{"id":"https://openalex.org/W4296270209","doi":"https://doi.org/10.1145/3563212","title":"Precise Quantitative Analysis of Binarized Neural Networks: A BDD-based Approach","display_name":"Precise Quantitative Analysis of Binarized Neural Networks: A BDD-based Approach","publication_year":2022,"publication_date":"2022-09-10","ids":{"openalex":"https://openalex.org/W4296270209","doi":"https://doi.org/10.1145/3563212"},"language":"en","primary_location":{"id":"doi:10.1145/3563212","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3563212","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3563212","source":{"id":"https://openalex.org/S142627899","display_name":"ACM Transactions on Software Engineering and Methodology","issn_l":"1049-331X","issn":["1049-331X","1557-7392"],"is_oa":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Software Engineering and Methodology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3563212","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046247329","display_name":"Yedi Zhang","orcid":"https://orcid.org/0000-0003-1005-2114"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yedi Zhang","raw_affiliation_strings":["ShanghaiTech University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"ShanghaiTech University, Shanghai, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100631152","display_name":"Zhe Zhao","orcid":"https://orcid.org/0000-0003-4189-3258"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhe Zhao","raw_affiliation_strings":["ShanghaiTech University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"ShanghaiTech University, Shanghai, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010348592","display_name":"Guangke Chen","orcid":"https://orcid.org/0000-0001-8277-3119"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangke Chen","raw_affiliation_strings":["ShanghaiTech University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"ShanghaiTech University, Shanghai, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027425633","display_name":"Fu Song","orcid":"https://orcid.org/0000-0002-0581-2679"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fu Song","raw_affiliation_strings":["ShanghaiTech University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"ShanghaiTech University, Shanghai, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030747944","display_name":"Taolue Chen","orcid":"https://orcid.org/0000-0002-5993-1665"},"institutions":[{"id":"https://openalex.org/I98259816","display_name":"Birkbeck, University of London","ror":"https://ror.org/02mb95055","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Taolue Chen","raw_affiliation_strings":["Birkbeck, University of London, London, UK"],"affiliations":[{"raw_affiliation_string":"Birkbeck, University of London, London, UK","institution_ids":["https://openalex.org/I98259816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5046247329"],"corresponding_institution_ids":["https://openalex.org/I30809798"],"apc_list":null,"apc_paid":null,"fwci":0.9717,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.79853267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"32","issue":"3","first_page":"1","last_page":"51"},"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9901000261306763,"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/T11005","display_name":"Radiation Effects in Electronics","score":0.9344000220298767,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8237919807434082},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6019308567047119},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.51987624168396},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.48970773816108704},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.45984968543052673},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.42952775955200195},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42201653122901917},{"id":"https://openalex.org/keywords/binary-decision-diagram","display_name":"Binary decision diagram","score":0.41346603631973267}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8237919807434082},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6019308567047119},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.51987624168396},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.48970773816108704},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.45984968543052673},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.42952775955200195},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42201653122901917},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.41346603631973267},{"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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3563212","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3563212","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3563212","source":{"id":"https://openalex.org/S142627899","display_name":"ACM