{"id":"https://openalex.org/W4395022132","doi":"https://doi.org/10.48550/arxiv.2404.12597","title":"The phase diagram of kernel interpolation in large dimensions","display_name":"The phase diagram of kernel interpolation in large dimensions","publication_year":2024,"publication_date":"2024-04-19","ids":{"openalex":"https://openalex.org/W4395022132","doi":"https://doi.org/10.48550/arxiv.2404.12597"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2404.12597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.12597","pdf_url":"https://arxiv.org/pdf/2404.12597","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2404.12597","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100753684","display_name":"Haobo Zhang","orcid":"https://orcid.org/0009-0007-3539-6315"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Haobo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101693216","display_name":"Weihao Lu","orcid":"https://orcid.org/0009-0002-8135-4865"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Weihao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100659445","display_name":"Qian Lin","orcid":"https://orcid.org/0009-0000-7034-7331"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Qian","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":true,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9708999991416931,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9708999991416931,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9684000015258789,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9613999724388123,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6360487341880798},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5923677086830139},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.5457344651222229},{"id":"https://openalex.org/keywords/phase-diagram","display_name":"Phase diagram","score":0.5301533341407776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43162935972213745},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.37133386731147766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36865806579589844},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3519485592842102},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25575387477874756},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2317267656326294},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18159690499305725},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1506524384021759}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6360487341880798},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5923677086830139},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.5457344651222229},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.5301533341407776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43162935972213745},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.37133386731147766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36865806579589844},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3519485592842102},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25575387477874756},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2317267656326294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18159690499305725},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1506524384021759},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2404.12597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.12597","pdf_url":"https://arxiv.org/pdf/2404.12597","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2404.12597","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2404.12597","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2404.12597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.12597","pdf_url":"https://arxiv.org/pdf/2404.12597","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4395022132.pdf","grobid_xml":"https://content.openalex.org/works/W4395022132.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2030742537","https://openalex.org/W2075062329","https://openalex.org/W1978089009","https://openalex.org/W2030693616","https://openalex.org/W1998520214","https://openalex.org/W2332383162","https://openalex.org/W4205332007","https://openalex.org/W2514159064","https://openalex.org/W2016936228","https://openalex.org/W2022416154"],"abstract_inverted_index":{"The":[0],"generalization":[1],"ability":[2],"of":[3,19,28,62,68,84],"kernel":[4,29,52,70,86,97],"interpolation":[5,71,98],"in":[6,24,42,93],"large":[7],"dimensions":[8],"(i.e.,":[9],"$n":[10],"\\asymp":[11],"d^\u03b3$":[12],"for":[13],"some":[14],"$\u03b3&gt;0$)":[15],"might":[16],"be":[17],"one":[18],"the":[20,25,37,43,49,54,59,64,81,91,96],"most":[21],"interesting":[22],"problems":[23],"recent":[26],"renaissance":[27],"regression,":[30],"since":[31],"it":[32],"may":[33],"help":[34],"us":[35],"understand":[36],"'benign":[38],"overfitting":[39],"phenomenon'":[40],"reported":[41],"neural":[44],"networks":[45],"literature.":[46],"Focusing":[47],"on":[48,53],"inner":[50],"product":[51],"sphere,":[55],"we":[56,79,89],"fully":[57],"characterized":[58],"exact":[60],"order":[61],"both":[63],"variance":[65],"and":[66,103],"bias":[67],"large-dimensional":[69,85],"under":[72],"various":[73],"source":[74],"conditions":[75],"$s\\geq":[76],"0$.":[77],"Consequently,":[78],"obtained":[80],"$(s,\u03b3)$-phase":[82],"diagram":[83],"interpolation,":[87],"i.e.,":[88],"determined":[90],"regions":[92],"$(s,\u03b3)$-plane":[94],"where":[95],"is":[99],"minimax":[100],"optimal,":[101],"sub-optimal":[102],"inconsistent.":[104]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
