{"id":"https://openalex.org/W7161176866","doi":"https://doi.org/10.48550/arxiv.2605.13753","title":"Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein","display_name":"Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein","publication_year":2026,"publication_date":"2026-05-13","ids":{"openalex":"https://openalex.org/W7161176866","doi":"https://doi.org/10.48550/arxiv.2605.13753"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.13753","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13753","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.2605.13753","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128622935","display_name":"Ashkan Shahbazi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shahbazi, Ashkan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136116478","display_name":"Xinran Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xinran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136134188","display_name":"Ping He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Ping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068682350","display_name":"Soheil Kolouri","orcid":"https://orcid.org/0000-0001-8495-5362"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kolouri, Soheil","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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9154999852180481,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9154999852180481,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10653","display_name":"Robot Manipulation and Learning","score":0.04479999840259552,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.018300000578165054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6074000000953674},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6014999747276306},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5386000275611877},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5221999883651733},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.49309998750686646},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.4352000057697296},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.41999998688697815},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.41440001130104065}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.612500011920929},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6074000000953674},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6014999747276306},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5386000275611877},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5221999883651733},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45350000262260437},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4323999881744385},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3806999921798706},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3212999999523163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31850001215934753},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.28790000081062317},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2694000005722046},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C2776505523","wikidata":"https://www.wikidata.org/wiki/Q4785468","display_name":"Plan (archaeology)","level":2,"score":0.25920000672340393}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.13753","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13753","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.2605.13753","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13753","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,77,137],"propose":[1],"min":[2],"Generalized":[3],"Sliced":[4],"Gromov--Wasserstein":[5,12],"(min-GSGW),":[6],"a":[7,47,63,85,112,130],"sliced":[8,106],"formulation":[9],"for":[10,88,133],"the":[11,42,52,56,74,105],"(GW)":[13],"problem":[14],"using":[15],"expressive":[16],"generalized":[17,102],"slicers.":[18],"The":[19,59],"key":[20],"idea":[21],"is":[22,82],"to":[23,33,46],"learn":[24],"coupled":[25],"nonlinear":[26],"slicers":[27,103],"that":[28,38,80,125,153],"assign":[29],"compatible":[30],"push-forward":[31],"values":[32,162],"both":[34],"input":[35,135],"measures,":[36],"so":[37],"monotone":[39],"coupling":[40],"in":[41,55,73],"projected":[43],"domain":[44],"lifts":[45],"transport":[48,116],"plan":[49,61],"evaluated":[50],"against":[51],"GW":[53,64,107,115,160,170],"objective":[54,65,161],"original":[57,75],"spaces.":[58,76],"resulting":[60],"induces":[62],"value,":[66],"and":[67,91,118,147,159],"min-GSGW":[68,81,154],"minimizes":[69],"this":[70],"cost":[71,167],"directly":[72],"further":[78],"show":[79,152],"rigid-motion":[83],"invariant,":[84],"crucial":[86],"property":[87],"geometric":[89,157],"matching":[90],"shape":[92],"analysis":[93],"tasks.":[94],"Our":[95],"contributions":[96],"are":[97],"threefold:":[98],"1)":[99],"we":[100,110,120],"introduce":[101],"into":[104],"framework,":[108],"2)":[109],"construct":[111],"slicing-based":[113],"efficient":[114],"plan;":[117],"3)":[119],"develop":[121],"an":[122],"amortized":[123],"variant":[124],"replaces":[126],"per-instance":[127],"optimization":[128],"with":[129],"learned":[131],"slicer":[132],"unseen":[134],"pairs.":[136],"perform":[138],"experiments":[139],"on":[140],"animal":[141],"mesh":[142,145],"matching,":[143],"horse":[144],"interpolation,":[146],"ShapeNet":[148],"part":[149],"transfer.":[150],"Results":[151],"produces":[155],"meaningful":[156],"correspondences":[158],"at":[163],"substantially":[164],"lower":[165],"computational":[166],"than":[168],"existing":[169],"solvers.":[171]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-15T00:00:00"}