{"id":"https://openalex.org/W3122363971","doi":"https://doi.org/10.34727/2020/isbn.978-3-85448-042-6_20","title":"Parallelization Techniques for Verifying Neural Networks","display_name":"Parallelization Techniques for Verifying Neural Networks","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3122363971","doi":"https://doi.org/10.34727/2020/isbn.978-3-85448-042-6_20","mag":"3122363971"},"language":"en","primary_location":{"id":"pmh:oai:repositum.tuwien.at:20.500.12708/15516","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12708/15516","pdf_url":"http://hdl.handle.net/20.500.12708/15516","source":{"id":"https://openalex.org/S4306400494","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Inproceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/20.500.12708/15516","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100637734","display_name":"Haoze Wu","orcid":"https://orcid.org/0000-0002-5077-144X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wu, Haoze","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062208593","display_name":"Alex Ozdemir","orcid":"https://orcid.org/0000-0002-0181-6752"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ozdemir, Alex","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036219926","display_name":"Aleksandar Zelji\u0107","orcid":"https://orcid.org/0000-0003-0673-9327"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zeljic, Aleksandar","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036845773","display_name":"Kyle D. Julian","orcid":"https://orcid.org/0000-0002-6247-1874"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julian, Kyle","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051886672","display_name":"Ahmed Irfan","orcid":"https://orcid.org/0000-0001-7791-9021"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Irfan, Ahmed","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055334891","display_name":"Divya Gopinath","orcid":"https://orcid.org/0000-0002-4279-7420"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gopinath, Divya","raw_affiliation_strings":["NASA Ames, KBR Inc"],"affiliations":[{"raw_affiliation_string":"NASA Ames, KBR Inc","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051868950","display_name":"Sadjad Fouladi","orcid":"https://orcid.org/0000-0002-9451-1877"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fouladi, Sadjad","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044509944","display_name":"Guy Katz","orcid":"https://orcid.org/0000-0001-5292-801X"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Katz, Guy","raw_affiliation_strings":["[The Hebrew University of Jerusalem, Israel]"],"affiliations":[{"raw_affiliation_string":"[The Hebrew University of Jerusalem, Israel]","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053134485","display_name":"Corina S. P\u0103s\u0103reanu","orcid":"https://orcid.org/0000-0002-5579-6961"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pasareanu, Corina","raw_affiliation_strings":["Carnegie -Mellon University, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie -Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026961968","display_name":"Clark Barrett","orcid":"https://orcid.org/0000-0002-9522-3084"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Barrett, Clark","raw_affiliation_strings":["Stanford Univ USA"],"affiliations":[{"raw_affiliation_string":"Stanford Univ USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":["https://openalex.org/A5100637734"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":18,"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":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/T10142","display_name":"Formal Methods in Verification","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9937999844551086,"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/computer-science","display_name":"Computer science","score":0.8263161778450012},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6380782127380371},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6268922686576843},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5502455830574036},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5106082558631897},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5103902220726013},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.46847406029701233},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.46219804883003235},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4404727816581726},{"id":"https://openalex.org/keywords/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.43533411622047424},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.42697596549987793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3234729766845703},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26913291215896606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.09433692693710327}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8263161778450012},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6380782127380371},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6268922686576843},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5502455830574036},