.org/W2279743781","https://openalex.org/W2756100583"],"abstract_inverted_index":{"Real-world":[0],"data":[1,34,108,131,137,180],"is":[2],"often":[3],"assumed":[4],"to":[5,30,142],"lie":[6],"within":[7,63,177],"a":[8,21,91,95,100,122],"low-dimensional":[9],"structure":[10],"embedded":[11],"in":[12,53],"high-dimensional":[13],"space.":[14],"In":[15,74],"practical":[16],"settings,":[17],"we":[18,28,77,112,145],"observe":[19],"only":[20],"finite":[22],"set":[23],"of":[24],"samples,":[25],"forming":[26],"what":[27],"refer":[29],"as":[31,44,110],"the":[32,71,106,117,135,147,156,168,173,178],"sample":[33,136,179],"subspace.":[35],"It":[36],"serves":[37],"an":[38],"essential":[39],"approximation":[40],"supporting":[41],"tasks":[42],"such":[43],"dimensionality":[45],"reduction":[46],"and":[47,133,161,188],"generation.":[48],"A":[49],"major":[50],"challenge":[51,83],"lies":[52],"whether":[54],"generative":[55],"models":[56],"can":[57],"reliably":[58],"synthesize":[59],"samples":[60,128,184],"that":[61,126,167],"stay":[62],"this":[64,75,82],"subspace":[65,138,160,174],"rather":[66],"than":[67],"drifting":[68],"away":[69],"from":[70],"underlying":[72],"structure.":[73],"work,":[76],"provide":[78],"theoretical":[79],"insights":[80],"into":[81,94,159],"by":[84],"leveraging":[85],"Flow":[86],"Matching":[87],"models,":[88],"which":[89,153],"transform":[90],"simple":[92],"prior":[93],"complex":[96],"target":[97],"distribution":[98,109],"via":[99],"learned":[101],"velocity":[102,119,157],"field.":[103],"By":[104],"treating":[105],"real":[107,130],"discrete,":[111],"derive":[113],"analytical":[114],"expressions":[115],"for":[116],"optimal":[118],"field":[120,158],"under":[121],"Gaussian":[123],"prior,":[124],"showing":[125],"generated":[127,183],"memorize":[129],"points":[132],"represent":[134],"exactly.":[139],"To":[140],"generalize":[141],"suboptimal":[143],"scenarios,":[144],"introduce":[146],"Orthogonal":[148],"Subspace":[149],"Decomposition":[150],"Network":[151],"(OSDNet),":[152],"systematically":[154],"decomposes":[155],"off-subspace":[162,169],"components.":[163],"Our":[164],"analysis":[165],"shows":[166],"component":[170,175],"decays,":[171],"while":[172],"generalizes":[176],"subspace,":[181],"ensuring":[182],"preserve":[185],"both":[186],"proximity":[187],"diversity.":[189]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}