{"id":"https://openalex.org/W4285167337","doi":"https://doi.org/10.1109/tcss.2022.3179659","title":"Robustness Verification of Swish Neural Networks Embedded in Autonomous Driving Systems","display_name":"Robustness Verification of Swish Neural Networks Embedded in Autonomous Driving Systems","publication_year":2022,"publication_date":"2022-06-09","ids":{"openalex":"https://openalex.org/W4285167337","doi":"https://doi.org/10.1109/tcss.2022.3179659"},"language":"en","primary_location":{"id":"doi:10.1109/tcss.2022.3179659","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcss.2022.3179659","pdf_url":null,"source":{"id":"https://openalex.org/S2490693980","display_name":"IEEE Transactions on Computational Social Systems","issn_l":"2329-924X","issn":["2329-924X","2373-7476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computational Social Systems","raw_type":"journal-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/A5102797016","display_name":"Zhaodi Zhang","orcid":"https://orcid.org/0000-0002-0230-0301"},"institutions":[{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaodi Zhang","raw_affiliation_strings":["Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-0230-0301","affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100375018","display_name":"Jing Liu","orcid":"https://orcid.org/0000-0002-5347-8281"},"institutions":[{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Liu","raw_affiliation_strings":["Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-5347-8281","affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072386697","display_name":"Guanjun Liu","orcid":"https://orcid.org/0000-0002-7523-4827"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanjun Liu","raw_affiliation_strings":["Department of Computer Science, Tongji University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-7523-4827","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108025258","display_name":"Jiacun Wang","orcid":"https://orcid.org/0000-0001-6601-3515"},"institutions":[{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiacun Wang","raw_affiliation_strings":["Department of Computer Science and Software Engineering, Monmouth University, West Long Branch, NJ, USA"],"raw_orcid":"https://orcid.org/0000-0001-6601-3515","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Software Engineering, Monmouth University, West Long Branch, NJ, USA","institution_ids":["https://openalex.org/I141450709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070861971","display_name":"Yingsheng Zhang","orcid":"https://orcid.org/0000-0003-2520-3923"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"John Zhang","raw_affiliation_strings":["School of Electronic Engineering, Xidian University, Xi’an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Xidian University, Xi’an, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9861,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.95824481,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"10","issue":"4","first_page":"2041","last_page":"2050"},"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":0.9966999888420105,"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":0.9929999709129333,"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":0.7894726395606995},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6315079927444458},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.604505181312561},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.5269190669059753},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.5209566354751587},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.477627694606781},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.4407452344894409},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.43790048360824585},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4252963662147522},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3708442151546478},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.33694547414779663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18594878911972046}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7894726395606995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6315079927444458},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.604505181312561},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.5269190669059753},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.5209566354751587},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.477627694606781},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.4407452344894409},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.43790048360824585},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4252963662147522},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3708442151546478},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33694547414779663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18594878911972046},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcss.2022.3179659","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcss.2022.3179659","pdf_url":null,"source":{"id":"https://openalex.org/S2490693980","display_name":"IEEE Transactions on Computational Social Systems","issn_l":"2329-924X","issn":["2329-924X","2373-7476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computational