{"id":"https://openalex.org/W4312922768","doi":"https://doi.org/10.1109/ijcnn55064.2022.9892337","title":"Quasi-orthogonality and intrinsic dimensions as measures of learning and generalisation","display_name":"Quasi-orthogonality and intrinsic dimensions as measures of learning and generalisation","publication_year":2022,"publication_date":"2022-07-18","ids":{"openalex":"https://openalex.org/W4312922768","doi":"https://doi.org/10.1109/ijcnn55064.2022.9892337"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn55064.2022.9892337","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn55064.2022.9892337","pdf_url":null,"source":{"id":"https://openalex.org/S4363607707","display_name":"2022 International Joint Conference on Neural Networks (IJCNN)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024753869","display_name":"Qinghua Zhou","orcid":"https://orcid.org/0000-0002-3327-0440"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Qinghua Zhou","raw_affiliation_strings":["School of Computing and Mathematical Sciences, University of Leicester,Leicester,UK","School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK"],"affiliations":[{"raw_affiliation_string":"School of Computing and Mathematical Sciences, University of Leicester,Leicester,UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058069510","display_name":"Alexander N. Gorban","orcid":"https://orcid.org/0000-0001-6224-1430"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexander N. Gorban","raw_affiliation_strings":["School of Computing and Mathematical Sciences, University of Leicester,Leicester,UK","School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK"],"affiliations":[{"raw_affiliation_string":"School of Computing and Mathematical Sciences, University of Leicester,Leicester,UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069472885","display_name":"Evgeny M. Mirkes","orcid":"https://orcid.org/0000-0003-1474-1734"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Evgeny M. Mirkes","raw_affiliation_strings":["School of Computing and Mathematical Sciences, University of Leicester,Leicester,UK","School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK"],"affiliations":[{"raw_affiliation_string":"School of Computing and Mathematical Sciences, University of Leicester,Leicester,UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025746657","display_name":"Jonathan Bac","orcid":"https://orcid.org/0000-0002-8504-5448"},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I80043","display_name":"Institut Curie","ror":"https://ror.org/04t0gwh46","country_code":"FR","type":"funder","lineage":["https://openalex.org/I80043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jonathan Bac","raw_affiliation_strings":["Institut Curie, PSL Research University,Paris,France","Institut Curie, PSL Research University, Paris, France"],"affiliations":[{"raw_affiliation_string":"Institut Curie, PSL Research University,Paris,France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I80043"]},{"raw_affiliation_string":"Institut Curie, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I80043"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077253721","display_name":"Andre\u00ef Zinovyev","orcid":"https://orcid.org/0000-0002-9517-7284"},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I80043","display_name":"Institut Curie","ror":"https://ror.org/04t0gwh46","country_code":"FR","type":"funder","lineage":["https://openalex.org/I80043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andrei Zinovyev","raw_affiliation_strings":["Institut Curie, PSL Research University,Paris,France","Institut Curie, PSL Research University, Paris, France"],"affiliations":[{"raw_affiliation_string":"Institut Curie, PSL Research University,Paris,France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I80043"]},{"raw_affiliation_string":"Institut Curie, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I80043"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052143104","display_name":"Ivan Tyukin","orcid":"https://orcid.org/0000-0002-7359-7966"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ivan Y. Tyukin","raw_affiliation_strings":["King&#x0027;s College London,Department of Mathematics,London,UK"],"affiliations":[{"raw_affiliation_string":"King&#x0027;s College London,Department of Mathematics,London,UK","institution_ids":["https://openalex.org/I183935753"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5024753869"],"corresponding_institution_ids":["https://openalex.org/I153648349"],"apc_list":null,"apc_paid":null,"fwci":0.2081,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.44357054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994000196456909,"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/T10320","display_name":"Neural Networks and Applications","score":0.9994000196456909,"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/T10057","display_name":"Face and Expression Recognition","score":0.9957000017166138,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.8894269466400146},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6929208636283875},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6774019002914429},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.619723916053772},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6133550405502319},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5514932870864868},{"id":"https://openalex.org/keywords/feature-vector","display_name":"Feature vector","score":0.49201247096061707},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4910869598388672},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4720859229564667},{"id":"https://openalex.org/keywords/intrinsic-dimension","display_name":"Intrinsic