Transactions on Software Engineering and Methodology","issn_l":"1049-331X","issn":["1049-331X","1557-7392"],"is_oa":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Software Engineering and Methodology","raw_type":"journal-article"},{"id":"pmh:oai:eprints.bbk.ac.uk.oai2:52308","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.bbk.ac.uk/id/eprint/52308/8/52308.pdf","source":{"id":"https://openalex.org/S4306400466","display_name":"BIROn (Birkbeck, University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98259816","host_organization_name":"Birkbeck, University of London","host_organization_lineage":["https://openalex.org/I98259816"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":{"id":"doi:10.1145/3563212","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3563212","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3563212","source":{"id":"https://openalex.org/S142627899","display_name":"ACM Transactions on Software Engineering and Methodology","issn_l":"1049-331X","issn":["1049-331X","1557-7392"],"is_oa":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Software Engineering and Methodology","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7099999785423279,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G450653452","display_name":null,"funder_award_id":"62072309","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5509612950","display_name":null,"funder_award_id":"61872340","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5676270524","display_name":null,"funder_award_id":"2020AAA0107800","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G57223841","display_name":null,"funder_award_id":"62072309, 61872340","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7033253288","display_name":null,"funder_award_id":"Grants","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7761557567","display_name":null,"funder_award_id":"KFKT2022A03","funder_id":"https://openalex.org/F4320326895","funder_display_name":"State Key Laboratory of Novel Software Technology"},{"id":"https://openalex.org/G8863666567","display_name":null,"funder_award_id":"and No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324852","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760"},{"id":"https://openalex.org/F4320326895","display_name":"State Key Laboratory of Novel Software Technology","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4296270209.pdf","grobid_xml":"https://content.openalex.org/works/W4296270209.grobid-xml"},"referenced_works_count":99,"referenced_works":["https://openalex.org/W73507577","https://openalex.org/W178169250","https://openalex.org/W203949653","https://openalex.org/W1787224781","https://openalex.org/W1989445634","https://openalex.org/W2030224590","https://openalex.org/W2080267935","https://openalex.org/W2100659887","https://openalex.org/W2109731020","https://openalex.org/W2116758077","https://openalex.org/W2165073069","https://openalex.org/W2180612164","https://openalex.org/W2190212846","https://openalex.org/W2282821441","https://openalex.org/W2293768274","https://openalex.org/W2300242332","https://openalex.org/W2525936901","https://openalex.org/W2533800772","https://openalex.org/W2543296129","https://openalex.org/W2594877703","https://openalex.org/W2602856279","https://openalex.org/W2603766943","https://openalex.org/W2606462007","https://openalex.org/W2607662938","https://openalex.org/W2616028256","https://openalex.org/W2623381305","https://openalex.org/W2721006554","https://openalex.org/W2750384547","https://openalex.org/W2788645721","https://openalex.org/W2791251367","https://openalex.org/W2794609696","https://openalex.org/W2798302089","https://openalex.org/W2804337238","https://openalex.org/W2869036160","https://openalex.org/W2897652134","https://openalex.org/W2898868990","https://openalex.org/W2900153411","https://openalex.org/W2913668833","https://openalex.org/W2917325587","https://openalex.org/W2928747488","https://openalex.org/W2936674544","https://openalex.org/W2946149952","https://openalex.org/W2953796333","https://openalex.org/W2955171822","https://openalex.org/W2957311447","https://openalex.org/W2957905354","https://openalex.org/W2962692913","https://openalex.org/W2962938696","https://openalex.org/W2963054787","https://openalex.org/W2963208512","https://openalex.org/W2963327228","https://openalex.org/W2963353335","https://openalex.org/W2963600714","https://openalex.org/W2963673089","https://openalex.org/W2963857521","https://openalex.org/W2963913218","https://openalex.org/W2963983756","https://openalex.org/W2972713160","https://openalex.org/W2974147052","https://openalex.org/W2979997102","https://openalex.org/W2981639301","https://openalex.org/W2982540258","https://openalex.org/W2989358546","https://openalex.org/W3005807947","https://openalex.org/W3007157104","https://openalex.org/W3012981624","https://openalex.org/W3036286896","https://openalex.org/W3040611682","https://openalex.org/W3046