{"id":"https://openalex.org/W7162296391","doi":"https://doi.org/10.48550/arxiv.2605.23156","title":"Any-Dimensional Invariant Universality","display_name":"Any-Dimensional Invariant Universality","publication_year":2026,"publication_date":"2026-05-22","ids":{"openalex":"https://openalex.org/W7162296391","doi":"https://doi.org/10.48550/arxiv.2605.23156"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.23156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23156","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.23156","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021823635","display_name":"Shu\u2010Hua Yao","orcid":"https://orcid.org/0000-0002-4762-1002"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yao, Shengtai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051537424","display_name":"Eitan Levin","orcid":"https://orcid.org/0009-0002-5789-4191"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Levin, Eitan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014128725","display_name":"Mateo D\u00edaz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D\u00edaz, Mateo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.6877999901771545,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.6877999901771545,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1428000032901764,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.014000000432133675,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/universality","display_name":"Universality (dynamical systems)","score":0.854200005531311},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.555400013923645},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4580000042915344},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.3840999901294708},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.35569998621940613},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3116999864578247}],"concepts":[{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.854200005531311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7002999782562256},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39890000224113464},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3716999888420105},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30660000443458557},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.23156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23156","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.23156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23156","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"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":{"Several":[0],"machine":[1],"learning":[2],"models":[3,33,43,62],"are":[4],"defined":[5,50,70],"for":[6,42],"inputs":[7,45,104,112,127,131],"of":[8,17,25,30,46,55,68,113,125,132,148],"any":[9],"size,":[10,49],"such":[11,31],"as":[12,37,66,117,119],"graphs":[13],"with":[14,99,145],"different":[15,133],"numbers":[16,24],"nodes":[18],"and":[19,74,128,172],"point":[20],"clouds":[21],"containing":[22,111],"varying":[23],"points.":[26],"The":[27],"universality":[28,38,154],"properties":[29],"any-dimensional":[32,61,93,97,153],"remain":[34],"poorly":[35],"understood,":[36],"is":[39,76],"traditionally":[40],"studied":[41],"accepting":[44],"a":[47,52,88,100,106,142],"fixed":[48],"on":[51,71,151],"compact":[53,149],"subset":[54],"their":[56,120],"domain.":[57],"In":[58],"sharp":[59],"contrast,":[60],"can":[63,83,155],"be":[64,84,156,170],"viewed":[65],"sequences":[67],"functions":[69,98],"growing-sized":[72],"inputs,":[73],"it":[75],"not":[77],"clear":[78],"in":[79,105],"which":[80,152],"sense":[81],"they":[82],"universal.":[85],"We":[86,158],"develop":[87],"systematic":[89],"approach":[90,161],"to":[91,169],"establish":[92],"universality,":[94],"by":[95,162],"identifying":[96],"unique":[101],"function":[102],"taking":[103],"suitable":[107],"infinite-dimensional":[108],"limit":[109,139],"space":[110,140],"all":[114],"finite":[115],"sizes":[116],"well":[118],"limits.":[121],"Using":[122],"the":[123],"symmetries":[124],"these":[126],"relations":[129],"between":[130],"sizes,":[134],"we":[135,173],"show":[136],"that":[137,164,177],"this":[138],"admits":[141],"natural":[143],"topology":[144],"rich":[146],"families":[147],"sets":[150],"established.":[157],"illustrate":[159],"our":[160],"showing":[163],"several":[165],"existing":[166],"architectures":[167],"fail":[168],"universal,":[171],"propose":[174],"simple":[175],"modifications":[176],"restore":[178],"universality.":[179]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-26T00:00:00"}