dimension","score":0.46182969212532043},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4481750726699829},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4353329539299011},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4336591362953186},{"id":"https://openalex.org/keywords/composability","display_name":"Composability","score":0.4256761074066162},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.41264018416404724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.284900963306427},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.19406184554100037},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17318832874298096},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.1024114191532135},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07170245051383972}],"concepts":[{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.8894269466400146},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6929208636283875},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6774019002914429},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.619723916053772},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6133550405502319},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5514932870864868},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.49201247096061707},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4910869598388672},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4720859229564667},{"id":"https://openalex.org/C30732413","wikidata":"https://www.wikidata.org/wiki/Q17092636","display_name":"Intrinsic dimension","level":3,"score":0.46182969212532043},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4481750726699829},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4353329539299011},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4336591362953186},{"id":"https://openalex.org/C2778814252","wikidata":"https://www.wikidata.org/wiki/Q5156715","display_name":"Composability","level":2,"score":0.4256761074066162},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.41264018416404724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.284900963306427},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.19406184554100037},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17318832874298096},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.1024114191532135},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07170245051383972},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ijcnn55064.2022.9892337","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn55064.2022.9892337","pdf_url":null,"source":{"id":"https://openalex.org/S4363607707","display_name":"2022 International Joint Conference on Neural Networks (IJCNN)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/fb488d81-94ef-4d8a-9512-d87b4d298f0b","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/fb488d81-94ef-4d8a-9512-d87b4d298f0b","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Zhou, Q, Gorban, A N, Mirkes, E M, Bac, J, Zinovyev, A & Tyukin, I Y 2022, Quasi-orthogonality and intrinsic dimensions as measures of learning and generalisation. in 2022 International Joint Conference on Neural Networks, IJCNN 2022 - Proceedings. Proceedings of the International Joint Conference on Neural Networks, vol. 2022-July, 2022 International Joint Conference on Neural Networks, IJCNN 2022, Padua, Italy, 18/07/2022. https://doi.org/10.1109/IJCNN55064.2022.9892337","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1445524271","display_name":null,"funder_award_id":"EP/V025295/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1786513448","https://openalex.org/W2022845879","https://openalex.org/W2028569884","https://openalex.org/W2030499717","https://openalex.org/W2040549971","https://openalex.org/W2124477890","https://openalex.org/W2754478492","https://openalex.org/W2784010521","https://openalex.org/W2884063665","https://openalex.org/W2884716758","https://openalex.org/W2892053535","https://openalex.org/W2951245151","https://openalex.org/W2977886961","https://openalex.org/W2981563141","https://openalex.org/W2999270366","https://openalex.org/W3018252856","https://openalex.org/W3099661174","https://openalex.org/W3104335155","https://openalex.org/W3166395393","https://openalex.org/W3198796775","https://openalex.org/W3204954825","https://openalex.org/W3206571981","https://openalex.org/W4234345389","https://openalex.org/W6759402996","https://openalex.org/W6771859737","https://openalex.org/W6779348065"],"related_works":["https://openalex.org/W2383601311","https://openalex.org/W2388607015","https://openalex.org/W186132510","https://openalex.org/W2542453320","https://openalex.org/W2630947271","https://openalex.org/W2159423485","https://openalex.org/W2162232804","https://openalex.org/W1974408264","https://openalex.org/W2484376704","https://openalex.org/W2786419579"],"abstract_inverted_index":{"Finding":[0],"the":[1,33,39,54,70,76,92,95,111,124,137,145,181],"best":[2],"architectures":[3,62],"for":[4],"learning":[5],"machines,":[6],"such":[7,80],"as":[8,79,108,147,160],"deep":[9],"neural":[10,61,117,129,172],"networks,":[11],"is":[12],"a":[13,81,115],"well-known":[14],"technical":[15],"and":[16,38,99,126,155,185,195],"theoretical":[17],"challenge.":[18],"Recent":[19],"work":[20],"by":[21,84],"Mellor":[22,65,149],"et":[23,66,150],"al":[24,67,151],"[1]":[25,68],"showed":[26],"that":[27,153],"there":[28],"may":[29,52,157],"exist":[30],"correlations":[31],"between":[32,180],"accuracies":[34],"of":[35,41,56,58,60,94,97,110,114,128,187],"trained":[36],"networks":[37,50],"values":[40],"some":[42],"easily":[43],"computable":[44],"measures":[45,103],"defined":[46],"on":[47],"randomly":[48,189],"initialised":[49,190],"which":[51,104],"enable":[53],"search":[55],"tens":[57],"thousands":[59],"without":[63],"training.":[64,141],"used":[69,107],"Hamming":[71],"distance":[72],"evaluated":[73],"over":[74],"all":[75],"ReLU":[77],"neurons":[78],"measure.":[82],"Motivated":[83],"these":[85],"findings,":[86],"in":[87,148],"our":[88,175],"work,":[89],"we":[90,121],"ask":[91],"question":[93],"existence":[96],"other":[98],"perhaps":[100],"more":[101],"principled":[102],"could":[105,133],"be":[106,134],"determinants":[109],"potential":[112],"success":[113],"given":[116],"architecture.":[118],"In":[119,164],"particular,":[120],"examine":[122],"if":[123],"dimensionality":[125,154],"quasi-orthogonality":[127,156],"networks'":[130,161,182],"feature":[131,191],"space":[132],"correlated":[135],"with":[136],"network's":[138],"performance":[139,162,184],"after":[140],"We":[142],"showed,":[143],"using":[144],"setup":[146],"[1],":[152],"jointly":[158],"serve":[159],"discriminants.":[163],"addition":[165],"to":[166,170],"offering":[167],"new":[168],"opportunities":[169],"accelerate":[171],"architecture":[173],"search,":[174],"findings":[176],"suggest":[177],"important":[178],"relationships":[179],"final":[183],"properties":[186],"their":[188],"spaces:":[192],"data":[193],"dimension":[194],"quasi-orthogonality.":[196]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
