{"id":"https://openalex.org/W7127635943","doi":"https://doi.org/10.48550/arxiv.2602.03506","title":"Explaining the Explainer: Understanding the Inner Workings of Transformer-based Symbolic Regression Models","display_name":"Explaining the Explainer: Understanding the Inner Workings of Transformer-based Symbolic Regression Models","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7127635943","doi":"https://doi.org/10.48550/arxiv.2602.03506"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.03506","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125060024","display_name":"Arco van Breda","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"van Breda, Arco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042454545","display_name":"Erman Acar","orcid":"https://orcid.org/0000-0001-7541-2999"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Acar, Erman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.1551000028848648,"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":0.1551000028848648,"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":0.11999999731779099,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.09730000048875809,"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/interpretability","display_name":"Interpretability","score":0.9490000009536743},{"id":"https://openalex.org/keywords/symbolic-data-analysis","display_name":"Symbolic data analysis","score":0.4677000045776367},{"id":"https://openalex.org/keywords/causal-model","display_name":"Causal model","score":0.4334000051021576},{"id":"https://openalex.org/keywords/symbolic-regression","display_name":"Symbolic regression","score":0.41830000281333923},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4058000147342682},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.3896999955177307},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"Logistic regression","score":0.373199999332428},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.3677999973297119}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.9490000009536743},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5787000060081482},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5364999771118164},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5133000016212463},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.4334000051021576},{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.41830000281333923},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3677999973297119},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.3652999997138977},{"id":"https://openalex.org/C143299363","wikidata":"https://www.wikidata.org/wiki/Q900584","display_name":"Attribution","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3061999976634979},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.26510000228881836},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C140331021","wikidata":"https://www.wikidata.org/wiki/Q1868104","display_name":"Logit","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C3020202489","wikidata":"https://www.wikidata.org/wiki/Q2032038","display_name":"Authorship attribution","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.03506","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.03506","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.03506","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.03506","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Following":[0],"their":[1,20,137],"success":[2],"across":[3],"many":[4],"domains,":[5],"transformers":[6],"have":[7],"also":[8],"proven":[9],"effective":[10],"for":[11,65,139,152,160],"symbolic":[12],"regression":[13],"(SR);":[14],"however,":[15],"the":[16,74],"internal":[17],"mechanisms":[18],"underlying":[19],"generation":[21],"of":[22,78],"mathematical":[23],"operators":[24],"remain":[25],"largely":[26],"unexplored.":[27],"Although":[28],"mechanistic":[29,153],"interpretability":[30,154],"has":[31,41],"successfully":[32],"identified":[33],"circuits":[34,64],"in":[35],"language":[36],"and":[37,62,100,125,155],"vision":[38],"models,":[39],"it":[40],"not":[42],"yet":[43],"been":[44],"applied":[45],"to":[46],"SR.":[47,66],"In":[48,117],"this":[49],"article,":[50],"we":[51,69,119],"introduce":[52],"PATCHES,":[53,68],"an":[54,79],"evolutionary":[55],"circuit":[56,140,161],"discovery":[57],"algorithm":[58],"that":[59,105,121],"identifies":[60],"compact":[61],"correct":[63,115],"Using":[67],"isolate":[70],"28":[71],"circuits,":[72],"providing":[73],"first":[75],"circuit-level":[76],"characterisation":[77],"SR":[80,146],"transformer.":[81],"We":[82],"validate":[83],"these":[84,143],"findings":[85],"through":[86],"a":[87,148,157],"robust":[88],"causal":[89,134],"evaluation":[90,110],"framework":[91],"based":[92],"on":[93],"key":[94],"notions":[95],"such":[96],"as":[97,147],"faithfulness,":[98],"completeness,":[99],"minimality.":[101],"Our":[102],"analysis":[103],"shows":[104],"mean":[106],"patching":[107],"with":[108],"performance-based":[109],"most":[111],"reliably":[112],"isolates":[113],"functionally":[114],"circuits.":[116],"contrast,":[118],"demonstrate":[120],"direct":[122],"logit":[123],"attribution":[124],"probing":[126],"classifiers":[127],"primarily":[128],"capture":[129],"correlational":[130],"features":[131],"rather":[132],"than":[133],"ones,":[135],"limiting":[136],"utility":[138],"discovery.":[141,162],"Overall,":[142],"results":[144],"establish":[145],"high-potential":[149],"application":[150],"domain":[151],"propose":[156],"principled":[158],"methodology":[159]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-06T00:00:00"}
