{"id":"https://openalex.org/W7170153675","doi":"https://doi.org/10.1007/978-3-032-32526-6_24","title":"ATKVerifier: Adaptive Top-K Constraints for\u00a0Tighter Verification of\u00a0Semantic Segmentation Networks","display_name":"ATKVerifier: Adaptive Top-K Constraints for\u00a0Tighter Verification of\u00a0Semantic Segmentation Networks","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7170153675","doi":"https://doi.org/10.1007/978-3-032-32526-6_24"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-32526-6_24","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-32526-6_24","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-32526-6_24.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/10.1007/978-3-032-32526-6_24.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100644814","display_name":"Ying Liu","orcid":"https://orcid.org/0000-0002-8951-2648"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuehao Liu","raw_affiliation_strings":["School of Computer Science and Technology, Xidian University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143475164","display_name":"Cong Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cong Tian","raw_affiliation_strings":["School of Computer Science and Technology, Xidian University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136466952","display_name":"Y H Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108461","display_name":"Kingsoft (China)","ror":"https://ror.org/01stnfn33","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210108461"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yansong Dong","raw_affiliation_strings":["KylinSoft Co., Ltd., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KylinSoft Co., Ltd., Beijing, China","institution_ids":["https://openalex.org/I4210108461"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143524010","display_name":"Liang Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Zhao","raw_affiliation_strings":["School of Computer Science and Technology, Xidian University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085945118","display_name":"Chao Huang","orcid":"https://orcid.org/0000-0003-4974-2649"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Huang","raw_affiliation_strings":["School of Computer Science and Technology, Xidian University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100720713","display_name":"Wensheng Wang","orcid":"https://orcid.org/0000-0002-8842-3432"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wensheng Wang","raw_affiliation_strings":["School of Computer Science and Technology, Xidian University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5143475164"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"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":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"504","last_page":"526"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.633899986743927},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6011999845504761},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.47279998660087585},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47119998931884766},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.4246000051498413},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4077000021934509},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.39800000190734863},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.3628999888896942},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.35409998893737793}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8528000116348267},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.633899986743927},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6011999845504761},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4959000051021576},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.4246000051498413},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41530001163482666},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.39800000190734863},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32350000739097595},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C27511587","wikidata":"https://www.wikidata.org/wiki/Q2178623","display_name":"Spatial relation","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-32526-6_24","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-32526-6_24","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-32526-6_24.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:10.1007/978-3-032-32526-6_24","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-32526-6_24","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-32526-6_24.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/G4041341759","display_name":null,"funder_award_id":"62192734","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7170153675.pdf","grobid_xml":"https://content.openalex.org/works/W7170153675.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1901129140","https://openalex.org/W1903029394","https://openalex.org/W2043100293","https://openalex.org/W2150066425","https://openalex.org/W2412782625","https://openalex.org/W2560023338","https://openalex.org/W2592929672","https://openalex.org/W2594877703","https://openalex.org/W2604505099","https://openalex.org/W2721006554","https://openalex.org/W2794609696","https://openalex.org/W2898963688","https://openalex.org/W2900153411","https://openalex.org/W2950048339","https://openalex.org/W2957311447","https://openalex.org/W2963054787","https://openalex.org/W2963150697","https://openalex.org/W2963881378","https://openalex.org/W2964097310","https://openalex.org/W2974147052","https://openalex.org/W3046272654","https://openalex.org/W3046662910","https://openalex.org/W3186627997","https://openalex.org/W4206840646","https://openalex.org/W4293580221","https://openalex.org/W4293846201","https://openalex.org/W4301187031","https://openalex.org/W4381571085"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Formal":[1],"verification":[2,22,50],"of":[3,134,192],"Semantic":[4],"Segmentation":[5],"Networks":[6],"is":[7],"challenging":[8],"due":[9],"to":[10,117],"high-dimensional":[11],"output":[12],"spaces":[13],"and":[14,94,99,122],"cumulative":[15],"over-approximation":[16],"errors":[17],"in":[18,165],"deep":[19],"architectures.":[20],"Existing":[21],"methods":[23],"based":[24,90],"on":[25,55,91,140],"specific":[26],"Star-set":[27],"reachability":[28],"suffer":[29],"from":[30],"either":[31],"exponential":[32],"state":[33],"explosion":[34],"(exact":[35],"splitting)":[36],"or":[37],"excessive":[38],"conservativeness":[39],"(interval-based":[40],"relaxation).":[41],"In":[42],"this":[43],"work,":[44],"we":[45],"present":[46],"ATKVerifier":[47,186],",":[48],"a":[49,127],"framework":[51,75],"for":[52],"SSNs":[53],"operating":[54],"an":[56,78,106],"abstract":[57],"domain":[58],"named":[59],"constrained-star":[60],"(C-star),":[61],"which":[62],"captures":[63],"spatial":[64,128],"dependencies":[65],"within":[66],"MaxPool":[67],"receptive":[68],"fields":[69],"through":[70,102],"explicit":[71],"predicate":[72],"constraints.":[73],"Our":[74],"features:":[76],"(1)":[77],"adaptive":[79,107],"top-K":[80],"lower":[81],"bound":[82,110],"mechanism":[83],"that":[84],"dynamically":[85],"encodes":[86],"K":[87],"potential":[88],"maximizers":[89],"layer":[92],"depth":[93],"interval":[95],"overlap,":[96],"balancing":[97],"precision":[98],"computational":[100],"cost":[101],"parameter-free":[103],"adaptation;":[104],"(2)":[105],"affine":[108],"upper":[109],"exploiting":[111],"linear":[112],"relationships":[113],"between":[114],"top":[115],"candidates":[116],"replace":[118],"conservative":[119],"constant":[120],"bounds;":[121],"(3)":[123],"region-level":[124],"completeness":[125],"(RLC),":[126],"robustness":[129],"metric":[130],"quantifying":[131],"the":[132,170,175,179,183],"integrity":[133],"verified":[135],"contiguous":[136],"object":[137],"regions.":[138],"Experiments":[139],"M2NIST":[141],"with":[142,174,178],"three":[143],"SSN":[144],"architectures":[145],"(16":[146],"$$\\sim":[147,157],"$$":[148,158],"<mml:math":[149,159],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[150,160],"<mml:mo>\u223c</mml:mo>":[151,161],"</mml:math>":[152,162],"24":[153],"layers)":[154],"demonstrate":[155],"8":[156],"25%":[163],"improvement":[164,176],"robust":[166],"Intersection-over-Union":[167],"(IoU)":[168],"over":[169],"ImageStar-based":[171],"NNV":[172],"baseline,":[173],"scaling":[177],"network\u2019s":[180],"depth.":[181],"For":[182],"24-layer":[184],"architecture,":[185],"achieves":[187],"59.2%":[188],"RLC":[189],"versus":[190],"43.8%":[191],"NNV,":[193],"certifying":[194],"35.2%":[195],"more":[196],"complete":[197],"semantic":[198],"objects.":[199]},"counts_by_year":[],"updated_date":"2026-07-25T05:54:39.514286","created_date":"2026-07-24T00:00:00"}