{"id":"https://openalex.org/W4385768113","doi":"https://doi.org/10.24963/ijcai.2023/409","title":"Cardinality-Minimal Explanations for Monotonic Neural Networks","display_name":"Cardinality-Minimal Explanations for Monotonic Neural Networks","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4385768113","doi":"https://doi.org/10.24963/ijcai.2023/409"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2023/409","is_oa":true,"landing_page_url":"http://dx.doi.org/10.24963/ijcai.2023/409","pdf_url":"https://www.ijcai.org/proceedings/2023/0409.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.ijcai.org/proceedings/2023/0409.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037018920","display_name":"Ouns El Harzli","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ouns El Harzli","raw_affiliation_strings":["University of Oxford","Department of Computer Science, University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Computer Science, University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023732514","display_name":"Bernardo Cuenca Grau","orcid":"https://orcid.org/0000-0003-2909-5923"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bernardo Cuenca Grau","raw_affiliation_strings":["University of Oxford","Department of Computer Science, University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Computer Science, University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060350556","display_name":"Ian Horrocks","orcid":"https://orcid.org/0000-0002-2685-7462"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ian Horrocks","raw_affiliation_strings":["University of Oxford","Department of Computer Science, University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Computer Science, University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037018920"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.1728,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55846541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"3677","last_page":"3685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9998999834060669,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9998999834060669,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9986000061035156,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9919000267982483,"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/monotonic-function","display_name":"Monotonic function","score":0.8381941318511963},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.8305161595344543},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6277116537094116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5712275505065918},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5632782578468323},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4700806438922882},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.4367116689682007},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40222105383872986},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39555251598358154},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38518089056015015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3619096875190735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3484426736831665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11639612913131714},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07764977216720581}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8381941318511963},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8305161595344543},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6277116537094116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5712275505065918},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5632782578468323},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4700806438922882},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.4367116689682007},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40222105383872986},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39555251598358154},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38518089056015015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3619096875190735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3484426736831665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11639612913131714},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07764977216720581},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/ijcai.2023/409","is_oa":true,"landing_page_url":"http://dx.doi.org/10.24963/ijcai.2023/409","pdf_url":"https://www.ijcai.org/proceedings/2023/0409.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/ijcai.2023/409","is_oa":true,"landing_page_url":"http://dx.doi.org/10.24963/ijcai.2023/409","pdf_url":"https://www.ijcai.org/proceedings/2023/0409.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3253514882","display_name":"ConCur: Knowledge Base Construction and Curation","funder_award_id":"EP/V050869/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5652537686","display_name":"UK FIRES: Locating Resource Efficiency at the heart of Future Industrial Strategy in the UK","funder_award_id":"EP/S019111/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G667038190","display_name":"OASIS: Ontology Reasoning over Frequently-changing and Streaming Data","funder_award_id":"EP/S032347/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7097328358","display_name":null,"funder_award_id":"EP/S019111/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7351134993","display_name":null,"funder_award_id":"EP/S032347/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320332195","display_name":"Samsung","ror":"https://ror.org/04w3jy968"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4385768113.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W104441265","https://openalex.org/W1522301498","https://openalex.org/W1787224781","https://openalex.org/W1922655562","https://openalex.org/W2008279136","https://openalex.org/W2069773274","https://openalex.org/W2076063813","https://openalex.org/W2108030384","https://openalex.org/W2128865943","https://openalex.org/W2163605009","https://openalex.org/W2195388612","https://openalex.org/W2257979135","https://openalex.org/W2594633041","https://openalex.org/W2597603852","https://openalex.org/W2605409611","https://openalex.org/W2765813195","https://openalex.org/W2789209926","https://openalex.org/W2950690147","https://openalex.org/W2953073956","https://openalex.org/W2962851944","https://openalex.org/W2962936809","https://openalex.org/W2963420481","https://openalex.org/W2963715038","https://openalex.org/W2963971242","https://openalex.org/W2964359568","https://openalex.org/W3081335478","https://openalex.org/W3088830384","https://openalex.org/W3094592118","https://openalex.org/W3097993002","https://openalex.org/W3121385025","https://openalex.org/W3166668003","https://openalex.org/W3179413940","https://openalex.org/W3187997433","https://openalex.org/W3190685737","https://openalex.org/W3199717448","https://openalex.org/W3208478805","https://openalex.org/W4252440002","https://openalex.org/W4283820034","https://openalex.org/W4287331425","https://openalex.org/W4288046512","https://openalex.org/W4288347287","https://openalex.org/W4293507378","https://openalex.org/W4295312788","https://openalex.org/W4298061300","https://openalex.org/W4367281679"],"related_works":["https://openalex.org/W2009727205","https://openalex.org/W2081864705","https://openalex.org/W4321174801","https://openalex.org/W2300851791","https://openalex.org/W2417049975","https://openalex.org/W2238407353","https://openalex.org/W2390465610","https://openalex.org/W2044841127","https://openalex.org/W1996226968","https://openalex.org/W2027961552"],"abstract_inverted_index":{"In":[0,60],"recent":[1],"years,":[2],"there":[3],"has":[4],"been":[5],"increasing":[6],"interest":[7],"in":[8,93],"explanation":[9],"methods":[10],"for":[11,38],"neural":[12,73],"model":[13],"predictions":[14],"that":[15,35,89,105],"offer":[16],"precise":[17],"formal":[18],"guarantees.":[19],"These":[20],"include":[21],"abductive":[22],"(respectively,":[23,44],"contrastive)":[24],"methods,":[25],"which":[26],"aim":[27],"to":[28,42,45,57],"compute":[29],"minimal":[30],"subsets":[31],"of":[32,98,121],"input":[33],"features":[34],"are":[36,109],"sufficient":[37],"a":[39,47,76],"given":[40,48],"prediction":[41],"hold":[43],"change":[46],"prediction).":[49],"The":[50],"corresponding":[51],"decision":[52,82],"problems":[53,83],"are,":[54],"however,":[55],"known":[56],"be":[58,68],"intractable.":[59],"this":[61],"paper,":[62],"we":[63,86,102],"investigate":[64],"whether":[65],"tractability":[66],"can":[67,87],"regained":[69],"by":[70,96],"focusing":[71],"on":[72],"models":[74],"implementing":[75],"monotonic":[77],"function.":[78],"Although":[79],"the":[80,106],"relevant":[81],"remain":[84],"intractable,":[85],"show":[88],"they":[90],"become":[91],"solvable":[92],"polynomial":[94],"time":[95],"means":[97],"greedy":[99],"algorithms":[100],"if":[101],"additionally":[103],"assume":[104],"activation":[107],"functions":[108],"continuous":[110],"everywhere":[111],"and":[112],"differentiable":[113],"almost":[114],"everywhere.":[115],"Our":[116],"experiments":[117],"suggest":[118],"favourable":[119],"performance":[120],"our":[122],"algorithms.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}