{"id":"https://openalex.org/W7155089732","doi":"https://doi.org/10.48550/arxiv.2604.17402","title":"On the Generalization Bounds of Symbolic Regression with Genetic Programming","display_name":"On the Generalization Bounds of Symbolic Regression with Genetic Programming","publication_year":2026,"publication_date":"2026-04-19","ids":{"openalex":"https://openalex.org/W7155089732","doi":"https://doi.org/10.48550/arxiv.2604.17402"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.17402","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.17402","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.17402","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134137125","display_name":"Masahiro Nomura","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nomura, Masahiro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055965903","display_name":"Ryoki Hamano","orcid":"https://orcid.org/0000-0002-4425-1683"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hamano, Ryoki","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134133112","display_name":"Isao Ono","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ono, Isao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5134137125"],"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9975000023841858,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9975000023841858,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.0003000000142492354,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.84170001745224},{"id":"https://openalex.org/keywords/symbolic-regression","display_name":"Symbolic regression","score":0.771399974822998},{"id":"https://openalex.org/keywords/genetic-programming","display_name":"Genetic programming","score":0.7354999780654907},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.4823000133037567},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.48069998621940613},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.39969998598098755},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.3874000012874603},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.37040001153945923},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.36390000581741333}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.84170001745224},{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.771399974822998},{"id":"https://openalex.org/C110332635","wikidata":"https://www.wikidata.org/wiki/Q629498","display_name":"Genetic programming","level":2,"score":0.7354999780654907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5566999912261963},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.39969998598098755},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.37040001153945923},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36039999127388},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.2948000133037567},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.28380000591278076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28029999136924744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2797999978065491},{"id":"https://openalex.org/C62360110","wikidata":"https://www.wikidata.org/wiki/Q96777007","display_name":"Circumscription","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2743000090122223},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25949999690055847},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.17402","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.17402","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.17402","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.17402","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"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":{"Symbolic":[0],"regression":[1],"(SR)":[2],"with":[3],"genetic":[4],"programming":[5],"(GP)":[6],"aims":[7],"to":[8,147,156],"discover":[9],"interpretable":[10,75],"mathematical":[11],"expressions":[12],"directly":[13],"from":[14],"data.":[15],"Despite":[16],"its":[17,186],"strong":[18],"empirical":[19,173],"success,":[20],"the":[21,30,70,81,94,143,161],"theoretical":[22,108],"understanding":[23,184],"of":[24,43,84,96,145,185],"why":[25],"GP-based":[26,176],"SR":[27,44,57,177],"generalizes":[28],"beyond":[29],"training":[31],"data":[32],"remains":[33],"limited.":[34],"In":[35,128],"this":[36],"work,":[37],"we":[38],"provide":[39],"a":[40,52,77,90,101,107,167,181],"learning-theoretic":[41],"analysis":[42,131],"models":[45],"represented":[46],"as":[47],"expression":[48],"trees.":[49],"We":[50],"derive":[51],"generalization":[53,71,162,187],"bound":[54],"for":[55,170],"GP-style":[56],"under":[58],"constraints":[59],"on":[60,110],"tree":[61],"size,":[62],"depth,":[63],"and":[64,89,125,178],"learnable":[65],"constants.":[66],"Our":[67],"result":[68],"decomposes":[69],"gap":[72],"into":[73],"two":[74],"components:":[76],"structure-selection":[78],"term,":[79,92],"reflecting":[80],"combinatorial":[82],"complexity":[83,95,158],"choosing":[85],"an":[86],"expression-tree":[87],"structure,":[88],"constant-fitting":[91],"capturing":[93],"optimizing":[97],"numerical":[98],"constants":[99],"within":[100],"fixed":[102],"structure.":[103],"This":[104],"decomposition":[105],"provides":[106],"perspective":[109],"several":[111],"widely":[112],"used":[113],"practices":[114],"in":[115,160,175],"GP,":[116],"including":[117],"parsimony":[118],"pressure,":[119],"depth":[120],"limits,":[121],"numerically":[122],"stable":[123],"operators,":[124],"interval":[126],"arithmetic.":[127],"particular,":[129],"our":[130,164],"shows":[132],"how":[133],"structural":[134],"restrictions":[135],"reduce":[136],"hypothesis-class":[137],"growth":[138],"while":[139],"stability":[140],"mechanisms":[141],"control":[142],"sensitivity":[144],"predictions":[146],"parameter":[148],"perturbations.":[149],"By":[150],"linking":[151],"these":[152],"practical":[153],"design":[154],"choices":[155],"explicit":[157],"terms":[159],"bound,":[163],"work":[165],"offers":[166],"principled":[168],"explanation":[169],"commonly":[171],"observed":[172],"behaviors":[174],"contributes":[179],"towards":[180],"more":[182],"rigorous":[183],"properties.":[188]},"counts_by_year":[],"updated_date":"2026-04-22T06:07:44.442478","created_date":"2026-04-22T00:00:00"}
