{"id":"https://openalex.org/W7118194787","doi":"https://doi.org/10.1109/tmm.2026.3651076","title":"GeoTree: A Dynamic Tree-Based Geometry Problem Solver Through LLM-Symbolic Reasoning","display_name":"GeoTree: A Dynamic Tree-Based Geometry Problem Solver Through LLM-Symbolic Reasoning","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7118194787","doi":"https://doi.org/10.1109/tmm.2026.3651076"},"language":"en","primary_location":{"id":"doi:10.1109/tmm.2026.3651076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmm.2026.3651076","pdf_url":null,"source":{"id":"https://openalex.org/S137030581","display_name":"IEEE Transactions on Multimedia","issn_l":"1520-9210","issn":["1520-9210","1941-0077"],"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 Multimedia","raw_type":"journal-article"},"type":"article","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/A5121965234","display_name":"Yaxian Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I25355098","display_name":"Chang'an University","ror":"https://ror.org/05mxya461","country_code":"CN","type":"education","lineage":["https://openalex.org/I25355098"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaxian Wang","raw_affiliation_strings":["School of Information Engineering, Chang&#x0027;an University, Xi&#x0027;an, China"],"raw_orcid":"https://orcid.org/0000-0003-3193-3658","affiliations":[{"raw_affiliation_string":"School of Information Engineering, Chang&#x0027;an University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I25355098"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070094915","display_name":"Bifan Wei","orcid":"https://orcid.org/0000-0002-9732-3011"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bifan Wei","raw_affiliation_strings":["Ministry of Education Key Laboratory of Intelligent Networks and Network Security, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China"],"raw_orcid":"https://orcid.org/0000-0002-9732-3011","affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory of Intelligent Networks and Network Security, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121944768","display_name":"Yinghong Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinghong Ma","raw_affiliation_strings":["Shaanxi Province Key Laboratory of Big Data Knowledge Engineering, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shaanxi Province Key Laboratory of Big Data Knowledge Engineering, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121965222","display_name":"Lingling Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lingling Zhang","raw_affiliation_strings":["Shaanxi Province Key Laboratory of Big Data Knowledge Engineering, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China"],"raw_orcid":"https://orcid.org/0000-0001-8136-8795","affiliations":[{"raw_affiliation_string":"Shaanxi Province Key Laboratory of Big Data Knowledge Engineering, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055287990","display_name":"Xudong Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xudong Jiang","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University (NTU), Singapore"],"raw_orcid":"https://orcid.org/0000-0002-9104-2315","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University (NTU), Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036631624","display_name":"Henghui Ding","orcid":"https://orcid.org/0000-0003-4868-6526"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Henghui Ding","raw_affiliation_strings":["Institute of Big Data, Fudan University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-4868-6526","affiliations":[{"raw_affiliation_string":"Institute of Big Data, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121918575","display_name":"Jun Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Liu","raw_affiliation_strings":["Ministry of Education Key Laboratory of Intelligent Networks and Network Security, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China"],"raw_orcid":"https://orcid.org/0000-0002-6004-0675","affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory of Intelligent Networks and Network Security, and School of Computer Science and Technology, Xi&#x0027;an Jiaotong University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06302542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":null,"first_page":"2876","last_page":"2887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.4535999894142151,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.4535999894142151,"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"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.1501999944448471,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.05999999865889549,"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/solver","display_name":"Solver","score":0.7261999845504761},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6363000273704529},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.505299985408783},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.49480000138282776},{"id":"https://openalex.org/keywords/problem-solver","display_name":"Problem solver","score":0.47769999504089355},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.4505999982357025},{"id":"https://openalex.org/keywords/analytic-reasoning","display_name":"Analytic reasoning","score":0.4075999855995178},{"id":"https://openalex.org/keywords/spatial-intelligence","display_name":"Spatial intelligence","score":0.37869998812675476},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.36399999260902405}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7261999845504761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6467000246047974},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6363000273704529},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.49480000138282776},{"id":"https://openalex.org/C3019612716","wikidata":"https://www.wikidata.org/wiki/Q730920","display_name":"Problem