{"id":"https://openalex.org/W4409308655","doi":"https://doi.org/10.3389/fcomp.2025.1597931","title":"Editorial: Geometries of learning","display_name":"Editorial: Geometries of learning","publication_year":2025,"publication_date":"2025-04-09","ids":{"openalex":"https://openalex.org/W4409308655","doi":"https://doi.org/10.3389/fcomp.2025.1597931"},"language":"en","primary_location":{"id":"doi:10.3389/fcomp.2025.1597931","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fcomp.2025.1597931","pdf_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1597931/pdf","source":{"id":"https://openalex.org/S4210211086","display_name":"Frontiers in Computer Science","issn_l":"2624-9898","issn":["2624-9898"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computer Science","raw_type":"journal-article"},"type":"editorial","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1597931/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004105936","display_name":"Yunye Gong","orcid":null},"institutions":[{"id":"https://openalex.org/I1298353152","display_name":"SRI International","ror":"https://ror.org/05s570m15","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1298353152"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yunye Gong","raw_affiliation_strings":["Center for Vision Technologies, SRI International, Princeton, NJ, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Vision Technologies, SRI International, Princeton, NJ, United States","institution_ids":["https://openalex.org/I1298353152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062945520","display_name":"Pavan Turaga","orcid":"https://orcid.org/0000-0002-5263-5943"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pavan Turaga","raw_affiliation_strings":["School of Arts Media and Engineering, Arizona State University, Tempe, AZ, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Arts Media and Engineering, Arizona State University, Tempe, AZ, United States","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101931143","display_name":"Peter Fletcher","orcid":"https://orcid.org/0000-0002-6605-471X"},"institutions":[{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Thomas Fletcher","raw_affiliation_strings":["Department of Computer Science, University of Virginia, Charlottesville, VA, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Virginia, Charlottesville, VA, United States","institution_ids":["https://openalex.org/I51556381"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028124265","display_name":"Ajay Divakaran","orcid":"https://orcid.org/0000-0003-0371-5346"},"institutions":[{"id":"https://openalex.org/I1298353152","display_name":"SRI International","ror":"https://ror.org/05s570m15","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1298353152"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ajay Divakaran","raw_affiliation_strings":["Center for Vision Technologies, SRI International, Princeton, NJ, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Vision Technologies, SRI International, Princeton, NJ, United States","institution_ids":["https://openalex.org/I1298353152"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004105936"],"corresponding_institution_ids":["https://openalex.org/I1298353152"],"apc_list":{"value":1150,"currency":"USD","value_usd":1150},"apc_paid":{"value":1150,"currency":"USD","value_usd":1150},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06592788,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.7997000217437744,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.7997000217437744,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11904","display_name":"Spatial Cognition and Navigation","score":0.6851999759674072,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36015692353248596},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.3388892412185669},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.27701377868652344}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36015692353248596},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.3388892412185669},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.27701377868652344}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3389/fcomp.2025.1597931","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fcomp.2025.1597931","pdf_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1597931/pdf","source":{"id":"https://openalex.org/S4210211086","display_name":"Frontiers