{"id":"https://openalex.org/W4284967541","doi":"https://doi.org/10.1007/s40747-022-00790-x","title":"Quantifying safety risks of deep neural networks","display_name":"Quantifying safety risks of deep neural networks","publication_year":2022,"publication_date":"2022-07-09","ids":{"openalex":"https://openalex.org/W4284967541","doi":"https://doi.org/10.1007/s40747-022-00790-x"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-022-00790-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00790-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00790-x.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00790-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028614556","display_name":"Peipei Xu","orcid":"https://orcid.org/0000-0002-1781-3820"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Peipei Xu","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074225885","display_name":"Wenjie Ruan","orcid":"https://orcid.org/0000-0002-8311-8738"},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Wenjie Ruan","raw_affiliation_strings":["Department of Computer Science, University of Exeter, Exeter, EX4 4QF, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Exeter, Exeter, EX4 4QF, UK","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020085889","display_name":"Xiaowei Huang","orcid":"https://orcid.org/0000-0001-6267-0366"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Xiaowei Huang","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074225885"],"corresponding_institution_ids":["https://openalex.org/I23923803"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":1.6656,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86291663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"9","issue":"4","first_page":"3801","last_page":"3818"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9912999868392944,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9605000019073486,"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/reachability","display_name":"Reachability","score":0.7089925408363342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6544753313064575},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6412922739982605},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.6163057088851929},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5813003182411194},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5719246864318848},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.4533027410507202},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43971797823905945},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.35419702529907227},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.350785493850708},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.27571725845336914},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20472854375839233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1585177779197693}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.7089925408363342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6544753313064575},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6412922739982605},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.6163057088851929},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5813003182411194},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5719246864318848},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.4533027410507202},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43971797823905945},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.35419702529907227},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.350785493850708},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27571725845336914},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20472854375839233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1585177779197693},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s40747-022-00790-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00790-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00790-x.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:discovery.dundee.ac.uk:openaire_cris_publications/9b4e6757-e5e1-473e-80cd-70d61bff9fbf","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/9b4e6757-e5e1-473e-80cd-70d61bff9fbf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Xu, P, Ruan, W & Huang, X 2023, 'Quantifying safety risks of deep neural networks', Complex &amp; Intelligent Systems, vol. 9, pp. 3801\u20133818. https://doi.org/10.1007/s40747-022-00790-x","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:9cad346de7b1460bb19ee68e3a24f2f8","is_oa":true,"landing_page_url":"https://doaj.org/article/9cad346de7b1460bb19ee68e3a24f2f8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complex & Intelligent Systems, Vol 9, Iss 4, Pp 3801-3818 (2022)","raw_type":"article"},{"id":"pmh:oai:eprints.lancs.ac.uk:174032","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/174032/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s40747-022-00790-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00790-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00790-x.