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5106082558631897},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5103902220726013},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46847406029701233},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.46219804883003235},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4404727816581726},{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.43533411622047424},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.42697596549987793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3234729766845703},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26913291215896606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.09433692693710327},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:repositum.tuwien.at:20.500.12708/15516","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12708/15516","pdf_url":"http://hdl.handle.net/20.500.12708/15516","source":{"id":"https://openalex.org/S4306400494","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Inproceedings"},{"id":"doi:10.34727/2020/isbn.978-3-85448-042-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.34727/2020/isbn.978-3-85448-042-6_20","pdf_url":null,"source":{"id":"https://openalex.org/S4306400493","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:repositum.tuwien.at:20.500.12708/15516","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12708/15516","pdf_url":"http://hdl.handle.net/20.500.12708/15516","source":{"id":"https://openalex.org/S4306400494","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Inproceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3122363971.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W128869332","https://openalex.org/W140733995","https://openalex.org/W1480909796","https://openalex.org/W1486132939","https://openalex.org/W1496529478","https://openalex.org/W1665214252","https://openalex.org/W2022846948","https://openalex.org/W2160815625","https://openalex.org/W2163605009","https://openalex.org/W2165073069","https://openalex.org/W2257979135","https://openalex.org/W2281633864","https://openalex.org/W2345876752","https://openalex.org/W2521776546","https://openalex.org/W2594877703","https://openalex.org/W2738841453","https://openalex.org/W2754537581","https://openalex.org/W2794609696","https://openalex.org/W2890472662","https://openalex.org/W2890660842","https://openalex.org/W2896500468","https://openalex.org/W2900153411","https://openalex.org/W2922172279","https://openalex.org/W2957311447","https://openalex.org/W2961684981","https://openalex.org/W2963054787","https://openalex.org/W2963542245","https://openalex.org/W2963673089","https://openalex.org/W2963735478","https://openalex.org/W2964153729","https://openalex.org/W2999818223"],"related_works":["https://openalex.org/W2594877703","https://openalex.org/W2543296129","https://openalex.org/W2957311447","https://openalex.org/W2963735478","https://openalex.org/W2794609696","https://openalex.org/W2807040120","https://openalex.org/W3140205966","https://openalex.org/W3096553286","https://openalex.org/W2565186948","https://openalex.org/W3008543419","https://openalex.org/W184631345","https://openalex.org/W1495104714","https://openalex.org/W1989788024","https://openalex.org/W3102123232","https://openalex.org/W2963563691","https://openalex.org/W2165312568","https://openalex.org/W1585632470","https://openalex.org/W2110228982","https://openalex.org/W2963473542","https://openalex.org/W2166794693"],"abstract_inverted_index":{"Inspired":[0],"by":[1],"recent":[2],"successes":[3],"of":[4,15,26,35,68,88,111],"parallel":[5],"techniques":[6,113],"for":[7,98],"solving":[8],"Boolean":[9],"satisfiability,":[10],"we":[11,54],"investigate":[12],"a":[13,32,75,79,93,127],"set":[14],"strategies":[16],"and":[17,22,45,49,78,117],"heuristics":[18],"to":[19],"leverage":[20],"parallelism":[21],"improve":[23],"the":[24,36,42,62,66,69,86,109],"scalability":[25],"neural":[27,100],"network":[28,101],"verification.":[29],"We":[30,73,90],"present":[31],"general":[33],"description":[34],"Split-and-Conquer":[37],"partitioning":[38,58],"algorithm,":[39],"implemented":[40],"within":[41],"Marabou":[43],"framework,":[44],"discuss":[46],"its":[47],"parameters":[48],"heuristic":[50,77,81],"choices.":[51],"In":[52],"particular,":[53],"explore":[55],"two":[56],"novel":[57],"strategies,":[59],"that":[60,82],"partition":[61],"input":[63],"space":[64],"or":[65],"phases":[67],"neuron":[70],"activations,":[71],"respectively.":[72],"introduce":[74,92],"branching":[76],"direction":[80],"are":[83],"based":[84,132],"on":[85,114],"notion":[87],"polarity.":[89],"also":[91,134],"highly":[94],"parallelizable":[95],"pre-processing":[96],"algorithm":[97,125],"simplifying":[99],"verification":[102],"problems.":[103],"An":[104],"extensive":[105],"experimental":[106],"evaluation":[107],"shows":[108,135],"benefit":[110],"these":[112],"both":[115],"existing":[116],"new":[118],"benchmarks.":[119],"A":[120],"preliminary":[121],"experiment":[122],"ultra-scaling":[123],"our":[124],"using":[126],"large":[128],"distributed":[129],"cloud":[130],"-":[131],"platform":[133],"promising":[136],"results.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
