{"id":"https://openalex.org/W7155209226","doi":"https://doi.org/10.48550/arxiv.2604.19000","title":"Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Trees","display_name":"Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Trees","publication_year":2026,"publication_date":"2026-04-21","ids":{"openalex":"https://openalex.org/W7155209226","doi":"https://doi.org/10.48550/arxiv.2604.19000"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.19000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19000","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.19000","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134342470","display_name":"Xiaoyang Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xiaoyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134314577","display_name":"Zineng Dong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dong, Zineng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134276733","display_name":"Yifan Bai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bai, Yifan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134324091","display_name":"Yantao Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yantao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134337252","display_name":"Yuntian Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Yuntian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134289208","display_name":"Tao Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.3138999938964844,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.3138999938964844,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.09700000286102295,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.09399999678134918,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5548999905586243},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.5091999769210815},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.48579999804496765},{"id":"https://openalex.org/keywords/blueprint","display_name":"Blueprint","score":0.483599990606308},{"id":"https://openalex.org/keywords/natural-language","display_name":"Natural language","score":0.4611000120639801},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4489000141620636},{"id":"https://openalex.org/keywords/bridge","display_name":"Bridge (graph theory)","score":0.43220001459121704},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4226999878883362},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.38670000433921814},{"id":"https://openalex.org/keywords/formal-language","display_name":"Formal language","score":0.3853999972343445}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6477000117301941},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.5315999984741211},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.527999997138977},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.48579999804496765},{"id":"https://openalex.org/C155911762","wikidata":"https://www.wikidata.org/wiki/Q422321","display_name":"Blueprint","level":2,"score":0.483599990606308},{"id":"https://openalex.org/C195324797","wikidata":"https://www.wikidata.org/wiki/Q33742","display_name":"Natural language","level":2,"score":0.4611000120639801},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4226999878883362},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35589998960494995},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3544999957084656},{"id":"https://openalex.org/C12455157","wikidata":"https://www.wikidata.org/wiki/Q7835331","display_name":"Transposition (logic)","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3418999910354614},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C102315432","wikidata":"https://www.wikidata.org/wiki/Q649732","display_name":"Formal system","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C56666940","wikidata":"https://www.wikidata.org/wiki/Q788790","display_name":"Documentation","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C194989596","wikidata":"https://www.wikidata.org/wiki/Q211790","display_name":"Logical connective","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C116253237","wikidata":"https://www.wikidata.org/wiki/Q1437424","display_name":"Formal specification","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C2985583900","wikidata":"https://www.wikidata.org/wiki/Q722617","display_name":"Formal description","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2563999891281128},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C2776937656","wikidata":"https://www.wikidata.org/wiki/Q2229669","display_name":"Nesting (process)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.19000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19000","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.19000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19000","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.6396395564079285,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Statement":[0],"autoformalization":[1,71],"acts":[2],"as":[3,45],"a":[4,66,73,106,130],"critical":[5],"bridge":[6],"between":[7],"human":[8],"mathematics":[9,12],"and":[10,29,63,82,96,111,118,143],"formal":[11,19,43],"by":[13],"translating":[14],"natural":[15],"language":[16],"problems":[17],"into":[18,72,79],"language.":[20],"While":[21],"prior":[22],"works":[23],"have":[24],"focused":[25],"on":[26],"data":[27],"synthesis":[28],"diverse":[30],"training":[31],"paradigms":[32],"to":[33,85,93],"optimize":[34],"end-to-end":[35],"Large":[36],"Language":[37],"Models":[38],"(LLMs),":[39],"they":[40],"typically":[41],"treat":[42],"code":[44,144],"flat":[46],"sequences,":[47],"neglecting":[48],"the":[49],"hierarchical":[50],"logic":[51],"inherent":[52],"in":[53,121],"mathematical":[54],"statements.":[55],"In":[56],"this":[57,90],"work,":[58],"we":[59,103],"introduce":[60,104],"Decompose,":[61],"Structure,":[62],"Repair":[64],"(DSR),":[65],"neuro-symbolic":[67],"framework":[68],"that":[69,127],"restructures":[70],"modular":[74],"pipeline.":[75],"DSR":[76,128],"decomposes":[77],"statements":[78],"logical":[80],"components":[81],"maps":[83],"them":[84],"structured":[86],"operator":[87],"trees,":[88],"leveraging":[89],"topological":[91],"blueprint":[92],"precisely":[94],"localize":[95],"repair":[97],"errors":[98],"via":[99],"sub-tree":[100],"refinement.":[101],"Furthermore,":[102],"PRIME,":[105],"benchmark":[107],"of":[108],"156":[109],"undergraduate":[110],"graduate-level":[112],"theorems":[113],"selected":[114],"from":[115],"canonical":[116],"textbooks":[117],"expertly":[119],"annotated":[120],"Lean":[122],"4.":[123],"Experimental":[124],"results":[125],"demonstrate":[126],"establishes":[129],"new":[131],"state-of-the-art,":[132],"consistently":[133],"outperforming":[134],"baselines":[135],"under":[136],"equivalent":[137],"computational":[138],"budgets.":[139],"The":[140],"datasets,":[141],"model,":[142],"are":[145],"available":[146],"at":[147],"https://github.com/XiaoyangLiu-sjtu/DSR.":[148]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-23T00:00:00"}
