{"id":"https://openalex.org/W7163031422","doi":"https://doi.org/10.48550/arxiv.2605.30861","title":"Distilling LLM Feedback for Lean Theorem Proving","display_name":"Distilling LLM Feedback for Lean Theorem Proving","publication_year":2026,"publication_date":"2026-05-29","ids":{"openalex":"https://openalex.org/W7163031422","doi":"https://doi.org/10.48550/arxiv.2605.30861"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05642096v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05642096","pdf_url":"https://hal.science/hal-05642096v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-05642096v1/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119918624","display_name":"Ga\u00ebtan Narozniak","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Narozniak, Gaetan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137528229","display_name":"G\u00e9rard Biau","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Biau, G\u00e9rard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137524179","display_name":"R\u00e9mi Munos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Munos, R\u00e9mi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137540599","display_name":"Ahmad Rammal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rammal, Ahmad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137546549","display_name":"Pierre Marion","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marion, Pierre","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":true,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.654699981212616,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.654699981212616,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.0763000026345253,"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.04019999876618385,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/initialization","display_name":"Initialization","score":0.7509999871253967},{"id":"https://openalex.org/keywords/distillation","display_name":"Distillation","score":0.588699996471405},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4677000045776367},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.4408000111579895},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.4115999937057495},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.350600004196167}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7509999871253967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6973000168800354},{"id":"https://openalex.org/C204030448","wikidata":"https://www.wikidata.org/wiki/Q101017","display_name":"Distillation","level":2,"score":0.588699996471405},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.4115999937057495},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.350600004196167},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3197000026702881},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2955999970436096},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2921000123023987},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28529998660087585},{"id":"https://openalex.org/C3018623182","wikidata":"https://www.wikidata.org/wiki/Q154021","display_name":"Output feedback","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C2779795794","wikidata":"https://www.wikidata.org/wiki/Q7315343","display_name":"Reset (finance)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05642096v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05642096","pdf_url":"https://hal.science/hal-05642096v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2605.30861","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30861","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-05642096v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05642096","pdf_url":"https://hal.science/hal-05642096v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7163031422.pdf","grobid_xml":"https://content.openalex.org/works/W7163031422.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Post-training":[0],"for":[1,79,131],"reasoning":[2],"models":[3],"typically":[4],"combines":[5],"supervised":[6],"fine-tuning":[7],"with":[8,16],"reinforcement":[9],"learning":[10],"from":[11,22,110],"verifiable":[12],"rewards,":[13,24],"most":[14],"commonly":[15],"GRPO.":[17],"However,":[18],"this":[19],"algorithm":[20],"suffers":[21],"sparse":[23],"limited":[25],"exploration,":[26],"and":[27,71,99],"mode":[28],"collapse.":[29],"Building":[30],"upon":[31],"recent":[32],"works":[33],"on":[34,58],"self-distillation,":[35],"we":[36,82],"propose":[37],"Feedback":[38,66,85,112],"Distillation,":[39],"a":[40,63,111,125],"training":[41],"method":[42,78,117],"where":[43],"the":[44,51],"model":[45],"is":[46],"trained":[47],"to":[48,128],"match,":[49],"at":[50],"token":[52],"level,":[53],"its":[54],"own":[55],"distribution":[56],"conditioned":[57],"privileged":[59],"feedback":[60],"produced":[61],"by":[62],"language":[64],"model.":[65],"Distillation":[67,86,113],"offers":[68],"token-level":[69],"supervision":[70],"can":[72],"inject":[73],"external":[74],"knowledge.":[75],"Evaluating":[76],"our":[77,122],"Lean4":[80],"theorem-proving,":[81],"find":[83],"that":[84],"maintains":[87],"greater":[88],"diversity":[89],"in":[90,120],"generated":[91],"trajectories":[92],"than":[93],"GRPO,":[94],"yielding":[95],"higher":[96],"policy":[97],"entropy":[98],"better":[100],"pass@k":[101],"scaling.":[102],"The":[103],"two":[104],"methods":[105],"are":[106],"complementary:":[107],"initializing":[108],"GRPO":[109],"checkpoint":[114],"outperforms":[115],"either":[116],"alone.":[118],"All":[119],"all,":[121],"results":[123],"suggest":[124],"promising":[126],"avenue":[127],"improve":[129],"post-training":[130],"complex":[132],"reasoning.":[133]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-02T00:00:00"}