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2838024195","display_name":"UK Robotics and Artificial Intelligence Hub for Offshore Energy Asset Integrity Management","funder_award_id":"EP/R026173/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4483049737","display_name":null,"funder_award_id":"EP/R026173/1","funder_id":"https://openalex.org/F4320334245","funder_display_name":"Offshore Robotics for Certification of Assets"},{"id":"https://openalex.org/G6661291015","display_name":"EnnCore: End-to-End Conceptual Guarding of Neural Architectures","funder_award_id":"EP/T026995/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7329227181","display_name":null,"funder_award_id":"956123","funder_id":"https://openalex.org/F4320335254","funder_display_name":"Horizon 2020"},{"id":"https://openalex.org/G849311619","display_name":null,"funder_award_id":"EP/T026995/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8602921712","display_name":null,"funder_award_id":"EP/R026173","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334245","display_name":"Offshore Robotics for Certification of Assets","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335254","display_name":"Horizon 2020","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4284967541.pdf","grobid_xml":"https://content.openalex.org/works/W4284967541.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W569478347","https://openalex.org/W1998855065","https://openalex.org/W2014337138","https://openalex.org/W2117539524","https://openalex.org/W2148563791","https://openalex.org/W2165073069","https://openalex.org/W2180612164","https://openalex.org/W2543296129","https://openalex.org/W2543927648","https://openalex.org/W2581711117","https://openalex.org/W2594877703","https://openalex.org/W2765424254","https://openalex.org/W2766447205","https://openalex.org/W2772841103","https://openalex.org/W2790102940","https://openalex.org/W2791251367","https://openalex.org/W2794609696","https://openalex.org/W2796402180","https://openalex.org/W2800473699","https://openalex.org/W2869036160","https://openalex.org/W2905810301","https://openalex.org/W2917325587","https://openalex.org/W2919115771","https://openalex.org/W2936674544","https://openalex.org/W2955566917","https://openalex.org/W2963208512","https://openalex.org/W2963560523","https://openalex.org/W2963857521","https://openalex.org/W2963913218","https://openalex.org/W2979485058","https://openalex.org/W2981639301","https://openalex.org/W3011102739","https://openalex.org/W3036286896","https://openalex.org/W3042769859","https://openalex.org/W3102178346","https://openalex.org/W3103557498","https://openalex.org/W3105155462","https://openalex.org/W3128522683","https://openalex.org/W3199239810","https://openalex.org/W3208304128","https://openalex.org/W4212863985","https://openalex.org/W4367358859","https://openalex.org/W6600195515","https://openalex.org/W6603860191","https://openalex.org/W6633963571","https://openalex.org/W6727693337"],"related_works":["https://openalex.org/W4386603768","https://openalex.org/W2950475743","https://openalex.org/W2886711096","https://openalex.org/W2750384547","https://openalex.org/W4380078352","https://openalex.org/W3046591097","https://openalex.org/W4389249638","https://openalex.org/W2733410219","https://openalex.org/W2734358244","https://openalex.org/W4388700941"],"abstract_inverted_index":{"Abstract":[0],"Safety":[1],"concerns":[2],"on":[3,147,160,182,214],"the":[4,28,60,66,82,89,103,129,155,188,191,215],"deep":[5],"neural":[6,163,218],"networks":[7],"(DNNs)":[8],"have":[9],"been":[10],"raised":[11],"when":[12],"they":[13],"are":[14],"applied":[15],"to":[16,54,88,97,102,149],"critical":[17],"sectors.":[18],"In":[19,100],"this":[20,113],"paper,":[21,114],"we":[22,45,64,115],"define":[23,46],"safety":[24,43,49,57,76,183,209],"risks":[25,210],"by":[26,138,144],"requesting":[27],"alignment":[29],"of":[30,62,69,81,91,120,154,187,193,208,217],"network\u2019s":[31],"decision":[32],"with":[33,204],"human":[34],"perception.":[35],"To":[36],"enable":[37],"a":[38,47,117,197,205],"general":[39],"methodology":[40],"for":[41],"quantifying":[42],"risks,":[44,63],"generic":[48,198],"property":[50],"and":[51,109,142,169,190,211],"instantiate":[52],"it":[53],"express":[55],"various":[56],"risks.":[58],"For":[59],"quantification":[61,184],"take":[65],"maximum":[67,83],"radius":[68,85],"safe":[70,84],"norm":[71],"balls,":[72],"in":[73,112,185],"which":[74,123],"no":[75],"risk":[77],"exists.":[78],"The":[79,172],"computation":[80,90,153],"is":[86,131],"reduced":[87],"their":[92],"respective":[93],"Lipschitz":[94],"metrics\u2014the":[95],"quantities":[96],"be":[98],"computed.":[99],"addition":[101],"known":[104],"adversarial":[105],"example,":[106,108,111],"reachability":[107],"invariant":[110],"identify":[116],"new":[118],"class":[119,207],"risk\u2014uncertainty":[121],"example\u2014on":[122],"humans":[124],"can":[125,178,202],"tell":[126],"easily,":[127],"but":[128],"network":[130],"unsure.":[132],"We":[133,157],"develop":[134],"an":[135,151],"algorithm,":[136],"inspired":[137],"derivative-free":[139],"optimization":[140],"techniques":[141],"accelerated":[143],"tensor-based":[145],"parallelization":[146],"GPUs,":[148],"support":[150],"efficient":[152],"metrics.":[156],"perform":[158],"evaluations":[159],"several":[161],"benchmark":[162],"networks,":[164],"including":[165],"ACSC-Xu,":[166],"MNIST,":[167],"CIFAR-10,":[168],"ImageNet":[170],"networks.":[171,219],"experiments":[173],"show":[174],"that":[175],"our":[176,200],"method":[177,201],"achieve":[179],"competitive":[180],"performance":[181],"terms":[186],"tightness":[189],"efficiency":[192],"computation.":[194],"Importantly,":[195],"as":[196],"approach,":[199],"work":[203],"broad":[206],"without":[212],"restrictions":[213],"structure":[216]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
