{"id":"https://openalex.org/W7214723379","doi":"https://doi.org/10.48550/arxiv.2609.32409","title":"Recovery-Directed Symbolic Distillation of Neural Likelihoods","display_name":"Recovery-Directed Symbolic Distillation of Neural Likelihoods","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214723379","doi":"https://doi.org/10.48550/arxiv.2609.32409"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32409","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32409","pdf_url":"https://arxiv.org/pdf/2609.32409","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.32409","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137085869","display_name":"Kiante Fernandez","orcid":"https://orcid.org/0000-0002-8493-880X","observed_orcids":["https://orcid.org/0000-0002-8493-880X"]},"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":"Fernandez, Kiant\u00e9","raw_affiliation_strings":["Department of Psychology University of California , Los Angeles Los Angeles , CA 90095 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychology University of California , Los Angeles Los Angeles , CA 90095 , USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5124295900","display_name":"Xinwei Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Li, Xinwei","raw_affiliation_strings":["Department of Civil and Environmental Engineering National University of Singapore Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering National University of Singapore Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.5551999807357788,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.5551999807357788,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.2754000127315521,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.024000000208616257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/symbolic-regression","display_name":"symbolic regression","score":0.9290000200271606},{"id":"https://openalex.org/keywords/parameter-recovery","display_name":"parameter recovery","score":0.7749999761581421},{"id":"https://openalex.org/keywords/interpretable-models","display_name":"interpretable models","score":0.5740000009536743},{"id":"https://openalex.org/keywords/diffusion-decision-model","display_name":"diffusion decision model","score":0.9580000042915344},{"id":"https://openalex.org/keywords/cognitive-models","display_name":"cognitive models","score":0.6230000257492065},{"id":"https://openalex.org/keywords/simulation-based-inference","display_name":"simulation-based inference","score":0.9359999895095825}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.7016000151634216},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.6912999749183655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6586999893188477},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5697000026702881},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4887000024318695},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4681999981403351},{"id":"https://openalex.org/C204030448","wikidata":"https://www.wikidata.org/wiki/Q101017","display_name":"Distillation","level":2,"score":0.45820000767707825},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.44040000438690186},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.40059998631477356},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3986000120639801},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35179999470710754},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.329800009727478},{"id":"https://openalex.org/C917703","wikidata":"https://www.wikidata.org/wiki/Q7239668","display_name":"Predictive inference","level":5,"score":0.2856000065803528},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2703000009059906},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.26499998569488525},{"id":"https://openalex.org/C2779377595","wikidata":"https://www.wikidata.org/wiki/Q21045424","display_name":"Approximate Bayesian computation","level":3,"score":0.258899986743927}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32409","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32409","pdf_url":"https://arxiv.org/pdf/2609.32409","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.32409","doi":"https://doi.org/10.48550/arxiv.2609.32409","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32409","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32409","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32409","pdf_url":"https://arxiv.org/pdf/2609.32409","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214723379.pdf","grobid_xml":"https://content.openalex.org/works/W7214723379.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2797452937","https://openalex.org/W3097857172","https://openalex.org/W4368303491","https://openalex.org/W4412671660","https://openalex.org/W7131672243","https://openalex.org/W7147714367","https://openalex.org/W7162121238"],"related_works":["https://openalex.org/W7131672243","https://openalex.org/W7212462404","https://openalex.org/W3147590228","https://openalex.org/W2900947730","https://openalex.org/W7133212886","https://openalex.org/W7160311517","https://openalex.org/W7164824908","https://openalex.org/W7162121238","https://openalex.org/W7202226437","https://openalex.org/W4406692102"],"abstract_inverted_index":{"Amortized":[0],"neural":[1,30,138],"likelihoods":[2,31,128,139],"enable":[3,129],"computationally":[4],"expensive":[5],"inference":[6,162,190],"for":[7,37,79,111,172],"models":[8],"with":[9,176],"analytically":[10,105],"intractable":[11],"or":[12],"unspecified":[13],"likelihoods,":[14],"but":[15],"their":[16],"black-box":[17],"nature":[18],"limits":[19],"interpretability.":[20],"We":[21,91,153],"introduce":[22],"a":[23,44,74,100,148,169,186],"symbolic":[24,49,127,174],"distillation":[25,175],"pipeline":[26,94,167],"that":[27,53,76],"converts":[28],"trained":[29],"into":[32],"explicit,":[33],"interpretable":[34],"expressions":[35,52,65],"optimized":[36],"efficient":[38],"parameter":[39,119,134],"estimation.":[40],"Our":[41,166],"approach":[42],"uses":[43],"recovery-directed":[45,116],"objective":[46,117],"to":[47,185],"guide":[48],"regression":[50],"toward":[51],"preserve":[54],"parameter-recovery":[55,82],"accuracy":[56],"rather":[57],"than":[58,136],"merely":[59],"approximating":[60],"the":[61,88,93,96,143],"likelihood":[62,107],"function.":[63],"Candidate":[64],"are":[66],"evaluated":[67],"on":[68,95,163],"held-out":[69],"datasets":[70],"and":[71,84,181],"selected":[72],"using":[73],"criterion":[75],"jointly":[77],"accounts":[78],"expression":[80],"complexity,":[81],"performance,":[83],"distributional":[85],"distance":[86],"from":[87],"learned":[89],"likelihood.":[90],"evaluate":[92],"diffusion":[97],"decision":[98],"model,":[99,103],"classical":[101],"cognitive":[102],"whose":[104],"tractable":[106],"provides":[108,168],"ground":[109],"truth":[110],"controlled":[112],"evaluation.":[113],"The":[114,125],"proposed":[115],"improves":[118],"recovery":[120],"over":[121,130],"standard":[122],"symbolic-regression":[123],"objectives.":[124],"resulting":[126],"100":[131],"times":[132],"faster":[133],"evaluation":[135],"both":[137],"and,":[140],"when":[141],"available,":[142],"exact":[144],"likelihood,":[145],"while":[146],"maintaining":[147],"manageable":[149],"loss":[150],"in":[151,159],"precision.":[152],"further":[154],"demonstrate":[155],"these":[156],"computational":[157],"benefits":[158],"Bayesian":[160],"hierarchical":[161],"empirical":[164],"data.":[165],"lightweight":[170],"interface":[171],"integrating":[173],"existing":[177],"neural-likelihood":[178],"estimation":[179],"methods":[180],"can":[182],"be":[183],"adapted":[184],"range":[187],"of":[188],"simulation-based":[189],"settings.":[191]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}