{"id":"https://openalex.org/W7166516293","doi":"https://doi.org/10.48550/arxiv.2606.27582","title":"Beyond Points: Spherical Distributional Part Prototypes for Interpretable Classification","display_name":"Beyond Points: Spherical Distributional Part Prototypes for Interpretable Classification","publication_year":2026,"publication_date":"2026-06-25","ids":{"openalex":"https://openalex.org/W7166516293","doi":"https://doi.org/10.48550/arxiv.2606.27582"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.27582","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27582","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.27582","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139609507","display_name":"Duarte Le\u00e3o","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Le\u00e3o, Duarte","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139562921","display_name":"Diogo Pereira Ara\u00fajo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ara\u00fajo, Diogo Pereira","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018897159","display_name":"Catarina Barata","orcid":"https://orcid.org/0000-0002-2852-7723"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barata, Catarina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136455783","display_name":"Carlos Santiago","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Santiago, Carlos","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.29829999804496765,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.29829999804496765,"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"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.289900004863739,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.09570000320672989,"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/interpretability","display_name":"Interpretability","score":0.9232000112533569},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6703000068664551},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6154999732971191},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6013000011444092},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5730999708175659},{"id":"https://openalex.org/keywords/quality","display_name":"Quality (philosophy)","score":0.5641999840736389},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.5005999803543091},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.38019999861717224}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.9232000112533569},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6703000068664551},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6402000188827515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6338000297546387},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6154999732971191},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6013000011444092},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5730999708175659},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.5641999840736389},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.45980000495910645},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C204030448","wikidata":"https://www.wikidata.org/wiki/Q101017","display_name":"Distillation","level":2,"score":0.3125},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2800999879837036},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.2648000121116638},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.260699987411499}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.27582","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27582","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.27582","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27582","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,"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"},"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":{"Prototype-based":[0],"neural":[1],"networks":[2],"aim":[3],"to":[4,90],"provide":[5],"intrinsic":[6],"interpretability":[7],"by":[8,104],"grounding":[9],"predictions":[10],"in":[11,24],"a":[12,38,56,65],"small":[13],"set":[14],"of":[15,67],"part":[16,32,148],"prototypes.":[17],"However,":[18],"modern":[19],"vision":[20],"backbones":[21,118],"typically":[22],"operate":[23],"normalized,":[25],"directional":[26],"embedding":[27],"spaces":[28],"where":[29],"each":[30,62],"semantic":[31],"exhibits":[33],"substantial":[34],"intra-class":[35],"variability.":[36],"As":[37],"result,":[39],"point":[40],"prototypes":[41],"often":[42],"become":[43],"redundant":[44],"or":[45],"unstable,":[46],"hurting":[47],"both":[48],"explanation":[49],"quality":[50],"and":[51,83,110,125,129,137],"robustness.":[52],"We":[53],"propose":[54],"vMFProto,":[55],"distributional":[57],"part-prototype":[58],"framework":[59],"that":[60,120,143],"models":[61],"class":[63],"as":[64],"mixture":[66],"von":[68],"Mises-Fisher":[69],"components":[70],"on":[71,127],"the":[72],"hypersphere.":[73],"Each":[74],"prototype":[75,101],"learns":[76],"its":[77],"own":[78],"concentration,":[79],"capturing":[80],"part-specific":[81],"variability,":[82],"we":[84],"use":[85],"entropic":[86],"optimal":[87],"transport":[88],"(OT)":[89],"obtain":[91],"structured":[92],"patch-to-prototype":[93],"assignments.":[94],"A":[95],"two-stage":[96],"training":[97],"schedule":[98],"performs":[99],"OT-driven":[100],"discovery":[102],"followed":[103],"end-to-end":[105],"refinement":[106],"with":[107,115],"patch-level":[108],"distillation":[109],"distribution-aware":[111],"diversity":[112],"regularization.":[113],"Experiments":[114],"frozen":[116],"DINO":[117],"show":[119],"vMFProto":[121,144],"achieves":[122],"leading":[123],"consistency":[124],"distinctiveness":[126],"CUB-200-2011":[128],"competitive":[130],"classification":[131],"accuracy":[132],"across":[133],"CUB,":[134],"Stanford":[135,138],"Dogs,":[136],"Cars.":[139],"Qualitative":[140],"results":[141],"confirm":[142],"yields":[145],"localized,":[146],"non-redundant":[147],"evidence.":[149]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-30T00:00:00"}
