{"id":"https://openalex.org/W3216234792","doi":"https://doi.org/10.48550/arxiv.2106.08365","title":"Test Sample Accuracy Scales with Training Sample Density in Neural Networks","display_name":"Test Sample Accuracy Scales with Training Sample Density in Neural Networks","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3216234792","doi":"https://doi.org/10.48550/arxiv.2106.08365","mag":"3216234792"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2106.08365","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.08365","pdf_url":"https://arxiv.org/pdf/2106.08365","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.08365","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023545041","display_name":"Xu Ji","orcid":"https://orcid.org/0000-0002-3754-228X","observed_orcids":["https://orcid.org/0000-0002-3754-228X"]},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ji, Xu","raw_affiliation_strings":["Google Brain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Brain","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043910056","display_name":"Razvan Pascanu","orcid":"https://orcid.org/0000-0002-5470-1238","observed_orcids":["https://orcid.org/0000-0002-5470-1238"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pascanu, Razvan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062650781","display_name":"Devon Hjelm","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hjelm, Devon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012859570","display_name":"Balaji Lakshminarayanan","orcid":"https://orcid.org/0000-0002-3334-1659","observed_orcids":["https://orcid.org/0000-0002-3334-1659"]},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lakshminarayanan, Balaji","raw_affiliation_strings":["Google Brain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Brain","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060511349","display_name":"Andrea Vedaldi","orcid":"https://orcid.org/0000-0003-1374-2858","observed_orcids":["https://orcid.org/0000-0003-1374-2858"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Vedaldi, Andrea","raw_affiliation_strings":["Oxford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford University","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.32350000739097595,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.32350000739097595,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.2565999925136566,"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":0.16380000114440918,"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/neural-network-generalization","display_name":"neural network generalization","score":0.597000002861023},{"id":"https://openalex.org/keywords/representation-space","display_name":"representation space","score":0.8629999756813049},{"id":"https://openalex.org/keywords/out-of-distribution-samples","display_name":"out-of-distribution samples","score":0.8970000147819519},{"id":"https://openalex.org/keywords/image-classification","display_name":"image classification","score":0.6029999852180481},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.35100001096725464}],"concepts":[{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.6803792119026184},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6708346605300903},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.6534446477890015},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6278197765350342},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5428625345230103},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.5345344543457031},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.5174891948699951},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5044358968734741},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5022096633911133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4653404951095581},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4503088593482971},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44619399309158325},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.44538819789886475},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4386196434497833},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.42129606008529663},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4125412404537201},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3711063861846924},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0890580415725708},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2106.08365","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.08365","pdf_url":"https://arxiv.org/pdf/2106.08365","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2106.08365","doi":"https://doi.org/10.48550/arxiv.2106.08365","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2106.08365","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2106.08365","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.08365","pdf_url":"https://arxiv.org/pdf/2106.08365","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3216234792.pdf","grobid_xml":"https://content.openalex.org/works/W3216234792.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1944672","https://openalex.org/W582134693","https://openalex.org/W1580375566","https://openalex.org/W1686946872","https://openalex.org/W1995875735","https://openalex.org/W2142635246","https://openalex.org/W2147947791","https://openalex.org/W2161388792","https://openalex.org/W2169413195","https://openalex.org/W2335728318","https://openalex.org/W2433379750","https://openalex.org/W2531327146","https://openalex.org/W2560321925","https://openalex.org/W2767414122","https://openalex.org/W2806075129","https://openalex.org/W2867167548","https://openalex.org/W2948194985","https://openalex.org/W2963613748","https://openalex.org/W2963693742","https://openalex.org/W2970338090","https://openalex.org/W2970641149","https://openalex.org/W2990500698","https://openalex.org/W2996179709","https://openalex.org/W3035898727","https://openalex.org/W3043138801","https://openalex.org/W3108981297","https://openalex.org/W3115571254","https://openalex.org/W3118608800","https://openalex.org/W3125314187","https://openalex.org/W3168441138","https://openalex.org/W3209355693"],"related_works":["https://openalex.org/W3113742260","https://openalex.org/W4393335834","https://openalex.org/W3167073794","https://openalex.org/W4392026285","https://openalex.org/W4281842394","https://openalex.org/W2969940440","https://openalex.org/W117245955","https://openalex.org/W7169664186","https://openalex.org/W7222421027","https://openalex.org/W2566079294"],"abstract_inverted_index":{"Intuitively,":[0],"one":[1],"would":[2],"expect":[3],"accuracy":[4,99],"of":[5,62,65],"a":[6,33,59],"trained":[7],"neural":[8],"network's":[9,67],"prediction":[10,68,98],"on":[11,35,69,111],"test":[12,70,74,82],"samples":[13,20,26,83,92],"to":[14,102],"correlate":[15],"with":[16,46,78,93],"how":[17],"densely":[18],"the":[19,63,66,94],"are":[21],"surrounded":[22],"by":[23,84,100],"seen":[24],"training":[25,37,47],"in":[27,50,104],"representation":[28,51],"space.":[29,52],"We":[30],"find":[31],"that":[32],"bound":[34,57,89],"empirical":[36],"error":[38,88],"smoothed":[39],"across":[40],"linear":[41],"activation":[42],"regions":[43],"scales":[44],"inversely":[45],"sample":[48],"density":[49],"Empirically,":[53],"we":[54],"verify":[55],"this":[56],"is":[58],"strong":[60],"predictor":[61],"inaccuracy":[64],"samples.":[71],"For":[72],"unseen":[73],"sets,":[75],"including":[76],"those":[77],"out-of-distribution":[79],"samples,":[80],"ranking":[81],"their":[85],"local":[86],"region's":[87],"and":[90],"discarding":[91],"highest":[95],"bounds":[96],"raises":[97],"up":[101],"20%":[103],"absolute":[105],"terms":[106],"for":[107],"image":[108],"classification":[109],"datasets,":[110],"average":[112],"over":[113],"thresholds.":[114]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2021-12-06T00:00:00"}
