{"id":"https://openalex.org/W4383068540","doi":"https://doi.org/10.3390/sym15071352","title":"Oracle-Preserving Latent Flows","display_name":"Oracle-Preserving Latent Flows","publication_year":2023,"publication_date":"2023-07-03","ids":{"openalex":"https://openalex.org/W4383068540","doi":"https://doi.org/10.3390/sym15071352"},"language":"en","primary_location":{"id":"doi:10.3390/sym15071352","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15071352","pdf_url":"https://www.mdpi.com/2073-8994/15/7/1352/pdf?version=1688380847","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/7/1352/pdf?version=1688380847","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001566718","display_name":"Alexander Roman","orcid":"https://orcid.org/0000-0003-2719-221X"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Roman","raw_affiliation_strings":["Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0003-2719-221X","affiliations":[{"raw_affiliation_string":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015598518","display_name":"Roy T. Forestano","orcid":"https://orcid.org/0000-0002-0355-2076"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roy T. Forestano","raw_affiliation_strings":["Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0002-0355-2076","affiliations":[{"raw_affiliation_string":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100659526","display_name":"K. Matchev","orcid":"https://orcid.org/0000-0003-4182-9096"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Konstantin T. Matchev","raw_affiliation_strings":["Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0003-4182-9096","affiliations":[{"raw_affiliation_string":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041886570","display_name":"Katia Matcheva","orcid":"https://orcid.org/0000-0003-3074-998X"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Katia Matcheva","raw_affiliation_strings":["Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0003-3074-998X","affiliations":[{"raw_affiliation_string":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015322002","display_name":"Eyup B. Unlu","orcid":"https://orcid.org/0000-0002-6683-6463"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eyup B. Unlu","raw_affiliation_strings":["Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0002-6683-6463","affiliations":[{"raw_affiliation_string":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100659526"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1796,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82680613,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"15","issue":"7","first_page":"1352","last_page":"1352"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.9937000274658203,"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"}},"topics":[{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.9937000274658203,"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/T12859","display_name":"Cell Image Analysis Techniques","score":0.9751999974250793,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.970300018787384,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.6759566068649292},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.6504555344581604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6127170920372009},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5510530471801758},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.5420435667037964},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5179589986801147},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.4891410171985626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4567076861858368},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4363994598388672},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.40128952264785767},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.373374342918396},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.31332558393478394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.285638689994812},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11311089992523193},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10556048154830933}],"concepts":[{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.6759566068649292},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6504555344581604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6127170920372009},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5510530471801758},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.5420435667037964},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5179589986801147},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.4891410171985626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4567076861858368},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4363994598388672},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.40128952264785767},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.373374342918396},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.31332558393478394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.285638689994812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11311089992523193},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10556048154830933},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/sym15071352","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15071352","pdf_url":"https://www.mdpi.com/2073-8994/15/7/1352/pdf?version=1688380847","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:83310083b06a44328d3d2ebc186d27b9","is_oa":false,"landing_page_url":"https://doaj.org/article/83310083b06a44328d3d2ebc186d27b9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 