{"id":"https://openalex.org/W4409974447","doi":"https://doi.org/10.1007/978-3-031-90643-5_17","title":"Neural Network Verification with Branch-and-Bound for General Nonlinearities","display_name":"Neural Network Verification with Branch-and-Bound for General Nonlinearities","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409974447","doi":"https://doi.org/10.1007/978-3-031-90643-5_17"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-90643-5_17","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-90643-5_17","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90643-5_17.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":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90643-5_17.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022925266","display_name":"Zhouxing Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhouxing Shi","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101465329","display_name":"Qirui Jin","orcid":"https://orcid.org/0009-0002-0698-0903"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qirui Jin","raw_affiliation_strings":["University of Michigan, Ann Arbor, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075035644","display_name":"J. Zico Kolter","orcid":"https://orcid.org/0000-0002-8106-5759"},"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":"Zico Kolter","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016425387","display_name":"Suman Jana","orcid":"https://orcid.org/0000-0002-9850-2169"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Suman Jana","raw_affiliation_strings":["Columbia University, New York, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University, New York, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010841999","display_name":"Cho\u2010Jui Hsieh","orcid":"https://orcid.org/0000-0002-3520-9627"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cho-Jui Hsieh","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100356977","display_name":"Huan Zhang","orcid":"https://orcid.org/0000-0003-1265-2447"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huan Zhang","raw_affiliation_strings":["University of Illinois Urbana-Champaign, Champaign, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois Urbana-Champaign, Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5022925266"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":19.5938,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.99304025,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"315","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9988999962806702,"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":0.9988999962806702,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9180999994277954,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8512275815010071},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5721441507339478},{"id":"https://openalex.org/keywords/branch-predictor","display_name":"Branch predictor","score":0.5060579180717468},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.45698219537734985},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4322316646575928},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27976280450820923},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.22147449851036072}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8512275815010071},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5721441507339478},{"id":"https://openalex.org/C168522837","wikidata":"https://www.wikidata.org/wiki/Q679552","display_name":"Branch predictor","level":2,"score":0.5060579180717468},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.45698219537734985},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4322316646575928},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27976280450820923},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.22147449851036072}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-90643-5_17","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-90643-5_17","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90643-5_17.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:10.1007/978-3-031-90643-5_17","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-90643-5_17","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90643-5_17.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":[],"awards":[{"id":"https://openalex.org/G3812866752","display_name":"CAREER: Robustness Verification and Certified Defense for Machine Learning Models","funder_award_id":"2048280","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4943346501","display_name":"Collaborative Research: SLES: Verifying and Enforcing Safety Constraints in AI-based Sequential Generation","funder_award_id":"2331967","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G703596469","display_name":"Collaborative Research: SLES: Verifying and Enforcing Safety Constraints in AI-based Sequential Generation","funder_award_id":"2331966","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409974447.pdf","grobid_xml":"https://content.openalex.org/works/W4409974447.