{"id":"https://openalex.org/W4289643732","doi":"https://doi.org/10.1109/tnnls.2022.3190820","title":"Probabilistic Neural\u2013Symbolic Models With Inductive Posterior Constraints","display_name":"Probabilistic Neural\u2013Symbolic Models With Inductive Posterior Constraints","publication_year":2022,"publication_date":"2022-08-05","ids":{"openalex":"https://openalex.org/W4289643732","doi":"https://doi.org/10.1109/tnnls.2022.3190820","pmid":"https://pubmed.ncbi.nlm.nih.gov/35914034"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2022.3190820","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3190820","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101514073","display_name":"Ke Su","orcid":"https://orcid.org/0000-0001-8110-9486"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ke Su","raw_affiliation_strings":["Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035606234","display_name":"Hang Su","orcid":"https://orcid.org/0000-0003-4889-1669"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hang Su","raw_affiliation_strings":["Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China","Pazhou Laboratory (Huangpu), Guangzhou, China","Peng Cheng Laboratory, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Pazhou Laboratory (Huangpu), Guangzhou, China","institution_ids":[]},{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072905534","display_name":"Chongxuan Li","orcid":"https://orcid.org/0000-0002-0912-9076"},"institutions":[{"id":"https://openalex.org/I4210096250","display_name":"Beijing Institute of Big Data Research","ror":"https://ror.org/00s1sz824","country_code":"CN","type":"facility","lineage":["https://openalex.org/I20231570","https://openalex.org/I37796252","https://openalex.org/I4210096250"]},{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chongxuan Li","raw_affiliation_strings":["Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China","Beijing Key Laboratory of Big Data Management and Analysis Methods, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]},{"raw_affiliation_string":"Beijing Key Laboratory of Big Data Management and Analysis Methods, Beijing, China","institution_ids":["https://openalex.org/I4210096250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100606995","display_name":"Jun Zhu","orcid":"https://orcid.org/0000-0002-6254-2388"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Zhu","raw_affiliation_strings":["Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China","Peng Cheng Laboratory, Shenzhen, China","Pazhou Laboratory (Huangpu), Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]},{"raw_affiliation_string":"Pazhou Laboratory (Huangpu), Guangzhou, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100335188","display_name":"Bo Zhang","orcid":"https://orcid.org/0009-0005-2722-8990"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Zhang","raw_affiliation_strings":["Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, THBI Laboratory, Tsinghua-Bosch Joint ML Center, Institute for AI, and the BNRist Center, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101514073"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.1019,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.3798812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"2","first_page":"2667","last_page":"2679"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9994999766349792,"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":0.9940000176429749,"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/computer-science","display_name":"Computer science","score":0.7587255239486694},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.700092077255249},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6624271869659424},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6388359069824219},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5383034944534302},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5279147624969482},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.510019838809967},{"id":"https://openalex.org/keywords/domain-knowledge","display_name":"Domain knowledge","score":0.47478339076042175},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4191184937953949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.11902818083763123}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7587255239486694},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.700092077255249},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6624271869659424},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6388359069824219},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5383034944534302},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5279147624969482},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.510019838809967},{"id":"https://openalex.org/C207685749","wikidata":"https://www.wikidata.org/wiki/Q2088941","display_name":"Domain knowledge","level":2,"score":0.47478339076042175},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4191184937953949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.11902818083763123},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2022.3190820","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3190820","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:35914034","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35914034","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G162864083","display_name":null,"funder_award_id":"U19A2081","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1948779041","display_name":null,"funder_award_id":"62076147","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2873699935","display_name":null,"funder_award_id":"2021YFB2701000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3763772386","display_name":null,"funder_award_id":"2020AAA0106302","