{"id":"https://openalex.org/W3032926390","doi":"https://doi.org/10.1145/3385412.3385986","title":"Learning Nonlinear Loop Invariants with Gated Continuous Logic Networks (Extended Version)","display_name":"Learning Nonlinear Loop Invariants with Gated Continuous Logic Networks (Extended Version)","publication_year":2020,"publication_date":"2020-03-17","ids":{"openalex":"https://openalex.org/W3032926390","doi":"https://doi.org/10.1145/3385412.3385986","mag":"3032926390"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2003.07959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.07959","pdf_url":"https://arxiv.org/pdf/2003.07959","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.07959","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yao, Jianan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yao, Jianan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ryan, Gabriel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ryan, Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Wong, Justin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wong, Justin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Jana, Suman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jana, Suman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Gu, Ronghui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gu, Ronghui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":38,"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/T10142","display_name":"Formal Methods in Verification","score":0.22910000383853912,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.22910000383853912,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.09449999779462814,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.08089999854564667,"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/nonlinear-system","display_name":"Nonlinear system","score":0.5480999946594238},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4715999960899353},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.4163999855518341},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.40369999408721924},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.3589000105857849},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.3441999852657318},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3352000117301941}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5480999946594238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48489999771118164},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4715999960899353},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.4163999855518341},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37779998779296875},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.3589000105857849},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.3441999852657318},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3125999867916107},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3095000088214874},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.30889999866485596},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28040000796318054},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2720000147819519},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26159998774528503}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:2003.07959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.07959","pdf_url":"https://arxiv.org/pdf/2003.07959","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.07959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.07959","pdf_url":"https://arxiv.org/pdf/2003.07959","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Verifying":[0],"real-world":[1],"programs":[2,16],"often":[3],"requires":[4],"inferring":[5],"loop":[6,35,51,108,154,193,202,213],"invariants":[7,52,132,214],"with":[8,119,229],"nonlinear":[9,50,107,192,201,212],"constraints.":[10],"This":[11],"is":[12,53],"especially":[13,41],"true":[14],"in":[15,250],"that":[17,141,159,197],"perform":[18,257],"many":[19],"numerical":[20],"operations,":[21],"such":[22],"as":[23],"control":[24],"systems":[25],"for":[26,34,68,93,180],"avionics":[27],"or":[28],"industrial":[29],"plants.":[30],"Recently,":[31],"data-driven":[32,47],"methods":[33,189],"invariant":[36,109,194],"inference":[37,48,195],"have":[38,265],"shown":[39],"promise,":[40],"on":[42,70,163,208,271],"linear":[43,252],"invariants.":[44,203],"However,":[45],"applying":[46],"to":[49,56,106,128,156],"challenging":[54],"due":[55],"the":[57,66,77,97,113,126,174,239,251],"large":[58,78,134],"numbers":[59,135],"of":[60,63,74,80,136,153,211,221,233,243,269],"and":[61,76,103,122,215,262],"magnitudes":[62],"high-order":[64],"terms,":[65],"potential":[67],"overfitting":[69,140],"a":[71,89,169,191,209,258,266,274],"small":[72],"number":[73],"samples,":[75],"space":[79],"possible":[81],"inequality":[82,184],"bounds.":[83,185],"In":[84],"this":[85],"paper,":[86],"we":[87,147],"introduce":[88,148],"new":[90,170],"neural":[91],"architecture":[92,118],"general":[94,131,200],"SMT":[95],"learning,":[96],"Gated":[98],"Continuous":[99,114],"Logic":[100,115],"Network":[101,116],"(G-CLN),":[102],"apply":[104],"it":[105,217],"learning.":[110],"G-CLNs":[111,244,264],"extend":[112],"(CLN)":[117],"gating":[120],"units":[121],"dropout,":[123],"which":[124],"allow":[125],"model":[127],"robustly":[129],"learn":[130,199],"over":[133,277],"terms.":[137],"To":[138],"address":[139],"arises":[142],"from":[143],"finite":[144],"program":[145],"sampling,":[146],"fractional":[149],"sampling---a":[150],"sound":[151],"relaxation":[152],"semantics":[155],"continuous":[157],"functions":[158],"facilitates":[160],"unbounded":[161],"sampling":[162],"real":[164],"domain.":[165],"We":[166,186,204,236,255],"additionally":[167],"design":[168],"CLN":[171,278],"activation":[172],"function,":[173],"Piecewise":[175],"Biased":[176],"Quadratic":[177],"Unit":[178],"(PBQU),":[179],"naturally":[181],"learning":[182,241],"tight":[183],"incorporate":[187],"these":[188],"into":[190],"system":[196,207],"can":[198],"evaluate":[205],"our":[206],"benchmark":[210],"show":[216,263],"solves":[218],"26":[219],"out":[220],"27":[222],"problems,":[223,273],"3":[224],"more":[225],"than":[226],"prior":[227],"work,":[228],"an":[230],"average":[231],"runtime":[232],"53.3":[234],"seconds.":[235],"further":[237],"demonstrate":[238],"generic":[240],"ability":[242],"by":[245],"solving":[246],"all":[247],"124":[248],"problems":[249],"Code2Inv":[253],"benchmark.":[254],"also":[256],"quantitative":[259],"stability":[260],"evaluation":[261],"convergence":[267],"rate":[268],"$97.5\\%$":[270],"quadratic":[272],"$39.2\\%$":[275],"improvement":[276],"models.":[279]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-03T06:15:21.484131","created_date":"2020-06-12T00:00:00"}