Social Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4844286744","display_name":"\u4fe1\u606f\u7269\u7406\u7cfb\u7edf\u65f6\u7a7a\u5efa\u6a21\u4e0e\u9a8c\u8bc1\u5173\u952e\u95ee\u9898\u7814\u7a76","funder_award_id":"61972150","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5788605144","display_name":null,"funder_award_id":"62172299","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8592490694","display_name":null,"funder_award_id":"62032019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W1511137409","https://openalex.org/W1945616565","https://openalex.org/W2067713319","https://openalex.org/W2112796928","https://openalex.org/W2165073069","https://openalex.org/W2169239645","https://openalex.org/W2543296129","https://openalex.org/W2594877703","https://openalex.org/W2618530766","https://openalex.org/W2750384547","https://openalex.org/W2768915615","https://openalex.org/W2789524546","https://openalex.org/W2792149140","https://openalex.org/W2807040120","https://openalex.org/W2891698621","https://openalex.org/W2898963688","https://openalex.org/W2900153411","https://openalex.org/W2931526455","https://openalex.org/W2950029838","https://openalex.org/W2953384591","https://openalex.org/W2954002255","https://openalex.org/W2962692913","https://openalex.org/W2963054787","https://openalex.org/W2963440492","https://openalex.org/W2963496101","https://openalex.org/W2963857521","https://openalex.org/W2973064640","https://openalex.org/W2978814280","https://openalex.org/W2998586455","https://openalex.org/W3009006131","https://openalex.org/W3107328188","https://openalex.org/W3107892667","https://openalex.org/W3115764869","https://openalex.org/W3115877967","https://openalex.org/W3118198986","https://openalex.org/W3118608800","https://openalex.org/W3190651425","https://openalex.org/W4200028901","https://openalex.org/W4205286934","https://openalex.org/W4226119909","https://openalex.org/W4288359148","https://openalex.org/W4320930577","https://openalex.org/W6640425456","https://openalex.org/W6713134421","https://openalex.org/W6734921443","https://openalex.org/W6737380770","https://openalex.org/W6743688258","https://openalex.org/W6745950489","https://openalex.org/W6746023985","https://openalex.org/W6750745550","https://openalex.org/W6751834733","https://openalex.org/W6754543342","https://openalex.org/W6754681091","https://openalex.org/W6755480234","https://openalex.org/W6761839128","https://openalex.org/W6765694979","https://openalex.org/W6787972765","https://openalex.org/W6805231973"],"related_works":["https://openalex.org/W2032258609","https://openalex.org/W3024979424","https://openalex.org/W4283785902","https://openalex.org/W3032499992","https://openalex.org/W2041004593","https://openalex.org/W3134817226","https://openalex.org/W2895192346","https://openalex.org/W3110577345","https://openalex.org/W3136579697","https://openalex.org/W2811324119"],"abstract_inverted_index":{"With":[0],"the":[1,22,30,66,74,101,106,133,142,149,178,184,189,192,209],"applications":[2],"of":[3,26,69,73,103,152,213],"deep":[4],"learning":[5],"in":[6,33,42],"safety-critical":[7],"domains":[8],"such":[9,34,86],"as":[10,87],"autonomous":[11],"driving":[12],"systems":[13],"gaining":[14],"ground,":[15],"it":[16,202],"demands":[17],"rigorous":[18],"verification":[19,68,135],"to":[20,52,65,99,117,171,182],"guarantee":[21],"safety":[23],"and":[24,90,200,211],"reliability":[25],"corresponding":[27],"systems.":[28],"As":[29],"intelligent":[31],"component":[32],"systems,":[35],"neural":[36],"networks":[37,113],"(NNs)":[38],"must":[39],"be":[40],"robust":[41],"that":[43,59,81,188],"their":[44],"outputs":[45],"are":[46,62,77],"not":[47],"affected":[48],"by":[49],"minor":[50],"perturbation":[51],"inputs.":[53],"Many":[54],"research":[55],"studies":[56],"have":[57,114,118],"shown":[58],"formal":[60],"methods":[61],"effective":[63],"ways":[64],"robustness":[67,102,134,193],"NNs.":[70,127,205],"However,":[71],"most":[72],"existing":[75],"approaches":[76],"focused":[78],"on":[79,122],"NNs":[80,104],"contain":[82],"monotonic":[83],"activation":[84,108,163],"functions,":[85,164],"ReLU,":[88],"Tanh,":[89],"Sigmoid.":[91],"In":[92,128],"this":[93],"work,":[94],"we":[95,131,165,176],"propose":[96],"an":[97,153,167],"approach":[98],"verify":[100],"with":[105,203],"nonmonotonic":[107],"function":[109,151],"called":[110],"Swish.":[111],"Such":[112],"been":[115],"proved":[116],"a":[119,138,156,197],"better":[120],"performance":[121],"image":[123],"classification":[124],"than":[125],"other":[126],"our":[129,214],"approach,":[130],"turn":[132],"problem":[136,140],"into":[137,155],"constraint-solving":[139],"using":[141],"linear":[143,157],"approximation":[144,169],"technique.":[145],"We":[146,195],"first":[147],"model":[148,190],"affine":[150],"NN":[154],"constraint":[158,179],"model.":[159],"Then,":[160],"for":[161],"nonlinear":[162],"leverage":[166],"efficient":[168],"strategy":[170],"linearly":[172],"approximate":[173],"them.":[174],"Finally,":[175],"utilize":[177],"solver":[180],"gurobi":[181],"solve":[183],"model,":[185],"which":[186],"reveals":[187],"satisfies":[191],"property.":[194],"develop":[196],"prototype":[198],"tool":[199],"evaluate":[201],"open-sourced":[204],"Experimental":[206],"results":[207],"showed":[208],"effectiveness":[210],"efficiency":[212],"approach.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}