{"id":"https://openalex.org/W4225813442","doi":"https://doi.org/10.1007/978-3-030-99524-9_8","title":"Efficient Neural Network Analysis with Sum-of-Infeasibilities","display_name":"Efficient Neural Network Analysis with Sum-of-Infeasibilities","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4225813442","doi":"https://doi.org/10.1007/978-3-030-99524-9_8"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-99524-9_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99524-9_8","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99524-9_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99524-9_8.pdf","any_repository_has_fulltext":false},"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":"Haoze Wu","raw_affiliation_strings":["Stanford University, Stanford, USA"],"raw_orcid":"https://orcid.org/0000-0002-5077-144X","affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, 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":"Aleksandar Zelji\u0107","raw_affiliation_strings":["Stanford University, Stanford, USA"],"raw_orcid":"https://orcid.org/0000-0003-0673-9327","affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, 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":"Guy Katz","raw_affiliation_strings":["The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":"https://orcid.org/0000-0001-5292-801X","affiliations":[{"raw_affiliation_string":"The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"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":"Clark Barrett","raw_affiliation_strings":["Stanford University, Stanford, USA"],"raw_orcid":"https://orcid.org/0000-0002-9522-3084","affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100637734"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":null,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"143","last_page":"163"},"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9872999787330627,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9854999780654907,"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":0.6686297059059143},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5213550329208374},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5010921955108643},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.46458083391189575},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.455486923456192},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4528946280479431},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4304681122303009},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.424960732460022},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41582614183425903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21097543835639954},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15457230806350708}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6686297059059143},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5213550329208374},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5010921955108643},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46458083391189575},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.455486923456192},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4528946280479431},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4304681122303009},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.424960732460022},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41582614183425903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21097543835639954},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15457230806350708},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-99524-9_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99524-9_8","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99524-9_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-99524-9_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99524-9_8","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99524-9_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"score":0.6499999761581421,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2494922147","display_name":null,"funder_award_id":"FA8750-18-C-0099","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4713059963","display_name":null,"funder_award_id":"FA8750","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G6352561560","display_name":"NSF-BSF:  SHF: Small: Certifiable Verification of Large Neural Networks","funder_award_id":"1814369","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225813442.pdf","grobid_xml":"https://content.openalex.org/works/W4225813442.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W621546036","https://openalex.org/W1971258090","https://openalex.org/W1981276685","https://openalex.org/W1996977322","https://openalex.org/W1999049191","https://openalex.org/W2032382981","https://openalex.org/W2108207895","https://openalex.org/W2117876524","https://openalex.org/W2135194391","https://openalex.org/W2160815625","https://openalex.org/W2257979135","https://openalex.org/W2543296129","https://openalex.org/W2594877703","https://openalex.org/W2794609696","https://openalex.org/W2900153411","https://openalex.org/W2901816197","https://openalex.org/W2910603373","https://openalex.org/W2936674544","https://openalex.org/W2957311447","https://openalex.org/W2962692913","https://openalex.org/W2963054787","https://openalex.org/W2963542245","https://openalex.org/W2963857521","https://openalex.org/W2963998105","https://openalex.org/W2998574230","https://openalex.org/W2998709064","https://openalex.org/W3043655933","https://openalex.org/W3046662910","https://openalex.org/W3105155462","https://openalex.org/W3115503695","https://openalex.org/W3184678361","https://openalex.org/W3192314570","https://openalex.org/W3196492090","https://openalex.org/W3205832376","https://openalex.org/W4250589301","https://openalex.org/W4299968636","https://openalex.org/W6600109629","https://openalex.org/W6600159499","https://openalex.org/W6601760687","https://openalex.org/W6601955380","https://openalex.org/W6969140880"],"related_works":["https://openalex.org/W2385263368","https://openalex.org/W2347422947","https://openalex.org/W2061292372","https://openalex.org/W328874995","https://openalex.org/W2353392568","https://openalex.org/W2377341410","https://openalex.org/W1454600515","https://openalex.org/W2005126053","https://openalex.org/W2988866178","https://openalex.org/W4387635768"],"abstract_inverted_index":{"Abstract":[0],"Inspired":[1],"by":[2,104,203],"sum-of-infeasibilities":[3],"methods":[4],"in":[5],"convex":[6,26,52,107],"optimization,":[7],"we":[8,34,166],"propose":[9,82],"a":[10,25,42,83,95,131,204],"novel":[11],"procedure":[12,100,108],"for":[13,146],"analyzing":[14],"verification":[15],"queries":[16],"on":[17],"neural":[18],"networks":[19],"with":[20,48,114,120],"piecewise-linear":[21],"activation":[22,32,39,77],"functions.":[23],"Given":[24],"relaxation":[27],"which":[28],"over-approximates":[29],"the":[30,36,51,60,76,90,106,117,128,158,161,172,181,199],"non-convex":[31],"functions,":[33],"encode":[35],"violations":[37],"of":[38,160,174],"functions":[40,78],"as":[41,59],"cost":[43,55],"function":[44],"and":[45,71,140,155],"optimize":[46],"it":[47,126,134,142],"respect":[49],"to":[50,58,87,94],"relaxation.":[53],"The":[54],"function,":[56],"referred":[57],"Sum-of-Infeasibilities":[61],"(SoI),":[62],"is":[63,69],"designed":[64],"so":[65],"that":[66,168,192],"its":[67],"minimum":[68],"zero":[70],"achieved":[72,103],"only":[73],"if":[74],"all":[75],"are":[79],"satisfied.":[80],"We":[81,189],"stochastic":[84],"procedure,":[85],",":[86],"efficiently":[88,196],"minimize":[89],"SoI.":[91],"An":[92,149],"extension":[93],"canonical":[96],"case-analysis-based":[97],"complete":[98,118,177,187],"search":[99,112,119,129,178],"can":[101,195],"be":[102],"replacing":[105],"executed":[109],"at":[110],"each":[111],"state":[113],".":[115],"Extending":[116],"achieves":[121],"multiple":[122],"simultaneous":[123],"goals:":[124],"1)":[125],"guides":[127],"towards":[130],"counter-example;":[132],"2)":[133],"enables":[135],"more":[136],"informed":[137],"branching":[138],"decisions;":[139],"3)":[141],"creates":[143],"additional":[144],"opportunities":[145],"bound":[147,201],"derivation.":[148],"extensive":[150],"evaluation":[151],"across":[152],"different":[153],"benchmarks":[154],"solvers":[156],"demonstrates":[157],"benefit":[159],"proposed":[162],"techniques.":[163],"In":[164],"particular,":[165],"demonstrate":[167],"SoI":[169],"significantly":[170],"improves":[171],"performance":[173],"an":[175],"existing":[176],"procedure.":[179],"Moreover,":[180],"SoI-based":[182],"implementation":[183],"outperforms":[184],"other":[185],"state-of-the-art":[186],"verifiers.":[188],"also":[190],"show":[191],"our":[193],"technique":[194],"improve":[197],"upon":[198],"perturbation":[200],"derived":[202],"recent":[205],"adversarial":[206],"attack":[207],"algorithm.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3}],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-10-10T00:00:00"}
