{"id":"https://openalex.org/W4414978507","doi":"https://doi.org/10.1145/3763086","title":"Convex Hull Approximation for Activation Functions","display_name":"Convex Hull Approximation for Activation Functions","publication_year":2025,"publication_date":"2025-10-09","ids":{"openalex":"https://openalex.org/W4414978507","doi":"https://doi.org/10.1145/3763086"},"language":"en","primary_location":{"id":"doi:10.1145/3763086","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3763086","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1145/3763086","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021033946","display_name":"Zhongkui Ma","orcid":"https://orcid.org/0000-0002-2392-3751"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Zhongkui Ma","raw_affiliation_strings":["The University of Queensland, Brisbane, Australia"],"affiliations":[{"raw_affiliation_string":"The University of Queensland, Brisbane, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091939001","display_name":"Zihan Wang","orcid":"https://orcid.org/0000-0002-6536-2948"},"institutions":[{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I1292875679","display_name":"Commonwealth Scientific and Industrial Research Organisation","ror":"https://ror.org/03qn8fb07","country_code":"AU","type":"funder","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zihan Wang","raw_affiliation_strings":["CSIRO's Data61, Brisbane, Australia","The University of Queensland, Brisbane, Australia"],"affiliations":[{"raw_affiliation_string":"CSIRO's Data61, Brisbane, Australia","institution_ids":["https://openalex.org/I42894916","https://openalex.org/I1292875679"]},{"raw_affiliation_string":"The University of Queensland, Brisbane, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015858067","display_name":"Guangdong Bai","orcid":"https://orcid.org/0000-0002-6390-9890"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guangdong Bai","raw_affiliation_strings":["The University of Queensland, Brisbane, Australia"],"affiliations":[{"raw_affiliation_string":"The University of Queensland, Brisbane, Australia","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021033946"],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15390887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"OOPSLA2","first_page":"1007","last_page":"1033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9984999895095825,"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":0.9984999895095825,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9922999739646912,"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/robustness","display_name":"Robustness (evolution)","score":0.6320000290870667},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6018999814987183},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5547999739646912},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5394999980926514},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.487199991941452},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4724999964237213},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4693000018596649},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.41440001130104065}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6320000290870667},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6018999814987183},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5573999881744385},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5394999980926514},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5327000021934509},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.487199991941452},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.41440001130104065},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.37209999561309814},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.32760000228881836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.326200008392334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2937000095844269},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.28279998898506165},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2563000023365021},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.25220000743865967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3763086","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3763086","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3763086","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3763086","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