{"id":"https://openalex.org/W4365509177","doi":"https://doi.org/10.3390/sym15040916","title":"BEM-SM: A BERT-Encoder Model with Symmetry Supervision Module for Solving Math Word Problem","display_name":"BEM-SM: A BERT-Encoder Model with Symmetry Supervision Module for Solving Math Word Problem","publication_year":2023,"publication_date":"2023-04-14","ids":{"openalex":"https://openalex.org/W4365509177","doi":"https://doi.org/10.3390/sym15040916"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040916","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040916","pdf_url":"https://www.mdpi.com/2073-8994/15/4/916/pdf?version=1681473967","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/4/916/pdf?version=1681473967","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071511474","display_name":"Yijia Zhang","orcid":"https://orcid.org/0009-0006-9507-9365"},"institutions":[{"id":"https://openalex.org/I42852656","display_name":"Shenyang University","ror":"https://ror.org/04ddfwm68","country_code":"CN","type":"education","lineage":["https://openalex.org/I42852656"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yijia Zhang","raw_affiliation_strings":["School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China"],"raw_orcid":"https://orcid.org/0009-0006-9507-9365","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I42852656"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100718334","display_name":"Tiancheng Zhang","orcid":"https://orcid.org/0000-0001-6902-9299"},"institutions":[{"id":"https://openalex.org/I42852656","display_name":"Shenyang University","ror":"https://ror.org/04ddfwm68","country_code":"CN","type":"education","lineage":["https://openalex.org/I42852656"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tiancheng Zhang","raw_affiliation_strings":["School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I42852656"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029282098","display_name":"Peng Xie","orcid":"https://orcid.org/0000-0002-7235-3230"},"institutions":[{"id":"https://openalex.org/I42852656","display_name":"Shenyang University","ror":"https://ror.org/04ddfwm68","country_code":"CN","type":"education","lineage":["https://openalex.org/I42852656"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Xie","raw_affiliation_strings":["School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I42852656"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073691234","display_name":"Minghe Yu","orcid":"https://orcid.org/0000-0002-0287-8867"},"institutions":[{"id":"https://openalex.org/I42852656","display_name":"Shenyang University","ror":"https://ror.org/04ddfwm68","country_code":"CN","type":"education","lineage":["https://openalex.org/I42852656"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Minghe Yu","raw_affiliation_strings":["School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China"],"raw_orcid":"https://orcid.org/0000-0002-0287-8867","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I42852656"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072406974","display_name":"Ge Yu","orcid":"https://orcid.org/0000-0002-3171-8889"},"institutions":[{"id":"https://openalex.org/I42852656","display_name":"Shenyang University","ror":"https://ror.org/04ddfwm68","country_code":"CN","type":"education","lineage":["https://openalex.org/I42852656"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ge Yu","raw_affiliation_strings":["School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China"],"raw_orcid":"https://orcid.org/0000-0002-3171-8889","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Notrheastern University, Shenyang 110819, China","institution_ids":["https://openalex.org/I42852656"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100718334"],"corresponding_institution_ids":["https://openalex.org/I42852656"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.269,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82445114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"15","issue":"4","first_page":"916","last_page":"916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.9961000084877014,"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/T10028","display_name":"Topic Modeling","score":0.9961000084877014,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9945999979972839,"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/T10260","display_name":"Software Engineering