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1981276685","https://openalex.org/W2064675550","https://openalex.org/W2594877703","https://openalex.org/W2900153411","https://openalex.org/W2963998105","https://openalex.org/W2998709064","https://openalex.org/W3090972680","https://openalex.org/W3118608800","https://openalex.org/W3176708290","https://openalex.org/W3184424313","https://openalex.org/W3190898705","https://openalex.org/W3192314570","https://openalex.org/W3197827783","https://openalex.org/W3214321642","https://openalex.org/W4206840646","https://openalex.org/W4226119909","https://openalex.org/W4375852575","https://openalex.org/W4378977211","https://openalex.org/W4381571085","https://openalex.org/W4387698463","https://openalex.org/W4393160642","https://openalex.org/W6600129504","https://openalex.org/W6600195515"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2061007994","https://openalex.org/W2408643487","https://openalex.org/W4256090683","https://openalex.org/W2145546531","https://openalex.org/W1586172811","https://openalex.org/W2389267844","https://openalex.org/W3141821934"],"abstract_inverted_index":{"Abstract":[0],"Branch-and-bound":[1],"(BaB)":[2],"is":[3,184,236],"among":[4],"the":[5,85,118,162,187,213,216,219,234],"most":[6],"effective":[7],"techniques":[8],"for":[9,19,61,95,177,232],"neural":[10],"network":[11],"(NN)":[12],"verification.":[13,63],"However,":[14],"existing":[15],"works":[16],"on":[17,25,47,57,123],"BaB":[18,46],"NN":[20,62],"verification":[21,111,163,171],"have":[22],"mostly":[23],"focused":[24],"NNs":[26,52,131,145],"with":[27,53,112,132],"piecewise":[28],"linear":[29,58,78],"activations,":[30],"especially":[31],"ReLU":[32],"networks.":[33],"In":[34],"this":[35],"paper,":[36],"we":[37,70,99],"develop":[38],"a":[39,72,113,125],"general":[40,48,54,96,165],"framework,":[41],"named":[42],"GenBaB,":[43],"to":[44,50,68,82,101],"conduct":[45],"nonlinearities":[49],"verify":[51],"architectures,":[55],"based":[56],"bound":[59],"propagation":[60],"To":[64,90],"decide":[65,91],"which":[66,76,105],"neuron":[67],"branch,":[69],"design":[71],"new":[73],"branching":[74,93,103],"heuristic":[75],"leverages":[77],"bounds":[79],"as":[80,136,142,144,151],"shortcuts":[81],"efficiently":[83,108],"estimate":[84],"potential":[86],"improvement":[87],"after":[88],"branching.":[89],"nontrivial":[92],"points":[94],"nonlinear":[97,148,166],"functions,":[98],"propose":[100],"pre-optimize":[102],"points,":[104],"can":[106,242],"be":[107,243],"leveraged":[109],"during":[110],"lookup":[114],"table.":[115],"We":[116],"demonstrate":[117],"effectiveness":[119],"of":[120,128,164,186,215,223],"our":[121],"GenBaB":[122,183],"verifying":[124],"wide":[126],"range":[127],"NNs,":[129,175],"including":[130],"activation":[133],"functions":[134],"such":[135,150],"Sigmoid,":[137],"Tanh,":[138],"Sine":[139],"and":[140,155,169,218,229],"GeLU,":[141],"well":[143],"involving":[146],"multi-dimensional":[147],"operations":[149],"multiplications":[152],"in":[153],"LSTMs":[154],"Vision":[156],"Transformers.":[157],"Our":[158],"framework":[159],"also":[160],"allows":[161],"computation":[167],"graphs":[168],"enables":[170],"applications":[172],"beyond":[173],"simple":[174],"particularly":[176],"AC":[178],"Optimal":[179],"Power":[180],"Flow":[181],"(ACOPF).":[182],"part":[185],"latest":[188],"$$\\alpha":[189],",\\!\\beta":[190],"$$":[191],"<mml:math":[192,203],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[193,204],"<mml:mrow>":[194],"<mml:mi>\u03b1</mml:mi>":[195],"<mml:mo>,</mml:mo>":[196],"<mml:mspace/>":[197],"<mml:mi>\u03b2</mml:mi>":[198],"</mml:mrow>":[199],"</mml:math>":[200,209],"-CROWN":[201],"$$^6$$":[202],"<mml:msup>":[205],"<mml:mrow/>":[206],"<mml:mn>6</mml:mn>":[207],"</mml:msup>":[208],"(":[210],"https://github.com/Verified-Intelligence/alpha-beta-CROWN":[211],"),":[212],"winner":[214],"4th":[217],"5th":[220],"International":[221],"Verification":[222],"Neural":[224],"Networks":[225],"Competition":[226],"(VNN-COMP":[227],"2023":[228],"2024).":[230],"Code":[231],"reproducing":[233],"experiments":[235],"available":[237],"at":[238,245],"https://github.com/shizhouxing/GenBaB":[239],".":[240,247],"Appendices":[241],"found":[244],"http://arxiv.org/abs/2405.21063":[246]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}