{"id":"https://openalex.org/W7140117568","doi":"https://doi.org/10.48550/arxiv.2603.19524","title":"Remarks on Lipschitz-Minimal Interpolation: Generalization Bounds and Neural Network Implementation","display_name":"Remarks on Lipschitz-Minimal Interpolation: Generalization Bounds and Neural Network Implementation","publication_year":2026,"publication_date":"2026-03-19","ids":{"openalex":"https://openalex.org/W7140117568","doi":"https://doi.org/10.48550/arxiv.2603.19524"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19524","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.2603.19524","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122851714","display_name":"Arthur C. B. de Oliveira","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"de Oliveira, Arthur C. B.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130325667","display_name":"Ruigang Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Ruigang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130362737","display_name":"Ian R. Manchester","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manchester, Ian R.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130346310","display_name":"Eduardo D. Sontag","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sontag, Eduardo D.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5122851714"],"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":0.732200026512146,"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":0.732200026512146,"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/T11236","display_name":"Control Systems and Identification","score":0.06780000030994415,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.04809999838471413,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8095999956130981},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6815999746322632},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5267999768257141},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.5138999819755554},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.503600001335144},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44850000739097595}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8095999956130981},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6815999746322632},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5267999768257141},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.5138999819755554},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4643000066280365},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44850000739097595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44190001487731934},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3806000053882599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35920000076293945},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2816999852657318},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19524","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.2603.19524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19524","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":{"This":[0],"note":[1],"establishes":[2,50],"a":[3,12,15,38,44,67,86],"theoretical":[4],"framework":[5],"for":[6,21,85],"finding":[7],"(potentially":[8],"overparameterized)":[9],"approximations":[10],"of":[11,58,88,92],"function":[13],"on":[14,72,100],"compact":[16],"set":[17],"with":[18,43,97],"a-priori":[19],"bounds":[20,53,99],"the":[22,90],"generalization":[23,52],"error.":[24,102],"The":[25,48,81],"approximation":[26],"method":[27],"considered":[28],"is":[29],"to":[30],"choose,":[31],"among":[32],"all":[33],"functions":[34],"that":[35],"(approximately)":[36],"interpolate":[37],"given":[39],"data":[40],"set,":[41],"one":[42],"minimal":[45],"Lipschitz":[46],"constant.":[47],"paper":[49],"rigorous":[51],"over":[54],"practically":[55],"relevant":[56],"classes":[57],"approximators,":[59],"including":[60],"deep":[61],"neural":[62,68],"networks.":[63],"It":[64],"also":[65],"presents":[66],"network":[69,74],"implementation":[70],"based":[71],"Lipschitz-bounded":[73],"layers":[75],"and":[76],"an":[77,93],"augmented":[78],"Lagrangian":[79],"method.":[80],"results":[82],"are":[83],"illustrated":[84],"problem":[87],"learning":[89],"dynamics":[91],"input-to-state":[94],"stable":[95],"system":[96],"certified":[98],"simulation":[101]},"counts_by_year":[],"updated_date":"2026-03-24T06:04:31.470712","created_date":"2026-03-24T00:00:00"}