{"id":"https://openalex.org/W4312887343","doi":"https://doi.org/10.1007/978-3-031-19842-7_40","title":"Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning","display_name":"Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312887343","doi":"https://doi.org/10.1007/978-3-031-19842-7_40"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-19842-7_40","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-19842-7_40","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"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/A5003022983","display_name":"Chi Zhang","orcid":"https://orcid.org/0000-0003-4948-0714"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chi Zhang","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003810400","display_name":"Sirui Xie","orcid":"https://orcid.org/0000-0002-0295-2588"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sirui Xie","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067007325","display_name":"Baoxiong Jia","orcid":"https://orcid.org/0000-0002-4968-3290"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Baoxiong Jia","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042765290","display_name":"Ying Wu","orcid":"https://orcid.org/0009-0000-6998-8924"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ying Nian Wu","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034228010","display_name":"Song\u2010Chun Zhu","orcid":"https://orcid.org/0009-0008-0876-8117"},"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"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Song-Chun Zhu","raw_affiliation_strings":["Beijing Institute for General Artificial Intelligence, Beijing, 10080, China","Institute for Artificial Intelligence, Peking University, Beijing, 10080, China","Tsinghua University, Beijing, 10080, China","University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"Beijing Institute for General Artificial Intelligence, Beijing, 10080, China","institution_ids":["https://openalex.org/I4210100255"]},{"raw_affiliation_string":"Institute for Artificial Intelligence, Peking University, Beijing, 10080, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I20231570"]},{"raw_affiliation_string":"Tsinghua University, Beijing, 10080, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051255725","display_name":"Yixin Zhu","orcid":"https://orcid.org/0000-0001-7024-1545"},"institutions":[{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yixin Zhu","raw_affiliation_strings":["Institute for Artificial Intelligence, Peking University, Beijing, 10080, China"],"affiliations":[{"raw_affiliation_string":"Institute for Artificial Intelligence, Peking University, Beijing, 10080, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5003022983"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.0859,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.93359413,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"692","last_page":"709"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9975000023841858,"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/T10320","display_name":"Neural Networks and Applications","score":0.9975000023841858,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9934999942779541,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9742000102996826,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/connectionism","display_name":"Connectionism","score":0.8263349533081055},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7300965189933777},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.598002016544342},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.590094268321991},{"id":"https://openalex.org/keywords/knowledge-representation-and-reasoning","display_name":"Knowledge representation and reasoning","score":0.5429768562316895},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4731346666812897},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47285914421081543},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.42909151315689087},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4248891770839691},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4196128845214844},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3358560800552368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14438244700431824}],"concepts":[{"id":"https://openalex.org/C8521452","wikidata":"https://www.wikidata.org/wiki/Q203790","display_name":"Connectionism","level":3,"score":0.8263349533081055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7300965189933777},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.598002016544342},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.590094268321991},{"id":"https://openalex.org/C161301231","wikidata":"https://www.wikidata.org/wiki/Q3478658","display_name":"Knowledge representation and reasoning","level":2,"score":0.5429768562316895},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4731346666812897},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47285914421081543},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.42909151315689087},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4248891770839691},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4196128845214844},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3358560800552368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14438244700431824},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-19842-7_40","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-19842-7_40","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W174941419","https://openalex.org/W569478347","https://openalex.org/W1565930783","https://openalex.org/W1662368540","https://openalex.org/W1676470423","https://openalex.org/W1979539191","https://openalex.org/W1981276685","https://openalex.org/W2018979488","https://openalex.org/W2062183687","https://openalex.org/W2067737176","https://openalex.org/W2080483844","https://openalex.org/W2101253926","https://openalex.org/W2118373646","https://openalex.org/W2119717200","https://openalex.org/W2123803218","https://openalex.org/W2124659975","https://openalex.org/W2194775991","https://openalex.org/W2319797207","https://openalex.org/W2399315682","https://openalex.org/W2566388524","https://openalex.org/W2595890440","https://openalex.org/W2624614404","https://openalex.org/W2624780181","https://openalex.org/W2739010165","https://openalex.org/W2788718740","https://openalex.org/W2798412078","https://openalex.org/W2862508255","https://openalex.org/W2903725113","https://openalex.org/W2962924847","https://openalex.org/W2963690694","https://openalex.org/W2998088552","https://openalex.org/W3007580291","https://openalex.org/W3105592015","https://openalex.org/W3176187895","https://openalex.org/W3177225079","https://openalex.org/W4205969993","https://openalex.org/W4235344441","https://openalex.org/W4248032712","https://openalex.org/W4249609777","https://openalex.org/W4283719116","https://openalex.org/W4310895557","https://openalex.org/W6601211009","https://openalex.org/W6601636429","https://openalex.org/W6601769173","https://openalex.org/W6602366224","https://openalex.org/W6620293842","https://openalex.org/W6632903747","https://openalex.org/W6634101208","https://openalex.org/W6640610544","https://openalex.org/W6703786156","https://openalex.org/W6756040250","https://openalex.org/W6802339985","https://openalex.org/W6822297646"],"related_works":["https://openalex.org/W4205841273","https://openalex.org/W4205525690","https://openalex.org/W1732468982","https://openalex.org/W1761388607","https://openalex.org/W1997922073","https://openalex.org/W350032239","https://openalex.org/W2604685715","https://openalex.org/W2412160900","https://openalex.org/W2136453575","https://openalex.org/W2053358180"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}