Research","score":0.9688000082969666,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.7756773233413696},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.7584952116012573},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.6711589097976685},{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.6611738204956055},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5259813666343689},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5110849142074585},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.49002373218536377},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3997880816459656},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3778890371322632},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35391107201576233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16934847831726074}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7756773233413696},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.7584952116012573},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.6711589097976685},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.6611738204956055},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5259813666343689},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5110849142074585},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.49002373218536377},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3997880816459656},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3778890371322632},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35391107201576233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16934847831726074},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040916","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040916","pdf_url":"https://www.mdpi.com/2073-8994/15/4/916/pdf?version=1681473967","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:16a569952ec94813993cdf5824a9e39a","is_oa":false,"landing_page_url":"https://doaj.org/article/16a569952ec94813993cdf5824a9e39a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 4, p 916 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/916/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15040916","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040916","pdf_url":"https://www.mdpi.com/2073-8994/15/4/916/pdf?version=1681473967","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8868937019","display_name":null,"funder_award_id":"62272093, 62137001","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"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4365509177.pdf"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W2013938288","https://openalex.org/W2739912489","https://openalex.org/W2757276219","https://openalex.org/W2905122540","https://openalex.org/W2951107864","https://openalex.org/W2962927633","https://openalex.org/W2963510263","https://openalex.org/W2963705839","https://openalex.org/W2964710271","https://openalex.org/W2971094176","https://openalex.org/W2997200074","https://openalex.org/W3021636956","https://openalex.org/W3034865274","https://openalex.org/W3035498813","https://openalex.org/W3101786725","https://openalex.org/W3102725307","https://openalex.org/W3173285067","https://openalex.org/W3187417884","https://openalex.org/W4385245566","https://openalex.org/W6739901393"],"related_works":["https://openalex.org/W4390516098","https://openalex.org/W2181948922","https://openalex.org/W2384362569","https://openalex.org/W2142795561","https://openalex.org/W4205302943","https://openalex.org/W2561132942","https://openalex.org/W3155418658","https://openalex.org/W4243199227","https://openalex.org/W2379948177","https://openalex.org/W2944691285"],"abstract_inverted_index":{"In":[0],"order":[1],"to":[2,5,14,65,109,119,136],"find":[3],"solutions":[4],"math":[6,28,70,92],"word":[7,29,71,93],"problems,":[8,81],"some":[9],"modules":[10,64],"have":[11],"been":[12],"designed":[13,135],"check":[15,137],"the":[16,25,40,67,111,117,121,125,128,138,144,149,161,165],"generated":[17,141],"expressions,":[18,35],"but":[19],"they":[20,38],"neither":[21],"take":[22],"into":[23],"account":[24],"symmetry":[26],"between":[27,124],"problems":[30,94,126],"and":[31,127,142,160,170],"their":[32],"corresponding":[33],"mathematical":[34],"nor":[36],"do":[37],"utilize":[39],"efficiency":[41],"of":[42,69,113,153,167],"pretrained":[43,56,101],"language":[44,48,57,102],"models":[45,58],"in":[46,82,116],"natural":[47],"understanding":[49],"tasks.":[50],"Anyway,":[51],"designing":[52],"fine-tuning":[53,107],"tasks":[54],"for":[55,90],"that":[59],"encourage":[60],"cooperation":[61],"with":[62,95],"other":[63],"improve":[66,143],"performance":[68,146],"problem":[72],"solvers":[73],"is":[74,134],"an":[75],"unaddressed":[76],"problem.":[77],"To":[78],"solve":[79],"these":[80],"this":[83],"paper":[84],"we":[85,104],"propose":[86],"a":[87,96,106,131],"BERT-based":[88],"model":[89,169],"solving":[91],"supervision":[97,132],"module.":[98],"Based":[99],"on":[100,157],"models,":[103],"present":[105],"task":[108],"predict":[110],"number":[112],"different":[114],"operators":[115],"expressions":[118,140],"learn":[120],"potential":[122],"relationships":[123],"expressions.":[129],"Meanwhile,":[130],"module":[133],"incorrect":[139],"model\u2019s":[145],"by":[147],"optimizing":[148],"encoder.":[150],"A":[151],"series":[152],"experiments":[154],"are":[155],"conducted":[156],"three":[158],"datasets,":[159],"experimental":[162],"results":[163],"demonstrate":[164],"effectiveness":[166],"our":[168],"its":[171],"component\u2019s":[172],"designs.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