W569478347","https://openalex.org/W1973033359","https://openalex.org/W2007339694","https://openalex.org/W2071094669","https://openalex.org/W2091045890","https://openalex.org/W2153504150","https://openalex.org/W2160815625","https://openalex.org/W2594877703","https://openalex.org/W2721006554","https://openalex.org/W2791251367","https://openalex.org/W2891698621","https://openalex.org/W2899663614","https://openalex.org/W2963285578","https://openalex.org/W3038078229","https://openalex.org/W3212827451","https://openalex.org/W4234356172","https://openalex.org/W4286609345","https://openalex.org/W4291238833","https://openalex.org/W4293580221","https://openalex.org/W4297775537","https://openalex.org/W4312838810","https://openalex.org/W4386006943","https://openalex.org/W4388510931","https://openalex.org/W4388511650","https://openalex.org/W4409657429","https://openalex.org/W7079142127"],"related_works":[],"abstract_inverted_index":{"The":[0,36],"wide":[1],"adoption":[2],"of":[3,18,33,39,225,292],"deep":[4],"learning":[5],"in":[6,24,28,76,106,145,231,247],"safety-critical":[7],"domains":[8],"has":[9,43,81],"driven":[10],"the":[11,16,30,40,143,146,156,162,180,223,257,268,290],"need":[12],"for":[13,92,111,128],"formally":[14],"verifying":[15],"robustness":[17],"neural":[19,240],"networks.":[20],"A":[21],"critical":[22],"challenge":[23],"this":[25,116,160],"endeavor":[26],"lies":[27],"addressing":[29],"inherent":[31],"non-linearity":[32],"activation":[34,41,113,129],"functions.":[35,114],"convex":[37,68],"hull":[38],"function":[42,130],"emerged":[44],"as":[45,49,96],"a":[46,103,239],"promising":[47],"solution,":[48],"it":[50,194,254,287],"effectively":[51],"tightens":[52],"variable":[53],"ranges":[54],"and":[55,73,98,201,209,266],"provides":[56],"multi-neuron":[57,183,269],"constraints,":[58],"which":[59,170],"together":[60],"enhance":[61],"verification":[62,248,259,291],"precision.":[63],"Given":[64],"that":[65],"constructing":[66,125,214],"exact":[67],"hulls":[69],"is":[70,135,164],"computationally":[71],"expensive":[72],"even":[74],"infeasible":[75],"most":[77],"cases,":[78],"existing":[79],"research":[80],"focused":[82],"on":[83,187,195],"over-approximating":[84,167],"them.":[85],"Several":[86],"ad-hoc":[87],"methods":[88],"have":[89],"been":[90],"devised":[91],"specific":[93],"functions":[94,153,189,197],"such":[95],"ReLU":[97],"Sigmoid.":[99],"Nonetheless,":[100],"there":[101],"remains":[102],"substantial":[104],"gap":[105],"developing":[107],"broadly":[108],"applicable":[109],"approaches":[110],"general":[112],"In":[115,159],"work,":[117],"we":[118],"propose":[119],"WraAct,":[120],"an":[121],"approach":[122],"to":[123,136,140,154,166,227,243,263,274],"efficiently":[124,173],"tight":[126],"over-approximations":[127],"hulls.":[131],"Its":[132],"core":[133],"idea":[134],"introduce":[137],"linear":[138],"constraints":[139,216],"smooth":[141],"out":[142],"fluctuations":[144],"target":[147],"function,":[148],"by":[149],"leveraging":[150],"double-linear-piece":[151],"(DLP)":[152],"simplify":[155],"local":[157],"geometry.":[158],"way,":[161],"problem":[163],"reduced":[165],"DLP":[168],"functions,":[169],"can":[171,221,288],"be":[172],"handled.":[174],"We":[175,234],"evaluate":[176,244],"WraAct":[177,192,237],"against":[178],"SBLM+PDDM,":[179],"state-of-the-art":[181],"(SOTA)":[182],"over-approximation":[184],"method":[185],"based":[186],"decompositing":[188],"into":[190,238],"segments.":[191],"outperforms":[193,267],"commonly-used":[196],"like":[198,282],"Sigmoid,":[199],"Tanh,":[200],"MaxPool,":[202],"offering":[203],"superior":[204],"efficiency":[205],"(average":[206,211,217],"400X":[207],"faster)":[208],"precision":[210],"150X)":[212],"while":[213],"fewer":[215],"50%":[218],"reduction).":[219],"It":[220],"complete":[222,289],"computation":[224],"up":[226,273],"8":[228],"input":[229],"dimensions":[230],"10":[232,262],"seconds.":[233],"also":[235],"integrate":[236],"network":[241],"verifier":[242,270],"its":[245],"capability":[246],"tasks.":[249],"On":[250,279],"100":[251],"benchmark":[252],"samples,":[253],"significantly":[255],"enhances":[256],"single-neuron":[258],"from":[260],"under":[261],"over":[264],"40,":[265],"PRIMA":[271],"with":[272,284],"additional":[275],"20":[276],"verified":[277],"samples.":[278],"large":[280],"networks":[281],"ResNets":[283],"22k":[285],"neurons,":[286],"one":[293,296],"sample":[294],"within":[295],"minute.":[297]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}