{"id":"https://openalex.org/W7156747052","doi":"https://doi.org/10.48550/arxiv.2604.24379","title":"Certified geometric robustness -- Super-DeepG","display_name":"Certified geometric robustness -- Super-DeepG","publication_year":2026,"publication_date":"2026-04-27","ids":{"openalex":"https://openalex.org/W7156747052","doi":"https://doi.org/10.48550/arxiv.2604.24379"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05601026v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05601026","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICCPS / HSCC 2026, CPS IoT Week, May 2026, Saint Malo (Palais du Grand Large), France","raw_type":"Conference papers"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-05601026","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134791372","display_name":"No\u00e9mie Cohen","orcid":null},"institutions":[{"id":"https://openalex.org/I33375025","display_name":"Airbus (India)","ror":"https://ror.org/05tw0wf88","country_code":"IN","type":"company","lineage":["https://openalex.org/I33375025","https://openalex.org/I4210121748"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Cohen, No\u00e9mie","raw_affiliation_strings":["Airbus CR\\&T"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Airbus CR\\&T","institution_ids":["https://openalex.org/I33375025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009303951","display_name":"M\u00e9lanie Ducoffe","orcid":"https://orcid.org/0000-0001-8440-8764"},"institutions":[{"id":"https://openalex.org/I33375025","display_name":"Airbus (India)","ror":"https://ror.org/05tw0wf88","country_code":"IN","type":"company","lineage":["https://openalex.org/I33375025","https://openalex.org/I4210121748"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ducoffe, M\u00e9lanie","raw_affiliation_strings":["Airbus CR\\&T"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Airbus CR\\&T","institution_ids":["https://openalex.org/I33375025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134799545","display_name":"Christophe Gabreau","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabreau, Christophe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081391554","display_name":"Claire Pagetti","orcid":"https://orcid.org/0000-0001-7265-1839"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pagetti, Claire","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055816251","display_name":"Xavier Pucel","orcid":"https://orcid.org/0000-0001-8747-0889"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pucel, Xavier","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5134791372"],"corresponding_institution_ids":["https://openalex.org/I33375025"],"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":0.6492000222206116,"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":0.6492000222206116,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.08889999985694885,"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":0.0575999990105629,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7627999782562256},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5928999781608582},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.45590001344680786},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.4551999866962433},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.310699999332428},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.29100000858306885},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.2872999906539917}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7627999782562256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6067000031471252},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5928999781608582},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4975999891757965},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4876999855041504},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.4551999866962433},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4440999925136566},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3052000105381012},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C49777392","wikidata":"https://www.wikidata.org/wiki/Q5535495","display_name":"Geometric networks","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2759000062942505},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C152279782","wikidata":"https://www.wikidata.org/wiki/Q13583542","display_name":"Shearing (physics)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.25110000371932983},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05601026v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05601026","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICCPS / HSCC 2026, CPS IoT Week, May 2026, Saint Malo (Palais du Grand Large), France","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.2604.24379","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.24379","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":"article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-05601026v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05601026","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICCPS / HSCC 2026, CPS IoT Week, May 2026, Saint Malo (Palais du Grand Large), France","raw_type":"Conference papers"},"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":{"Safety-critical":[0],"applications":[1],"are":[2,14],"required":[3,16],"to":[4,17,20,82],"perform":[5],"as":[6,25,92],"expected":[7],"in":[8,54],"normal":[9],"operations.":[10],"Image":[11],"processing":[12],"functions":[13],"often":[15],"be":[18],"insensitive":[19],"small":[21],"geometric":[22,41],"perturbations":[23,42],"such":[24],"rotation,":[26],"scaling,":[27],"shearing":[28],"or":[29],"translation.":[30],"This":[31],"paper":[32],"addresses":[33],"the":[34,51],"formal":[35],"verification":[36],"of":[37,79],"neural":[38],"networks":[39],"against":[40],"on":[43,96],"their":[44],"image":[45],"dataset.":[46],"Our":[47],"method":[48],"Super-DeepG":[49,72,89],"improves":[50],"reasoning":[52],"used":[53],"linear":[55],"relaxation":[56],"techniques":[57],"and":[58,61,76],"Lipschitz":[59],"optimization,":[60],"provides":[62],"an":[63,83,93],"implementation":[64],"that":[65,85],"leverages":[66],"GPU":[67],"hardware.":[68],"By":[69],"doing":[70],"so,":[71],"achieves":[73],"both":[74],"precision":[75],"computational":[77],"efficiency":[78],"robustness":[80],"certification,":[81],"extent":[84],"outperforms":[86],"prior":[87],"work.":[88],"is":[90],"shared":[91],"open-source":[94],"tool":[95],"GitHub.":[97]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2026-04-29T00:00:00"}