{"id":"https://openalex.org/W7127452999","doi":"https://doi.org/10.48550/arxiv.2602.00825","title":"Harmful Overfitting in Sobolev Spaces","display_name":"Harmful Overfitting in Sobolev Spaces","publication_year":2026,"publication_date":"2026-01-31","ids":{"openalex":"https://openalex.org/W7127452999","doi":"https://doi.org/10.48550/arxiv.2602.00825"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.00825","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/A5124930565","display_name":"Kedar Karhadkar","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Karhadkar, Kedar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044944038","display_name":"Alexander Sietsema","orcid":"https://orcid.org/0000-0003-2307-2747"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sietsema, Alexander","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124953096","display_name":"Deanna Needell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Needell, Deanna","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072280192","display_name":"Guido Mont\u00fafar","orcid":"https://orcid.org/0000-0002-0131-2669"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Montufar, Guido","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5124930565"],"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/T12535","display_name":"Machine Learning and Data Classification","score":0.3855000138282776,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.3855000138282776,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.16769999265670776,"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/T10136","display_name":"Statistical Methods and Inference","score":0.12729999423027039,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/overfitting","display_name":"Overfitting","score":0.843999981880188},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6765000224113464},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.637499988079071},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5971999764442444},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5892999768257141},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5181999802589417},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.41019999980926514},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.3921999931335449},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.37869998812675476}],"concepts":[{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.843999981880188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7538999915122986},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6765000224113464},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.637499988079071},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5971999764442444},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5892999768257141},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3930000066757202},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.37869998812675476},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.366100013256073},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3095000088214874},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.288100004196167},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.27900001406669617},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2662000060081482},{"id":"https://openalex.org/C165957305","wikidata":"https://www.wikidata.org/wiki/Q7550132","display_name":"Sobolev spaces for planar domains","level":5,"score":0.25780001282691956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2574999928474426},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2563999891281128}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.00825","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.2602.00825","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.00825","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.2602.00825","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":[{"score":0.5175260901451111,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Motivated":[0],"by":[1,54,75],"recent":[2],"work":[3],"on":[4],"benign":[5],"overfitting":[6],"in":[7,18,39,93],"overparameterized":[8],"machine":[9],"learning,":[10],"we":[11,43],"study":[12],"the":[13,40,62,69,99,120],"generalization":[14,70],"behavior":[15],"of":[16,33,88,119],"functions":[17],"Sobolev":[19,124],"spaces":[20],"$W^{k,":[21],"p}(\\mathbb{R}^d)$":[22],"that":[23,45],"perfectly":[24],"fit":[25],"a":[26,76,112],"noisy":[27],"training":[28,63,121],"data":[29,41,122],"set.":[30],"Under":[31],"assumptions":[32],"label":[34],"noise":[35],"and":[36],"sufficient":[37],"regularity":[38],"distribution,":[42],"show":[44],"approximately":[46],"norm-minimizing":[47],"interpolators,":[48],"which":[49,115],"are":[50],"canonical":[51],"solutions":[52],"selected":[53],"smoothness":[55],"bias,":[56],"exhibit":[57],"harmful":[58,117],"overfitting:":[59],"even":[60],"as":[61],"sample":[64],"size":[65],"$n":[66],"\\to":[67],"\\infty$,":[68],"error":[71],"remains":[72],"bounded":[73],"below":[74],"positive":[77],"constant":[78],"with":[79],"high":[80],"probability.":[81],"Our":[82,109],"results":[83,97],"hold":[84],"for":[85],"arbitrary":[86],"values":[87],"$p":[89],"\\in":[90],"[1,":[91],"\\infty)$,":[92],"contrast":[94],"to":[95],"prior":[96],"studying":[98],"Hilbert":[100],"space":[101],"case":[102],"($p":[103],"=":[104],"2$)":[105],"using":[106,123],"kernel":[107],"methods.":[108],"proof":[110],"uses":[111],"geometric":[113],"argument":[114],"identifies":[116],"neighborhoods":[118],"inequalities.":[125]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-04T00:00:00"}