solver","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.4505999982357025},{"id":"https://openalex.org/C103057564","wikidata":"https://www.wikidata.org/wiki/Q4751139","display_name":"Analytic reasoning","level":3,"score":0.4075999855995178},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37869998812675476},{"id":"https://openalex.org/C155911833","wikidata":"https://www.wikidata.org/wiki/Q3817354","display_name":"Spatial intelligence","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36579999327659607},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C97364631","wikidata":"https://www.wikidata.org/wiki/Q484284","display_name":"Deductive reasoning","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C89288958","wikidata":"https://www.wikidata.org/wiki/Q7301504","display_name":"Reasoning system","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C161771561","wikidata":"https://www.wikidata.org/wiki/Q1970286","display_name":"Process calculus","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28790000081062317},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28529998660087585},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.28209999203681946},{"id":"https://openalex.org/C43971567","wikidata":"https://www.wikidata.org/wiki/Q3142865","display_name":"Logical reasoning","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C158843486","wikidata":"https://www.wikidata.org/wiki/Q2137810","display_name":"Complex geometry","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C83725634","wikidata":"https://www.wikidata.org/wiki/Q7268699","display_name":"Qualitative reasoning","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C166088908","wikidata":"https://www.wikidata.org/wiki/Q308495","display_name":"Abductive reasoning","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C105653879","wikidata":"https://www.wikidata.org/wiki/Q7100712","display_name":"Ordered geometry","level":5,"score":0.26980000734329224},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tmm.2026.3651076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmm.2026.3651076","pdf_url":null,"source":{"id":"https://openalex.org/S137030581","display_name":"IEEE Transactions on Multimedia","issn_l":"1520-9210","issn":["1520-9210","1941-0077"],"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 Multimedia","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/212595","is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/212595","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Geometry":[0],"problem":[1,57,184],"solving":[2],"(GPS)":[3],"requires":[4],"high-level":[5],"symbolic":[6,69],"and":[7,94,122,171,228],"logical":[8],"reasoning":[9,74,81,101],"based":[10,86],"on":[11,87,152,218],"geometry":[12,41,56,73,80,100,141],"theorem":[13,142],"knowledge":[14],"to":[15,37,71,133,156,174,206],"arrive":[16],"at":[17],"the":[18,21,150,153,166,169,176,183,189,200,209,221],"answer.":[19],"Despite":[20],"remarkable":[22],"advances":[23],"achieved":[24],"by":[25],"Large":[26],"Language":[27],"Models":[28],"(LLMs)":[29],"in":[30,225],"various":[31],"problem-solving":[32,97],"tasks,":[33],"they":[34],"still":[35],"struggle":[36],"perform":[38,72],"rigorous":[39,68],"multi-step":[40,79],"reasoning,":[42],"which":[43,61,186,203],"is":[44,83,103],"essential":[45],"for":[46,182,192,213],"GPS.":[47],"In":[48],"this":[49],"paper,":[50],"we":[51],"propose":[52],"a":[53,63,67,88],"dynamic":[54],"tree-based":[55],"solver":[58,70],"named":[59],"GeoTree,":[60],"combines":[62],"knowledgeable":[64],"LLM":[65],"with":[66,138],"cooperatively.":[75],"Specifically,":[76],"an":[77],"iterative":[78],"process":[82],"performed":[84],"dynamically":[85],"tree-like":[89],"structure,":[90],"thereby":[91],"emulating":[92],"divergent":[93],"deliberate":[95],"human":[96],"thinking.":[98],"Each":[99],"step":[102],"completed":[104],"collaboratively":[105],"through":[106],"four":[107],"components,":[108],"consisting":[109],"of":[110,168,178,223],"<italic":[111,115,119,123,127,145,162,196],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[112,116,120,124,128,146,163,197],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Theorem":[113,129],"Seeker</i>,":[114],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Symbolic":[117,147],"Solver</i>,":[118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Evaluator</i>,":[121],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Controller</i>.":[125],"First,":[126],"Seeker</i>":[130],"prompts":[131,172],"LLMs":[132,173],"seek":[134],"out":[135],"candidate":[136],"theorems":[137,151,170],"their":[139],"inherent":[140],"knowledge.":[143],"Subsequently,":[144],"Solver</i>":[148],"applies":[149],"known":[154],"conditions":[155,181],"obtain":[157],"new":[158,180],"additional":[159],"conditions.":[160],"Then,":[161],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Evaluator</i>":[164],"assesses":[165],"availability":[167],"judge":[175],"usefulness":[177],"these":[179],"target,":[185],"serves":[187],"as":[188],"heuristic":[190],"guidance":[191],"subsequent":[193],"reasoning.":[194],"Finally,":[195],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Controller</i>":[198],"determines":[199],"termination":[201],"state,":[202],"decides":[204],"whether":[205],"continue":[207],"invoking":[208],"other":[210],"three":[211],"components":[212],"further":[214],"attempts.":[215],"Extensive":[216],"experiments":[217],"Geometry3K":[219],"demonstrate":[220],"superiority":[222],"GeoTree":[224],"accuracy,":[226],"efficiency,":[227],"explainability.":[229]},"counts_by_year":[],"updated_date":"2026-04-18T05:59:34.339393","created_date":"2026-01-05T00:00:00"}
