{"id":"https://openalex.org/W2900153411","doi":"https://doi.org/10.1145/3290354","title":"An abstract domain for certifying neural networks","display_name":"An abstract domain for certifying neural networks","publication_year":2019,"publication_date":"2019-01-02","ids":{"openalex":"https://openalex.org/W2900153411","doi":"https://doi.org/10.1145/3290354","mag":"2900153411"},"language":"en","primary_location":{"id":"doi:10.1145/3290354","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3290354","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3290354","source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3290354","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100760604","display_name":"Gagandeep Singh","orcid":"https://orcid.org/0000-0002-9299-2961"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Gagandeep Singh","raw_affiliation_strings":["ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045044745","display_name":"Timon Gehr","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Timon Gehr","raw_affiliation_strings":["ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076407181","display_name":"Markus P\u00fcschel","orcid":"https://orcid.org/0000-0001-8834-8551"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Markus P\u00fcschel","raw_affiliation_strings":["ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069901599","display_name":"Martin Vechev","orcid":"https://orcid.org/0000-0002-0054-9568"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Martin Vechev","raw_affiliation_strings":["ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":48.6606,"has_fulltext":true,"cited_by_count":610,"citation_normalized_percentile":{"value":0.99864225,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"3","issue":"POPL","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998000264167786,"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":0.9998000264167786,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9922999739646912,"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/computer-science","display_name":"Computer science","score":0.776198148727417},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.606357991695404},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5949689149856567},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5917388796806335},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.565844714641571},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.5304020643234253},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.5234503149986267},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4372027516365051},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4353695213794708},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.42535579204559326},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.3686540424823761},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1432839035987854}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.776198148727417},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.606357991695404},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5949689149856567},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5917388796806335},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.565844714641571},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.5304020643234253},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.5234503149986267},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4372027516365051},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4353695213794708},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42535579204559326},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.3686540424823761},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1432839035987854},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":3,"locations":[{"id":"doi:10.1145/3290354","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3290354","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3290354","source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/390873","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/390873","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the ACM on Programming Languages, 3 (POPL)","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.3929/ethz-b-000390873","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000390873","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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-journal"}],"best_oa_location":{"id":"doi:10.1145/3290354","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3290354","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3290354","source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1032463596","display_name":"Making Program Analysis Fast","funder_award_id":"163117","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2900153411.pdf","grobid_xml":"https://content.openalex.org/works/W2900153411.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W178079818","https://openalex.org/W1883420340","https://openalex.org/W1932198206","https://openalex.org/W2044870852","https://openalex.org/W2112796928","https://openalex.org/W2114614628","https://openalex.org/W2132661148","https://openalex.org/W2137687977","https://openalex.org/W2179402106","https://openalex.org/W2342840547","https://openalex.org/W2395317528","https://openalex.org/W2432142698","https://openalex.org/W2566919497","https://openalex.org/W2594877703","https://openalex.org/W2616028256","https://openalex.org/W2757182288","https://openalex.org/W2766462876","https://openalex.org/W2768915615","https://openalex.org/W2774644650","https://openalex.org/W2775273147","https://openalex.org/W2780061171","https://openalex.org/W2786163515","https://openalex.org/W2789524546","https://openalex.org/W2794609696","https://openalex.org/W2798356176","https://openalex.org/W2799107510","https://openalex.org/W2803850896","https://openalex.org/W2898998338","https://openalex.org/W2963003451","https://openalex.org/W2963054787","https://openalex.org/W2963207607","https://openalex.org/W2963857521","https://openalex.org/W2964253222","https://openalex.org/W3118608800","https://openalex.org/W6603885988"],"related_works":["https://openalex.org/W4385957115","https://openalex.org/W2916043681","https://openalex.org/W2061372042","https://openalex.org/W3047779762","https://openalex.org/W1520030019","https://openalex.org/W2071654592","https://openalex.org/W2391438543","https://openalex.org/W2008231869","https://openalex.org/W2088157920","https://openalex.org/W2551069560"],"abstract_inverted_index":{"We":[0,65,107],"present":[1],"a":[2,22,70,79,115],"novel":[3],"method":[4,68],"for":[5,52,129],"scalable":[6],"and":[7,33,62,74,88],"precise":[8,98],"certification":[9],"of":[10,44,81,117,135],"deep":[11],"neural":[12,45,83],"networks.":[13,46,106],"The":[14],"key":[15],"technical":[16],"insight":[17],"behind":[18],"our":[19,67],"approach":[20],"is":[21,34,96,142],"new":[23,50],"abstract":[24,37],"domain":[25],"which":[26],"combines":[27],"floating":[28],"point":[29],"polyhedra":[30],"with":[31,36,114],"intervals":[32],"equipped":[35],"transformers":[38,51],"specifically":[39],"tailored":[40],"to":[41,104,111,127,144],"the":[42,55,130,133,136,139],"setting":[43],"Concretely,":[47],"we":[48],"introduce":[49],"affine":[53],"transforms,":[54],"rectified":[56],"linear":[57,152],"unit":[58],"(ReLU),":[59],"sigmoid,":[60],"tanh,":[61],"maxpool":[63],"functions.":[64],"implemented":[66],"in":[69],"system":[71],"called":[72],"DeepPoly":[73,95,113],"evaluated":[75],"it":[76],"extensively":[77],"on":[78,121],"range":[80],"datasets,":[82],"architectures":[84],"(including":[85],"defended":[86],"networks),":[87],"specifications.":[89],"Our":[90],"experimental":[91],"results":[92],"indicate":[93],"that":[94,150],"more":[97],"than":[99],"prior":[100],"work":[101],"while":[102],"scaling":[103],"large":[105],"also":[108],"show":[109],"how":[110],"combine":[112],"form":[116],"abstraction":[118],"refinement":[119],"based":[120],"trace":[122],"partitioning.":[123],"This":[124],"enables":[125],"us":[126],"prove,":[128],"first":[131],"time,":[132],"robustness":[134],"network":[137],"when":[138],"input":[140],"image":[141],"subjected":[143],"complex":[145],"perturbations":[146],"such":[147],"as":[148],"rotations":[149],"employ":[151],"interpolation.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":25},{"year":2025,"cited_by_count":70},{"year":2024,"cited_by_count":89},{"year":2023,"cited_by_count":120},{"year":2022,"cited_by_count":75},{"year":2021,"cited_by_count":117},{"year":2020,"cited_by_count":80},{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}