in Computer Science","issn_l":"2624-9898","issn":["2624-9898"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c89d7c3f8ea0467da023bbfa50a0799d","is_oa":true,"landing_page_url":"https://doaj.org/article/c89d7c3f8ea0467da023bbfa50a0799d","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Computer Science, Vol 7 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fcomp.2025.1597931","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fcomp.2025.1597931","pdf_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1597931/pdf","source":{"id":"https://openalex.org/S4210211086","display_name":"Frontiers in Computer Science","issn_l":"2624-9898","issn":["2624-9898"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409308655.pdf","grobid_xml":"https://content.openalex.org/works/W4409308655.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Despite":[0],"the":[1,11,40,59,62,89,95,115,123,142,170,177,191,214,243,247,273,279,294],"widespread":[2],"application":[3],"and":[4,30,35,61,136,144,201,212,246,270,275,291],"empirical":[5],"success":[6],"of":[7,15,24,32,39,64,79,91,101,108,125,147,152,169,193,205,220,281],"deep":[8,65,120],"neural":[9,66],"networks,":[10],"theoretical":[12],"10":[13],"development":[14],"these":[16,80],"networks":[17,42,92],"remains":[18],"an":[19],"under-explored":[20],"area.":[21],"The":[22],"lack":[23],"theory":[25,63],"prevents":[26],"rigorous":[27,132],"11":[28],"explanation":[29],"prediction":[31],"networks'":[33],"performance":[34],"hinders":[36],"confident":[37],"deployment":[38],"12":[41],"especially":[43],"in":[44,103,196,272],"safety-critical":[45],"applications.":[46],"Geometric":[47],"analysis":[48,154],"provides":[49],"a":[50,131,217],"unique":[51],"perspective":[52],"13":[53],"to":[54,94,112,163,210,236,241,255,263],"bridge":[55],"this":[56,98,256,283],"gap":[57],"between":[58],"practice":[60],"networks.":[67],"As":[68],"complex":[69],"real-14":[70],"world":[71],"data":[72,225],"often":[73],"lie":[74],"on":[75,106,118],"low-dimensional":[76],"manifolds,":[77],"geometries":[78],"underlying":[81],"structures":[82],"provide":[83],"15":[84],"informative":[85],"insights":[86],"for":[87,183,216,251,267],"understanding":[88],"behavior":[90],"fitting":[93],"data.":[96],"16In":[97],"Research":[99,257,284],"Topic":[100,285],"Frontiers":[102],"Computer":[104],"Science":[105],"Geometries":[107],"Learning,":[109],"we":[110],"aim":[111],"17":[113],"present":[114],"latest":[116],"advances":[117],"inspecting":[119],"learning":[121,206],"through":[122],"lens":[124],"geometry.":[126],"We":[127],"have":[128],"18":[129],"followed":[130],"peer":[133],"review":[134],"process":[135],"collected":[137],"twelve":[138],"articles":[139],"that":[140,277],"showcase":[141],"depth":[143],"19":[145],"breadth":[146],"current":[148],"approaches":[149],"across":[150,155],"applications":[151,222],"geometric":[153,200],"diverse":[156,224],"problem":[157],"20":[158],"domains":[159],"from":[160],"adversarial":[161,185],"defense":[162],"object":[164],"pose":[165],"estimation.":[166],"A":[167],"summary":[168],"collection":[171],"is":[172],"21":[173],"introduced":[174],"below.":[175],"22In":[176],"paper":[178],"titled":[179],"\"Leveraging":[180],"linear":[181],"mapping":[182],"model-agnostic":[184],"defense\"":[186],"Jamil":[187],"et":[188],"al.":[189],"serve":[190],"core":[192],"recent":[194],"developments":[195],"language":[197],"modeling,":[198],"promoting":[199],"topological":[202],"97":[203],"interpretation":[204],"with":[207],"direct":[208],"links":[209],"semantics,":[211],"expanding":[213],"study":[215],"wide":[218],"range":[219],"98":[221],"involving":[223],"manifolds":[226],"at":[227],"real-world":[228],"complexities.":[229],"99The":[230],"guest":[231],"editor":[232],"team":[233,250],"would":[234],"like":[235],"extend":[237],"our":[238],"sincere":[239],"gratitude":[240],"all":[242],"authors,":[244],"reviewers":[245],"100":[248],"editorial":[249],"their":[252],"valuable":[253],"contribution":[254],"Topic.":[258],"Our":[259],"special":[260],"thanks":[261],"go":[262],"Dr.":[264],"101Bruce":[265],"Draper":[266],"his":[268,289],"vision":[269],"leadership":[271],"research":[274],"discussions":[276],"laid":[278],"foundation":[280],"102":[282],"as":[286,288],"well":[287],"guidance":[290],"support":[292],"throughout":[293],"editing":[295],"process.":[296],"103":[297]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}