{"id":"https://openalex.org/W7212036592","doi":"https://doi.org/10.48550/arxiv.2609.05700","title":"Sandwich Slice: Optimal Transport Potentials Are Optimal Generalized Slicers","display_name":"Sandwich Slice: Optimal Transport Potentials Are Optimal Generalized Slicers","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7212036592","doi":"https://doi.org/10.48550/arxiv.2609.05700"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05700","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05700","pdf_url":"https://arxiv.org/pdf/2609.05700","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":null,"license_id":null,"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/2609.05700","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108657503","display_name":"R. D. Martin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin, Rocio Diaz","raw_affiliation_strings":["Department of Mathematics , Florida State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Florida State University","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150946615","display_name":"Xinran Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Xinran","raw_affiliation_strings":["Harvard"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021002385","display_name":"Matthew Thorpe","orcid":"https://orcid.org/0000-0001-9268-1066","observed_orcids":["https://orcid.org/0000-0001-9268-1066","https://orcid.org/0000-0003-2480-5404"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thorpe, Matthew","raw_affiliation_strings":["School of Public Health"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Public Health","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068682350","display_name":"Soheil Kolouri","orcid":"https://orcid.org/0000-0001-8495-5362","observed_orcids":["https://orcid.org/0000-0001-8495-5362"]},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kolouri, Soheil","raw_affiliation_strings":["Department of Statistics , University of Warwick"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Warwick","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9990000128746033,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":9.999999747378752e-05,"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/T11716","display_name":"Random Matrices and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/wasserstein-distance","display_name":"Wasserstein distance","score":0.8069999814033508},{"id":"https://openalex.org/keywords/optimal-transport-plans","display_name":"optimal transport plans","score":0.4350000023841858}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7204999923706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6225000023841858},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5898000001907349},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5160999894142151},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4659999907016754},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45739999413490295},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.31380000710487366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30630001425743103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2754000127315521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27320000529289246},{"id":"https://openalex.org/C2988881298","wikidata":"https://www.wikidata.org/wiki/Q16884885","display_name":"Transport theory","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05700","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05700","pdf_url":"https://arxiv.org/pdf/2609.05700","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.05700","doi":"https://doi.org/10.48550/arxiv.2609.05700","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05700","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.05700","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05700","pdf_url":"https://arxiv.org/pdf/2609.05700","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2110430145","display_name":null,"funder_award_id":"EP/Y007174/1","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G2867940020","display_name":"CAREER: Optimal Transport Beyond Probability Measures for Robust Geometric Representation Learning","funder_award_id":"2339898","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4686938543","display_name":null,"funder_award_id":"RPG-2024-051","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309151","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34"},{"id":"https://openalex.org/F4320310960","display_name":"NHS Blood and Transplant","ror":"https://ror.org/0227qpa16"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212036592.pdf","grobid_xml":"https://content.openalex.org/works/W7212036592.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2913446963","https://openalex.org/W3158954158","https://openalex.org/W4383472594","https://openalex.org/W4415037860","https://openalex.org/W4415040677","https://openalex.org/W4415953526","https://openalex.org/W7220949897"],"related_works":["https://openalex.org/W4389116445","https://openalex.org/W7220949897","https://openalex.org/W2606224007","https://openalex.org/W2952382218","https://openalex.org/W7162401119","https://openalex.org/W7097600655","https://openalex.org/W7104687666","https://openalex.org/W1559049151","https://openalex.org/W2263839075","https://openalex.org/W4416284030"],"abstract_inverted_index":{"Sliced":[0],"optimal":[1,40,80,166],"transport":[2,5,111],"replaces":[3],"a":[4,38,62,109],"problem":[6],"in":[7,141,153],"Rd":[8],"by":[9,36],"one-dimensional":[10,39,119],"problems":[11],"along":[12],"scalar":[13],"slices,":[14],"and":[15,66,93,99,121,161],"has":[16],"been":[17],"used":[18],"both":[19,100],"to":[20,32,43,72,138,159],"lower":[21,91],"bound":[22,34],"the":[23,44,75,84,89,95,105,115,118,123,130,136,145],"Wasserstein":[24],"distance":[25],"W1":[26],"(max-sliced":[27],"distances)":[28],"and,":[29],"more":[30],"recently,":[31],"upper":[33,97,106],"it":[35,70],"lifting":[37],"plan":[41],"back":[42],"ambient":[45],"supports":[46],"(min-sliced":[47],"plans).":[48],"We":[49,103],"show":[50],"that":[51],"for":[52],"1-Lipschitz":[53],"slicers":[54],"these":[55],"two":[56,59],"directions":[57],"are":[58],"sides":[60],"of":[61,148],"single":[63],"sandwich":[64],"inequality":[65],"we":[67],"characterize":[68],"when":[69],"collapses":[71],"equality.":[73],"If":[74],"slicer":[76,86,137],"class":[77],"contains":[78],"an":[79],"Kantorovich-Rubinstein":[81,163],"potential,":[82],"then":[83],"same":[85],"simultaneously":[87],"maximizes":[88],"max-sliced":[90],"objective":[92,107],"minimizes":[94],"min-sliced":[96],"objective,":[98],"equal":[101,158],"W1.":[102],"define":[104],"through":[108],"tie-broken":[110],"problem,":[112],"which":[113],"removes":[114],"dependence":[116],"on":[117,129],"ordering":[120],"yields":[122],"identities":[124],"without":[125],"any":[126],"uniqueness":[127],"assumption":[128],"slice-optimal":[131],"coupling.":[132],"The":[133],"result":[134],"requires":[135],"be":[139],"nonlinear":[140],"general,":[142],"consistent":[143],"with":[144],"known":[146],"failure":[147],"exact":[149],"linear":[150],"max-sliced/W1":[151],"equivalence":[152],"dimension":[154],"greater":[155],"than":[156],"or":[157],"2,":[160],"identifies":[162],"potentials":[164],"as":[165],"generalized":[167],"slicers.":[168]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
