{"id":"https://openalex.org/W7140593277","doi":"https://doi.org/10.48550/arxiv.2603.23854","title":"Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning","display_name":"Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140593277","doi":"https://doi.org/10.48550/arxiv.2603.23854"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.23854","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23854","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.23854","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130659670","display_name":"Salah A Faroughi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Faroughi, Salah A","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039895974","display_name":"Farinaz Mostajeran","orcid":"https://orcid.org/0000-0003-4149-9066"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mostajeran, Farinaz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054293534","display_name":"Amirhossein Arzani","orcid":"https://orcid.org/0000-0002-3706-7909"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arzani, Amirhossein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111782243","display_name":"Shirko Faroughi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Faroughi, Shirko","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5130659670"],"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.6916000247001648,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.6916000247001648,"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":0.23919999599456787,"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"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.010400000028312206,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/interpretability","display_name":"Interpretability","score":0.6837999820709229},{"id":"https://openalex.org/keywords/symbolic-data-analysis","display_name":"Symbolic data analysis","score":0.5370000004768372},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.49480000138282776},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4884999990463257},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.43709999322891235},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4350000023841858},{"id":"https://openalex.org/keywords/the-symbolic","display_name":"The Symbolic","score":0.4162999987602234},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.3991999924182892},{"id":"https://openalex.org/keywords/symbolic-regression","display_name":"Symbolic regression","score":0.3955000042915344}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6837999820709229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5618000030517578},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5475000143051147},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.5370000004768372},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.49480000138282776},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.48899999260902405},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4884999990463257},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3991999924182892},{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.3955000042915344},{"id":"https://openalex.org/C30732413","wikidata":"https://www.wikidata.org/wiki/Q17092636","display_name":"Intrinsic dimension","level":3,"score":0.3612000048160553},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.35030001401901245},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.34389999508857727},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3431999981403351},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3409999907016754},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32350000739097595},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2994999885559082},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.26080000400543213},{"id":"https://openalex.org/C75165309","wikidata":"https://www.wikidata.org/wiki/Q2258979","display_name":"Search engine indexing","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.25440001487731934},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.23854","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23854","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":"doi:10.48550/arxiv.2603.23854","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23854","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":"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":[0,54],"discovery":[1,140],"of":[2,82,95,187,211,229],"governing":[3,168,196,230],"equations":[4],"is":[5],"a":[6,14,58,72,93,120,220],"long-standing":[7],"goal":[8],"in":[9,170],"scientific":[10],"machine":[11],"learning,":[12],"yet":[13],"fundamental":[15],"trade-off":[16],"persists":[17],"between":[18],"interpretability":[19],"and":[20,43,100,114,123,167,173,183,225],"scalable":[21,138],"learning.":[22],"Classical":[23],"symbolic":[24,68,101,132,201],"regression":[25,172],"methods":[26],"yield":[27],"explicit":[28],"analytic":[29,96,146],"expressions":[30,129],"but":[31,45],"rely":[32],"on":[33],"combinatorial":[34],"search,":[35],"whereas":[36],"neural":[37,59],"networks":[38],"scale":[39],"efficiently":[40],"with":[41],"data":[42],"dimensionality":[44],"produce":[46],"opaque":[47],"representations.":[48],"In":[49],"this":[50,63],"work,":[51],"we":[52],"introduce":[53],"Kolmogorov-Arnold":[55],"Networks":[56],"(Symbolic-KANs),":[57],"architecture":[60],"that":[61,103,148,160],"bridges":[62],"gap":[64],"by":[65,92],"embedding":[66],"discrete":[67],"structure":[69,210],"directly":[70,194],"within":[71],"trainable":[73],"deep":[74],"network.":[75],"Symbolic-KANs":[76,134],"represent":[77],"multivariate":[78],"functions":[79],"as":[80,137,219],"compositions":[81],"learned":[83,88],"univariate":[84],"primitives":[85,205],"applied":[86],"to":[87,181],"scalar":[89],"projections,":[90],"guided":[91],"library":[94],"primitives,":[97],"hierarchical":[98],"gating,":[99],"regularization":[102],"progressively":[104],"sharpens":[105],"continuous":[106],"mixtures":[107],"into":[108],"one-hot":[109],"selections.":[110],"After":[111],"gated":[112],"training":[113],"discretization,":[115],"each":[116],"active":[117],"unit":[118],"selects":[119],"single":[121],"primitive":[122,139,165],"projection":[124],"direction,":[125],"yielding":[126],"compact":[127,200],"closed-form":[128],"without":[130],"post-hoc":[131],"fitting.":[133],"further":[135],"act":[136],"mechanisms,":[141],"identifying":[142],"the":[143,178,207,212],"most":[144],"relevant":[145],"components":[147],"can":[149],"subsequently":[150],"inform":[151],"candidate":[152],"libraries":[153],"for":[154],"sparse":[155],"equation-learning":[156],"methods.":[157],"We":[158],"demonstrate":[159],"Symbolic-KAN":[161,218],"reliably":[162],"recovers":[163],"correct":[164],"terms":[166],"structures":[169],"data-driven":[171],"inverse":[174,184],"dynamical":[175],"systems.":[176],"Moreover,":[177],"framework":[179],"extends":[180],"forward":[182],"physics-informed":[185],"learning":[186,228],"partial":[188],"differential":[189],"equations,":[190],"producing":[191],"accurate":[192],"solutions":[193],"from":[195],"constraints":[197],"while":[198],"constructing":[199],"representations":[202],"whose":[203],"selected":[204],"reflect":[206],"true":[208],"analytical":[209],"underlying":[213],"equations.":[214],"These":[215],"results":[216],"position":[217],"step":[221],"toward":[222],"scalable,":[223],"interpretable,":[224],"mechanistically":[226],"grounded":[227],"laws.":[231]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-03-27T00:00:00"}