7, p 1352 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/7/1352/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15071352","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"},{"id":"pmh:oai:osti.gov:1988094","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1988094","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},{"id":"pmh:oai:osti.gov:2422062","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/2422062","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"doi:10.3390/sym15071352","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15071352","pdf_url":"https://www.mdpi.com/2073-8994/15/7/1352/pdf?version=1688380847","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5295059432","display_name":null,"funder_award_id":"DE-SC0022148","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383068540.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W2014041755","https://openalex.org/W2045505291","https://openalex.org/W2731335845","https://openalex.org/W2766409877","https://openalex.org/W2787586057","https://openalex.org/W2884775584","https://openalex.org/W2896377340","https://openalex.org/W2910230154","https://openalex.org/W2991376628","https://openalex.org/W3009084733","https://openalex.org/W3012274818","https://openalex.org/W3016401366","https://openalex.org/W3036548566","https://openalex.org/W3089384272","https://openalex.org/W3093022628","https://openalex.org/W3095769772","https://openalex.org/W3100050954","https://openalex.org/W3100170200","https://openalex.org/W3101699553","https://openalex.org/W3105570377","https://openalex.org/W3135458194","https://openalex.org/W3168202165","https://openalex.org/W3189302471","https://openalex.org/W3201377945","https://openalex.org/W3209534297","https://openalex.org/W3211679656","https://openalex.org/W4221140049","https://openalex.org/W4225286241","https://openalex.org/W4237111979","https://openalex.org/W4281488293","https://openalex.org/W4281640551","https://openalex.org/W4281786920","https://openalex.org/W4310363075","https://openalex.org/W4311637764","https://openalex.org/W4315782990","https://openalex.org/W4324100416","https://openalex.org/W4378470143","https://openalex.org/W4385075924","https://openalex.org/W6780561946","https://openalex.org/W6818430772"],"related_works":["https://openalex.org/W4386603768","https://openalex.org/W2950475743","https://openalex.org/W2886711096","https://openalex.org/W2750384547","https://openalex.org/W4380078352","https://openalex.org/W3046591097","https://openalex.org/W4389249638","https://openalex.org/W2733410219","https://openalex.org/W2734358244","https://openalex.org/W2734997742"],"abstract_inverted_index":{"A":[0],"fundamental":[1],"task":[2],"in":[3,16,69,151,161,175],"data":[4,163],"science":[5],"is":[6,93,106],"the":[7,17,26,43,61,73,81,99,104,109,128,136,139,152,162,176],"discovery,":[8],"description,":[9],"and":[10,42,80,169],"identification":[11],"of":[12,29,75,112,114,121,138,147],"any":[13],"symmetries":[14,33,122,160],"present":[15],"data.":[18],"We":[19,118,141],"developed":[20],"a":[21,55,76,115],"deep":[22],"learning":[23],"methodology":[24],"for":[25,168],"simultaneous":[27],"discovery":[28],"multiple":[30],"non-trivial":[31,173],"continuous":[32],"across":[34],"an":[35],"entire":[36],"labeled":[37],"dataset.":[38],"The":[39,65,91],"symmetry":[40,63],"transformations":[41,85,144,174],"corresponding":[44],"generators":[45],"are":[46,72],"modeled":[47],"with":[48,54,86,95],"fully":[49],"connected":[50],"neural":[51],"networks":[52],"trained":[53,116],"specially":[56],"constructed":[57],"loss":[58],"function,":[59],"ensuring":[60],"desired":[62],"properties.":[64],"two":[66],"new":[67,131],"elements":[68],"this":[70],"work":[71],"use":[74],"reduced-dimensionality":[77],"latent":[78,154,178],"space":[79],"generalization":[82],"to":[83,88],"invariant":[84],"respect":[87],"high-dimensional":[89],"oracles.":[90],"method":[92],"demonstrated":[94],"several":[96],"examples":[97],"on":[98],"MNIST":[100],"digit":[101],"dataset,":[102],"where":[103],"oracle":[105],"provided":[107],"by":[108],"10-dimensional":[110],"vector":[111],"logits":[113],"classifier.":[117],"find":[119],"classes":[120],"that":[123,159],"transform":[124],"each":[125],"image":[126],"from":[127],"dataset":[129],"into":[130],"synthetic":[132],"images":[133],"while":[134],"conserving":[135],"values":[137],"logits.":[140],"illustrate":[142],"these":[143],"as":[145,171],"lines":[146],"equal":[148],"probability":[149],"(\u201cflows\u201d)":[150],"reduced":[153],"space.":[155,179],"These":[156],"results":[157],"show":[158],"can":[164],"be":[165],"successfully":[166],"searched":[167],"identified":[170],"interpretable":[172],"equivalent":[177]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
