{"id":"https://openalex.org/W7084070768","doi":"https://doi.org/10.1109/tsp.2025.3615511","title":"Extracting Formulae in Many-Valued Logic From Deep Neural Networks","display_name":"Extracting Formulae in Many-Valued Logic From Deep Neural Networks","publication_year":2025,"publication_date":"2025-10-01","ids":{"openalex":"https://openalex.org/W7084070768","doi":"https://doi.org/10.1109/tsp.2025.3615511"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2025.3615511","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3615511","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tsp.2025.3615511","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yani Zhang","orcid":"https://orcid.org/0009-0007-3275-7939"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Yani Zhang","raw_affiliation_strings":["Chair for Mathematical Information Science, ETH Zurich, Zurich, Switzerland"],"raw_orcid":"https://orcid.org/0009-0007-3275-7939","affiliations":[{"raw_affiliation_string":"Chair for Mathematical Information Science, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":null,"display_name":"Helmut B\u00f6lcskei","orcid":"https://orcid.org/0000-0003-3047-5149"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Helmut B\u00f6lcskei","raw_affiliation_strings":["Chair for Mathematical Information Science, ETH Zurich, Zurich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-3047-5149","affiliations":[{"raw_affiliation_string":"Chair for Mathematical Information Science, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.44529959,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"74","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T13511","display_name":"Geodetic Measurements and Engineering Structures","score":0.29159998893737793,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13511","display_name":"Geodetic Measurements and Engineering Structures","score":0.29159998893737793,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14353","display_name":"Wireless Sensor Networks for Data Analysis","score":0.04639999940991402,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T13085","display_name":"Education, Psychology, and Social Research","score":0.03350000083446503,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.7512000203132629},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5857999920845032},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.546999990940094},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5309000015258789},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5031999945640564},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.45100000500679016},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4088999927043915},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3806000053882599}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7512000203132629},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5857999920845032},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.546999990940094},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5309000015258789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5217000246047974},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5092999935150146},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5031999945640564},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4772999882698059},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38190001249313354},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36250001192092896},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C2987117450","wikidata":"https://www.wikidata.org/wiki/Q275603","display_name":"Logic program","level":3,"score":0.25859999656677246},{"id":"https://openalex.org/C81409106","wikidata":"https://www.wikidata.org/wiki/Q76505","display_name":"Combinational logic","level":3,"score":0.2578999996185303}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2025.3615511","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3615511","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/tsp.2025.3615511","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3615511","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W151233894","https://openalex.org/W1566552629","https://openalex.org/W1981179930","https://openalex.org/W1989632075","https://openalex.org/W1993580992","https://openalex.org/W2012072427","https://openalex.org/W2013088431","https://openalex.org/W2042194938","https://openalex.org/W2043639987","https://openalex.org/W2054457993","https://openalex.org/W2060794945","https://openalex.org/W2080126541","https://openalex.org/W2084369441","https://openalex.org/W2089947415","https://openalex.org/W2110503949","https://openalex.org/W2119899470","https://openalex.org/W2511261638","https://openalex.org/W2528305538","https://openalex.org/W2749772809","https://openalex.org/W3102754027","https://openalex.org/W3133816032","https://openalex.org/W4254853073","https://openalex.org/W4298227433"],"related_works":[],"abstract_inverted_index":{"We":[0,116],"propose":[1,84],"a":[2,126],"new":[3],"perspective":[4],"on":[5],"deep":[6,38,123],"rectified":[7],"linear":[8],"unit":[9],"(ReLU)":[10],"networks,":[11],"namely":[12],"as":[13],"circuit":[14],"counterparts":[15],"of":[16,23,122],"\u0141ukasiewicz":[17],"infinite-valued":[18],"logic\u2014a":[19],"many-valued":[20],"(MV)":[21],"generalization":[22],"Boolean":[24],"logic.":[25],"An":[26],"algorithm<sup":[27],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[28],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sup>":[29],"for":[30,66,76],"extracting":[31],"formulae":[32,74,110],"in":[33,49,57,70,96,103],"MV":[34,71],"logic":[35,72,128],"from":[36,125],"(trained)":[37],"ReLU":[39],"networks":[40,124],"is":[41,91],"presented.":[42],"The":[43],"algorithm":[44,82],"respects":[45],"the":[46,58,62,77,81,104,112,119],"network":[47],"topology,":[48],"particular":[50],"compositionality,":[51],"thereby":[52],"honoring":[53],"algebraic":[54],"information":[55],"present":[56],"training":[59],"data.":[60],"While":[61],"two":[63,114],"existing":[64],"methods":[65],"turning":[67],"truth":[68],"functions":[69],"into":[73],"are":[75],"univariate":[78,105],"case":[79,99],"only,":[80],"we":[83],"applies":[85],"to":[86],"multivariate":[87],"functions.":[88],"Moreover,":[89],"it":[90],"demonstrated\u2014through":[92],"numerical":[93],"results":[94],"and":[95],"one":[97],"specific":[98],"analytically\u2014that":[100],"our":[101],"algorithm,":[102],"case,":[106],"can":[107],"deliver":[108],"shorter":[109],"than":[111],"other":[113],"methods.":[115],"also":[117],"establish":[118],"representation":[120],"benefits":[121],"mathematical":[127],"perspective.":[129]},"counts_by_year":[],"updated_date":"2026-01-11T23:08:45.486102","created_date":"2025-10-10T00:00:00"}