{"id":"https://openalex.org/W7162492649","doi":"https://doi.org/10.48550/arxiv.2605.26659","title":"FINOM: Fast Sinkhorn on Non-uniform Meshes","display_name":"FINOM: Fast Sinkhorn on Non-uniform Meshes","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162492649","doi":"https://doi.org/10.48550/arxiv.2605.26659"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.26659","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26659","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":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.2605.26659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137170477","display_name":"Qihao Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Qihao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002244430","display_name":"Qichen Liao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liao, Qichen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137171143","display_name":"Hao Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137089094","display_name":"Shuai Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Shuai","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/T11206","display_name":"Model Reduction and Neural Networks","score":0.24609999358654022,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.24609999358654022,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.10819999873638153,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T12303","display_name":"Tensor decomposition and applications","score":0.09019999951124191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.789900004863739},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5475000143051147},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5013999938964844},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4853000044822693},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.44020000100135803},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4043999910354614},{"id":"https://openalex.org/keywords/collinearity","display_name":"Collinearity","score":0.3950999975204468}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.789900004863739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6193000078201294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5939000248908997},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4465000033378601},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41359999775886536},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C106192678","wikidata":"https://www.wikidata.org/wiki/Q1419761","display_name":"Collinearity","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36649999022483826},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3549000024795532},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.2842000126838684}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.26659","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26659","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":"doi:10.48550/arxiv.2605.26659","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26659","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.44449809193611145}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"linear-complexity":[1],"algorithm":[2,131,148],"for":[3],"computing":[4],"the":[5,16,51,92,100,118,142,146],"Wasserstein-1":[6],"distance":[7],"on":[8,54,132,156],"non-uniform":[9,40,66],"meshes":[10,56,67],"is":[11],"proposed.":[12],"This":[13],"work":[14],"extends":[15],"fast":[17],"Sinkhorn":[18,147],"algorithms":[19],"from":[20,149],"[Q.":[21,30],"Liao":[22,31],"et":[23,32],"al.,":[24,33],"Commun.":[25],"Math.":[26],"Sci.,":[27],"20(2022)]":[28],"and":[29,77,158],"J.":[34],"Sci.":[35],"Comput.,":[36],"98":[37],"(2024)]":[38],"to":[39,151],"meshes.":[41,123],"In":[42,87],"those":[43],"prior":[44],"works,":[45],"a":[46,95,112,115,136],"distinctive":[47],"collinear":[48],"structure":[49,119],"of":[50,81,94,117,145,166,169],"kernel":[52,101],"matrix":[53,102],"uniform":[55,122],"was":[57],"identified,":[58],"enabling":[59],"\\(O(N)\\)":[60],"acceleration":[61],"via":[62],"dynamic":[63,137],"programming.":[64],"While":[65],"are":[68],"prevalent":[69],"in":[70,121],"practical":[71],"applications":[72],"like":[73],"computational":[74],"fluid":[75],"dynamics":[76],"finance,":[78],"their":[79],"lack":[80],"collinearity":[82],"has":[83],"hindered":[84],"direct":[85],"acceleration.":[86],"this":[88,125],"paper,":[89],"we":[90,127],"introduce":[91],"concept":[93],"``dividing":[96],"index'',":[97],"which":[98],"partitions":[99],"into":[103],"two":[104],"blocks.":[105],"We":[106],"demonstrate":[107],"that":[108,140],"each":[109],"block":[110],"exhibits":[111],"quasi-collinear":[113],"property,":[114],"generalization":[116],"found":[120],"Leveraging":[124],"insight,":[126],"develop":[128],"\\textbf{F}ast":[129],"S\\textbf{I}nkhorn":[130],"\\textbf{NO}n-uniform":[133],"\\textbf{M}eshes":[134],"(\\textbf{FINOM}),":[135],"programming":[138],"approach":[139],"reduces":[141],"per-iteration":[143],"complexity":[144],"\\(O(N^2)\\)":[150],"\\(O(N)\\).":[152],"Extensive":[153],"numerical":[154],"experiments":[155],"1D":[157],"2D":[159],"problems":[160],"confirm":[161],"these":[162],"improvements,":[163],"achieving":[164],"speed-ups":[165],"several":[167],"orders":[168],"magnitude":[170],"while":[171],"maintaining":[172],"accuracy.":[173]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-28T00:00:00"}