{"id":"https://openalex.org/W7134848402","doi":"https://doi.org/10.48550/arxiv.2603.08374","title":"This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse","display_name":"This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134848402","doi":"https://doi.org/10.48550/arxiv.2603.08374"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.08374","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020404219","display_name":"Junhao Jia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia, Junhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128663200","display_name":"Jiaqi Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jiaqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057659691","display_name":"Yunyou Liu","orcid":"https://orcid.org/0009-0005-1979-5215"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Yunyou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128639336","display_name":"Haodong Jing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jing, Haodong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127794884","display_name":"Yueyi Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Yueyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128640895","display_name":"Xian Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Xian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128658903","display_name":"Yefeng Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Yefeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.8118000030517578,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.8118000030517578,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.06750000268220901,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.02669999934732914,"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":0.8353999853134155},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.802299976348877},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.7723000049591064},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5665000081062317},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5164999961853027},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4927000105381012},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.47929999232292175},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.47690001130104065},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4738999903202057},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.4609000086784363}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.8353999853134155},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.802299976348877},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.7723000049591064},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5665000081062317},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4927000105381012},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.47929999232292175},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.47690001130104065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47600001096725464},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.4609000086784363},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.459199994802475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4345000088214874},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42559999227523804},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.3434999883174896},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.34220001101493835},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3231000006198883},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.3010999858379364},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.2711000144481659},{"id":"https://openalex.org/C135450995","wikidata":"https://www.wikidata.org/wiki/Q820272","display_name":"Hill climbing","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.259799987077713},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.08374","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.08374","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08374","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":"pmh:doi:10.48550/arxiv.2603.08374","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6707392930984497}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Prototype":[0],"networks":[1],"provide":[2],"an":[3],"intrinsic":[4],"case":[5],"based":[6],"explanation":[7],"mechanism,":[8],"but":[9],"their":[10],"interpretability":[11],"is":[12],"often":[13],"undermined":[14],"by":[15,89],"prototype":[16,86],"collapse,":[17],"where":[18,38],"multiple":[19],"prototypes":[20,78],"degenerate":[21],"to":[22,31,75],"highly":[23],"redundant":[24],"evidence.":[25,122],"We":[26],"attribute":[27],"this":[28],"failure":[29],"mode":[30],"the":[32,72],"terminal":[33],"dynamics":[34],"of":[35],"Neural":[36],"Collapse,":[37],"cross":[39],"entropy":[40],"optimization":[41,70],"suppresses":[42],"intra":[43],"class":[44,48,77,94],"variance":[45],"and":[46,82,108,116],"drives":[47],"conditional":[49],"features":[50],"toward":[51],"a":[52,65,99,104],"low":[53],"dimensional":[54],"limit.":[55],"To":[56],"mitigate":[57],"this,":[58],"we":[59],"propose":[60],"Adaptive":[61],"Manifold":[62],"Prototypes":[63],"(AMP),":[64],"framework":[66],"that":[67,112,129],"leverages":[68],"Riemannian":[69],"on":[71,103,125],"Stiefel":[73],"manifold":[74],"represent":[76],"as":[79],"orthonormal":[80],"bases":[81],"make":[83],"rank":[84,97],"one":[85],"collapse":[87],"infeasible":[88],"construction.":[90],"AMP":[91,130],"further":[92],"learns":[93],"specific":[95],"effective":[96],"via":[98],"proximal":[100],"gradient":[101],"update":[102],"nonnegative":[105],"capacity":[106],"vector,":[107],"introduces":[109],"spatial":[110],"regularizers":[111],"reduce":[113],"rotational":[114],"ambiguity":[115],"encourage":[117],"localized,":[118],"non":[119],"overlapping":[120],"part":[121],"Extensive":[123],"experiments":[124],"fine-grained":[126],"benchmarks":[127],"demonstrate":[128],"achieves":[131],"state-of-the-art":[132],"classification":[133],"accuracy":[134],"while":[135],"significantly":[136],"improving":[137],"causal":[138],"faithfulness":[139],"over":[140],"prior":[141],"interpretable":[142],"models.":[143]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-11T00:00:00"}
