{"id":"https://openalex.org/W4221035791","doi":"https://doi.org/10.1007/s10994-022-06132-9","title":"Robustness verification of ReLU networks via quadratic programming","display_name":"Robustness verification of ReLU networks via quadratic programming","publication_year":2022,"publication_date":"2022-03-16","ids":{"openalex":"https://openalex.org/W4221035791","doi":"https://doi.org/10.1007/s10994-022-06132-9"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-022-06132-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-022-06132-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-022-06132-9.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"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":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10994-022-06132-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005276383","display_name":"Aleksei Kuvshinov","orcid":"https://orcid.org/0000-0003-3674-7010"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Aleksei Kuvshinov","raw_affiliation_strings":["Data Analytics and Machine Learning Group, Department of Informatics, Technical University of Munich, Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3674-7010","affiliations":[{"raw_affiliation_string":"Data Analytics and Machine Learning Group, Department of Informatics, Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074504351","display_name":"Stephan G\u00fcnnemann","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stephan G\u00fcnnemann","raw_affiliation_strings":["Data Analytics and Machine Learning Group, Department of Informatics, Technical University of Munich, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Analytics and Machine Learning Group, Department of Informatics, Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005276383"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":{"value":3290,"currency":"USD","value_usd":3290},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02083482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"111","issue":"7","first_page":"2407","last_page":"2433"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":1.0,"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":1.0,"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/T14117","display_name":"Integrated Circuits and Semiconductor Failure Analysis","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12122","display_name":"Physical Unclonable Functions (PUFs) and Hardware Security","score":0.9355000257492065,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/quadratic-programming","display_name":"Quadratic programming","score":0.6773487329483032},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.653184175491333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6451122760772705},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6000739336013794},{"id":"https://openalex.org/keywords/decision-boundary","display_name":"Decision boundary","score":0.5774115920066833},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.5590248703956604},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5023603439331055},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4992794990539551},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.48660051822662354},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43518805503845215},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42462843656539917},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.4241373538970947},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.38237497210502625},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.37077122926712036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25442594289779663}],"concepts":[{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.6773487329483032},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.653184175491333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6451122760772705},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6000739336013794},{"id":"https://openalex.org/C42023084","wikidata":"https://www.wikidata.org/wiki/Q5249231","display_name":"Decision boundary","level":3,"score":0.5774115920066833},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.5590248703956604},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5023603439331055},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4992794990539551},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.48660051822662354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43518805503845215},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42462843656539917},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.4241373538970947},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.38237497210502625},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.37077122926712036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25442594289779663},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10994-022-06132-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-022-06132-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-022-06132-9.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"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":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1763985","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1763985","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1784411","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1784411","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10994-022-06132-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-022-06132-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-022-06132-9.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"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":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7599999904632568,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221035791.pdf","grobid_xml":"https://content.openalex.org/works/W4221035791.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1945616565","https://openalex.org/W1981276685","https://openalex.org/W2180612164","https://openalex.org/W2594877703","https://openalex.org/W2612690371","https://openalex.org/W2618235498","https://openalex.org/W2750384547","https://openalex.org/W2785755647","https://openalex.org/W2786163515","https://openalex.org/W2789524546","https://openalex.org/W2791251367","https://openalex.org/W2799107510","https://openalex.org/W2801079363","https://openalex.org/W2891698621","https://openalex.org/W2892354372","https://openalex.org/W2896266676","https://openalex.org/W2917875722","https://openalex.org/W2924630351","https://openalex.org/W2963054787","https://openalex.org/W2963496101","https://openalex.org/W2963857521","https://openalex.org/W2965187570","https://openalex.org/W6637162671","https://openalex.org/W6719080892"],"related_works":["https://openalex.org/W3206492465","https://openalex.org/W2099480561","https://openalex.org/W1909324310","https://openalex.org/W2379251597","https://openalex.org/W3036464408","https://openalex.org/W1984255470","https://openalex.org/W2020990755","https://openalex.org/W1985181089","https://openalex.org/W2348400506","https://openalex.org/W3020857762"],"abstract_inverted_index":{"Abstract":[0],"Neural":[1],"networks":[2],"are":[3],"known":[4],"to":[5,8,24,55],"be":[6],"sensitive":[7],"adversarial":[9],"perturbations.":[10],"To":[11],"investigate":[12],"this":[13,40],"undesired":[14],"behavior":[15],"we":[16,42,47],"consider":[17],"the":[18,22,25,61,72],"problem":[19],"of":[20,71,94],"computing":[21],"distance":[23],"decision":[26],"boundary":[27],"(DtDB)":[28],"from":[29],"a":[30,34,44,49,57,68,75,91],"given":[31,76],"sample":[32],"for":[33],"deep":[35],"neural":[36],"net":[37],"classifier.":[38],"In":[39],"work":[41],"present":[43],"procedure":[45],"where":[46],"solve":[48],"convex":[50],"quadratic":[51],"programming":[52],"(QP)":[53],"task":[54],"obtain":[56],"lower":[58],"bound":[59,64],"on":[60],"DtDB.":[62],"This":[63],"is":[65],"used":[66],"as":[67],"robustness":[69],"certificate":[70],"classifier":[73],"around":[74],"sample.":[77],"We":[78],"show":[79],"that":[80],"our":[81],"approach":[82],"provides":[83],"better":[84],"or":[85],"competitive":[86],"results":[87],"in":[88],"comparison":[89],"with":[90],"wide":[92],"range":[93],"existing":[95],"techniques.":[96]},"counts_by_year":[],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}
