{"id":"https://openalex.org/W7164897298","doi":"https://doi.org/10.48550/arxiv.2606.16883","title":"Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability","display_name":"Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability","publication_year":2026,"publication_date":"2026-06-15","ids":{"openalex":"https://openalex.org/W7164897298","doi":"https://doi.org/10.48550/arxiv.2606.16883"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.16883","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16883","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":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.2606.16883","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047883853","display_name":"Abdul-Rauf Nuhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nuhu, Abdul-Rauf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138694156","display_name":"Parham M. Kebria","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kebria, Parham M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093279939","display_name":"Vahid Hemmati","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hemmati, Vahid","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138720229","display_name":"Mahmoud N. Mahmoud","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mahmoud, Mahmoud N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138691251","display_name":"Edward Tunstel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tunstel, Edward","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054416654","display_name":"Abdollah Homaifar","orcid":"https://orcid.org/0000-0003-1179-3221"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Homaifar, Abdollah","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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9287999868392944,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9287999868392944,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.017999999225139618,"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":0.011500000022351742,"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/robustness","display_name":"Robustness (evolution)","score":0.8366000056266785},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6628999710083008},{"id":"https://openalex.org/keywords/generalization-error","display_name":"Generalization error","score":0.6014999747276306},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.532800018787384},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4964999854564667},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4586000144481659},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.430400013923645}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8366000056266785},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6628999710083008},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.6014999747276306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5666000247001648},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.532800018787384},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46880000829696655},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4586000144481659},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.430400013923645},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.41130000352859497},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.39239999651908875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3614000082015991},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3402999937534332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33379998803138733},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3190999925136566},{"id":"https://openalex.org/C5465570","wikidata":"https://www.wikidata.org/wiki/Q5326898","display_name":"Early stopping","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.28949999809265137}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.16883","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16883","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.16883","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16883","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Generalization":[0],"is":[1,69],"a":[2,23,35,76,101,119,191],"critical":[3],"property":[4],"of":[5,79,110,135,193],"data-driven":[6],"models,":[7],"particularly":[8,88],"deep":[9,195],"learning":[10],"models":[11,164],"deployed":[12],"in":[13,34,45],"safety-critical":[14],"applications.":[15],"Robustness-based":[16],"generalization":[17,31,120],"bounds":[18,41,51,144,158,173],"have":[19],"gained":[20],"attention":[21],"as":[22,100],"principled":[24],"way":[25],"to":[26,30,72,132],"link":[27],"robustness":[28,85,98,129],"properties":[29],"performance,":[32],"often":[33,70],"data-dependent":[36],"manner.":[37],"However,":[38],"most":[39],"existing":[40,183],"suffer":[42],"from":[43,83],"vacuousness":[44],"practical":[46,153],"settings,":[47],"yielding":[48],"loose":[49],"upper":[50,157],"that":[52,122,171],"greatly":[53],"exceed":[54],"the":[55,73,80,84,90,97,111,128,133,167,179],"actual":[56],"error":[57],"rates":[58],"and":[59,137,148,177],"limiting":[60],"their":[61],"usefulness":[62],"for":[63,89],"real-world":[64],"evaluation.":[65],"While":[66],"this":[67,115,124],"issue":[68],"attributed":[71],"uncertainty":[74],"term,":[75],"substantial":[77],"part":[78],"problem":[81],"originates":[82],"term":[86,99,130],"itself,":[87],"0-1":[91],"loss.":[92],"Existing":[93],"approaches":[94],"typically":[95],"treat":[96],"global":[102],"measure,":[103],"ignoring":[104],"its":[105],"variation":[106],"across":[107,190],"different":[108],"sub-regions":[109],"input":[112],"space.":[113],"In":[114],"work,":[116],"we":[117],"propose":[118],"bound":[121],"addresses":[123],"limitation":[125],"by":[126],"scaling":[127],"according":[131],"number":[134],"stable":[136],"unstable":[138],"samples":[139],"within":[140],"each":[141],"sub-region.":[142],"Our":[143],"incorporate":[145],"both":[146],"data-":[147],"model-dependent":[149],"factors":[150],"while":[151],"maintaining":[152],"relevance":[154],"(yielding":[155],"tighter":[156],"on":[159,163,166],"true":[160],"error).":[161],"Experiments":[162],"trained":[165],"ImageNet":[168],"dataset":[169],"show":[170],"our":[172],"remain":[174],"consistently":[175],"non-vacuous":[176],"achieve":[178],"tightest":[180],"estimates":[181],"among":[182],"methods,":[184],"closely":[185],"aligning":[186],"with":[187],"empirical":[188],"performance":[189],"range":[192],"robust":[194],"neural":[196],"networks.":[197]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-17T00:00:00"}
