{"id":"https://openalex.org/W7165152514","doi":"https://doi.org/10.48550/arxiv.2606.19145","title":"OrthoReg: Orthogonal Regularization for Hybrid Symbolic-Neural Dynamical Systems","display_name":"OrthoReg: Orthogonal Regularization for Hybrid Symbolic-Neural Dynamical Systems","publication_year":2026,"publication_date":"2026-06-17","ids":{"openalex":"https://openalex.org/W7165152514","doi":"https://doi.org/10.48550/arxiv.2606.19145"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.19145","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.19145","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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.19145","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002993826","display_name":"Till Richter","orcid":"https://orcid.org/0000-0001-6008-8209"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richter, Till","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000443214","display_name":"Niki Kilbertus","orcid":"https://orcid.org/0000-0001-8718-4305"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kilbertus, Niki","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":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":0.800599992275238,"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":0.800599992275238,"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":0.08209999650716782,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.019200000911951065,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6159999966621399},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5848000049591064},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5476999878883362},{"id":"https://openalex.org/keywords/the-symbolic","display_name":"The Symbolic","score":0.45190000534057617},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.42879998683929443},{"id":"https://openalex.org/keywords/symbolic-data-analysis","display_name":"Symbolic data analysis","score":0.4287000000476837},{"id":"https://openalex.org/keywords/neural-system","display_name":"Neural system","score":0.4237000048160553},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4097999930381775}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6159999966621399},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5848000049591064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5677000284194946},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5476999878883362},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.45190000534057617},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44130000472068787},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43959999084472656},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.4287000000476837},{"id":"https://openalex.org/C2986949344","wikidata":"https://www.wikidata.org/wiki/Q9404","display_name":"Neural system","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4097999930381775},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.365200012922287},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3346000015735626},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3301999866962433},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.31150001287460327},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28700000047683716},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.2815000116825104}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.19145","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.19145","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.19145","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.19145","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":"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"},"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":{"Dynamical":[0],"systems":[1,170],"are":[2,20],"fundamental":[3],"to":[4,116],"modeling":[5,10,40],"the":[6,43,67,81,104,113,131,143,151,156,161],"natural":[7],"world,":[8],"yet":[9],"them":[11],"involves":[12],"a":[13,50,57,98,148],"persistent":[14],"trade-off:":[15],"manually":[16],"prescribed":[17,51],"mechanistic":[18,72],"models":[19],"interpretable":[21],"by":[22,48,142],"design":[23],"but":[24],"often":[25],"overly":[26],"simplistic":[27],"and":[28,76,133,160,179],"misspecified;":[29],"in":[30],"contrast,":[31],"flexible":[32,58],"data-driven":[33],"neural":[34,59,68,114,134,144,162],"methods":[35,90],"lack":[36],"physical":[37],"insight.":[38],"Hybrid":[39],"aims":[41],"for":[42],"best":[44],"of":[45],"both":[46],"worlds":[47],"combining":[49],"or":[52],"symbolic,":[53],"physics-based":[54],"component":[55,69,106],"with":[56,118,171],"network.":[60],"A":[61],"critical":[62],"challenge,":[63],"however,":[64],"is":[65,85,107],"that":[66,101],"may":[70],"relearn":[71],"parts,":[73],"yielding":[74],"redundant":[75],"uninterpretable":[77],"models,":[78],"especially":[79],"when":[80,103],"symbolic":[82,105,119,132,137,152,177],"structure":[83,138],"itself":[84],"discovered":[86],"from":[87,139],"data.":[88],"Existing":[89],"based":[91],"on":[92,97],"standard":[93],"$L^2$":[94],"regularization":[95],"rely":[96],"projection":[99],"argument":[100],"breaks":[102],"learned":[108],"through":[109],"sparse":[110],"discovery,":[111],"allowing":[112],"augmentation":[115],"overlap":[117,129],"structure.":[120],"We":[121],"introduce":[122],"\\textbf{OrthoReg}":[123],"(Orthogonal":[124],"Regularization),":[125],"which":[126],"directly":[127],"penalizes":[128],"between":[130],"components,":[135],"preventing":[136],"being":[140],"absorbed":[141],"residual.":[145],"This":[146],"yields":[147],"complementary":[149],"decomposition:":[150],"part":[153,163],"captures":[154,164],"what":[155,165],"library":[157,173],"can":[158],"express,":[159],"remains.":[166],"On":[167],"benchmark":[168],"dynamical":[169],"partial":[172],"mismatch,":[174],"OrthoReg":[175],"improves":[176],"recovery":[178],"out-of-distribution":[180],"behavior.":[181]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-19T00:00:00"}