662910","https://openalex.org/W3086166649","https://openalex.org/W3092751871","https://openalex.org/W3093029790","https://openalex.org/W3094683669","https://openalex.org/W3097661056","https://openalex.org/W3101609372","https://openalex.org/W3102139284","https://openalex.org/W3102458427","https://openalex.org/W3105155462","https://openalex.org/W3111730161","https://openalex.org/W3111743621","https://openalex.org/W3133894893","https://openalex.org/W3153453329","https://openalex.org/W3166180472","https://openalex.org/W3168587836","https://openalex.org/W3178864044","https://openalex.org/W3183549096","https://openalex.org/W3198662695","https://openalex.org/W4211137390","https://openalex.org/W4221157827","https://openalex.org/W4281951480","https://openalex.org/W4283836968","https://openalex.org/W4287552268","https://openalex.org/W4287605209","https://openalex.org/W4293861706","https://openalex.org/W4300021588","https://openalex.org/W4312770063","https://openalex.org/W4313563880","https://openalex.org/W6739575509","https://openalex.org/W6755797642"],"related_works":["https://openalex.org/W2390183607","https://openalex.org/W2122917767","https://openalex.org/W4300631294","https://openalex.org/W3196342125","https://openalex.org/W86917440","https://openalex.org/W1819373035","https://openalex.org/W4309131146","https://openalex.org/W2188215366","https://openalex.org/W197248315","https://openalex.org/W1974942814"],"abstract_inverted_index":{"As":[0],"a":[1,57,61,66,87,97,114,175,187,232],"new":[2,227],"programming":[3],"paradigm,":[4],"neural-network-based":[5],"machine":[6],"learning":[7,140],"has":[8],"expanded":[9],"its":[10],"application":[11],"to":[12,17,215],"many":[13,75],"real-world":[14],"problems.":[15],"Due":[16],"the":[18,126,199,203,208,226,250,283],"black-box":[19],"nature":[20],"of":[21,107,129,166,171,202,211,243,252,266,287],"neural":[22,62,108,123,131],"networks,":[23,109],"verifying":[24],"and":[25,149,194,240,274,285],"explaining":[26],"their":[27],"behavior":[28],"are":[29,36,219],"becoming":[30],"increasingly":[31],"important,":[32],"especially":[33],"when":[34],"they":[35,143],"deployed":[37],"in":[38,74,138,158,191,213],"safety-critical":[39],"applications.":[40],"Existing":[41],"verification":[42,106,170,193,234,273],"work":[43],"mostly":[44],"focuses":[45],"on":[46,225],"qualitative":[47,88],"verification,":[48],"which":[49,85,110,155,218],"asks":[50,111],"whether":[51],"there":[52],"exists":[53],"an":[54,79],"input":[55,81],"(in":[56],"specified":[58],"region)":[59],"for":[60,164,179,236,276],"network":[63],"such":[64,78],"that":[65],"property":[67,115],"(e.g.,":[68],"local":[69],"robustness)":[70],"is":[71,116,156],"violated.":[72,119],"However,":[73],"practical":[76],"applications,":[77],"(adversarial)":[80],"almost":[82],"surely":[83],"exists,":[84],"makes":[86],"answer":[89],"less":[90],"meaningful.":[91],"In":[92],"this":[93],"work,":[94],"we":[95,173,230,255],"study":[96],"more":[98,101],"interesting":[99],"yet":[100],"challenging":[102],"problem,":[103],"i.e.,":[104],"quantitative":[105,169,233,271],"how":[112],"often":[113],"satisfied":[117],"or":[118],"We":[120,263],"target":[121],"binarized":[122],"networks":[124],"(BNNs),":[125],"1-bit":[127],"quantization":[128],"general":[130],"networks.":[132],"BNNs":[133,181,214,237,244],"have":[134],"attracted":[135],"increasing":[136],"attention":[137],"deep":[139],"recently,":[141],"as":[142,182],"can":[144,245],"drastically":[145],"reduce":[146],"memory":[147],"storage":[148],"execution":[150],"time":[151],"with":[152],"bit-wise":[153],"operations,":[154],"crucial":[157],"recourse-constrained":[159],"scenarios,":[160],"e.g.,":[161],"embedded":[162],"devices":[163],"Internet":[165],"Things.":[167],"Toward":[168],"BNNs,":[172,204],"propose":[174],"novel":[176],"algorithmic":[177],"approach":[178],"encoding":[180,206],"Binary":[183],"Decision":[184],"Diagrams":[185],"(BDDs),":[186],"widely":[188],"studied":[189],"model":[190],"formal":[192],"knowledge":[195],"representation.":[196],"By":[197],"exploiting":[198],"internal":[200],"structure":[201],"our":[205,267,288],"translates":[207],"input-output":[209],"relation":[210],"blocks":[212],"cardinality":[216],"constraints,":[217],"then":[220],"encoded":[221],"by":[222,269],"BDDs.":[223],"Based":[224],"BDD":[228,253],"encoding,":[229,254],"develop":[231],"framework":[235,268],"where":[238],"precise":[239],"comprehensive":[241],"analysis":[242],"be":[246],"performed.":[247],"To":[248],"improve":[249],"scalability":[251],"also":[256],"investigate":[257],"parallelization":[258],"strategies":[259],"at":[260],"various":[261],"levels.":[262],"demonstrate":[264],"applications":[265],"providing":[270],"robustness":[272],"interpretability":[275],"BNNs.":[277],"An":[278],"extensive":[279],"experimental":[280],"evaluation":[281],"confirms":[282],"effectiveness":[284],"efficiency":[286],"approach.":[289]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