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4381173361","display_name":null,"funder_award_id":"2020AAA0104304","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5372072380","display_name":null,"funder_award_id":"U1811461","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5379697419","display_name":null,"funder_award_id":"62061136001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5777954143","display_name":null,"funder_award_id":"61972224","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5875539830","display_name":null,"funder_award_id":"2017YFA0700904","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6645987955","display_name":null,"funder_award_id":"U19B2034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7024251178","display_name":null,"funder_award_id":"2020AAA0106000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7627358037","display_name":null,"funder_award_id":"62076145","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8884159131","display_name":null,"funder_award_id":"JQ19016","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322392","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W162608378","https://openalex.org/W1522301498","https://openalex.org/W1923184257","https://openalex.org/W1983164551","https://openalex.org/W2055986305","https://openalex.org/W2099972257","https://openalex.org/W2108598243","https://openalex.org/W2115763357","https://openalex.org/W2560730294","https://openalex.org/W2561715562","https://openalex.org/W2793546384","https://openalex.org/W2804180102","https://openalex.org/W2884093133","https://openalex.org/W2892051617","https://openalex.org/W2899771611","https://openalex.org/W2963143606","https://openalex.org/W2963224792","https://openalex.org/W2963466731","https://openalex.org/W2963641944","https://openalex.org/W2963690694","https://openalex.org/W2963938081","https://openalex.org/W2964105864","https://openalex.org/W2964118342","https://openalex.org/W2964138017","https://openalex.org/W2982373234","https://openalex.org/W3005742798","https://openalex.org/W3010865323","https://openalex.org/W3042061900","https://openalex.org/W3099455966","https://openalex.org/W3099849198","https://openalex.org/W3113149630","https://openalex.org/W3117577445","https://openalex.org/W3176187895","https://openalex.org/W4288023855","https://openalex.org/W6631190155","https://openalex.org/W6677106874","https://openalex.org/W6682833265","https://openalex.org/W6682991711","https://openalex.org/W6683408601","https://openalex.org/W6713693865","https://openalex.org/W6738893770","https://openalex.org/W6739901393","https://openalex.org/W6751569023","https://openalex.org/W6753027577","https://openalex.org/W6754408018","https://openalex.org/W6754944153","https://openalex.org/W6755002340","https://openalex.org/W6756040250","https://openalex.org/W6756222820","https://openalex.org/W6757812085","https://openalex.org/W6758488800","https://openalex.org/W6767094118","https://openalex.org/W6767328352","https://openalex.org/W6770346413","https://openalex.org/W6771084333","https://openalex.org/W6773631536","https://openalex.org/W6780562648"],"related_works":["https://openalex.org/W2905433371","https://openalex.org/W2888392564","https://openalex.org/W4310278675","https://openalex.org/W4388422664","https://openalex.org/W4390569940","https://openalex.org/W2368237856","https://openalex.org/W1583422155","https://openalex.org/W1649619740","https://openalex.org/W3213252596","https://openalex.org/W2165071883"],"abstract_inverted_index":{"Neural-symbolic":[0],"models":[1,31,114],"provide":[2],"a":[3,133],"powerful":[4],"tool":[5],"to":[6,52,88,100,131,166],"tackle":[7],"complex":[8],"visual":[9,24],"reasoning":[10,18,42,157,183],"tasks":[11],"by":[12,92],"combining":[13],"symbolic":[14,55,83],"program":[15],"execution":[16],"for":[17,23],"and":[19,40,73,185,190],"deep":[20],"representation":[21],"learning":[22,108],"recognition.":[25],"A":[26],"probabilistic":[27,111],"formulation":[28],"of":[29,60,81,110],"such":[30,82],"with":[32,44,70],"stochastic":[33],"latent":[34],"variables":[35],"can":[36,162],"obtain":[37],"an":[38,67,86],"interpretable":[39],"legible":[41],"system":[43],"less":[45],"supervision.":[46],"However,":[47],"it":[48,64],"is":[49,129],"still":[50],"nontrivial":[51],"generate":[53],"reasonable":[54],"structures":[56,84],"without":[57],"the":[58,77,79,102,107,121,137,159],"guidance":[59],"domain":[61,93,104,151],"knowledge,":[62],"since":[63],"generally":[65],"involves":[66],"optimization":[68],"problem":[69],"both":[71],"continuous":[72],"discrete":[74],"variables.":[75],"Despite":[76],"challenges,":[78],"interpretability":[80],"provides":[85],"interface":[87],"regularize":[89,120],"their":[90],"generation":[91,139],"knowledge.":[94,152],"In":[95,124],"this":[96,125],"article,":[97],"we":[98],"propose":[99],"incorporate":[101],"available":[103],"knowledge":[105],"into":[106],"process":[109,140],"neural-symbolic":[112],"(PNS)":[113],"via":[115],"posterior":[116,160],"constraints":[117,161],"that":[118,174],"directly":[119],"structure":[122,138],"posterior.":[123],"way,":[126],"our":[127,175],"model":[128],"able":[130],"identify":[132],"middle":[134],"point":[135],"where":[136,158],"mainly":[141],"learns":[142],"from":[143,150],"data":[144,191],"but":[145],"also":[146],"selectively":[147],"borrows":[148],"information":[149],"We":[153],"further":[154],"present":[155],"inductive":[156],"be":[163],"automatically":[164],"reweighted":[165],"handle":[167],"noisy":[168],"annotations.":[169],"The":[170],"experimental":[171],"results":[172],"show":[173],"method":[176],"achieves":[177],"state-of-the-art":[178],"performance":[179],"on":[180],"major":[181],"abstract":[182],"datasets":[184],"enjoys":[186],"good":[187],"generalization":[188],"capability":[189],"efficiency.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
