{"id":"https://openalex.org/W7134271190","doi":"https://doi.org/10.48550/arxiv.2603.05691","title":"Improved Scaling Laws via Weak-to-Strong Generalization in Random Feature Ridge Regression","display_name":"Improved Scaling Laws via Weak-to-Strong Generalization in Random Feature Ridge Regression","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W7134271190","doi":"https://doi.org/10.48550/arxiv.2603.05691"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.05691","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/A5114236173","display_name":"D.-S. Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wu, Diyuan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128495209","display_name":"Lehan Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Lehan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063392474","display_name":"Theodor Misiakiewicz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Misiakiewicz, Theodor","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061114394","display_name":"Marco Mondelli","orcid":"https://orcid.org/0000-0002-3242-7020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mondelli, Marco","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5114236173"],"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.20360000431537628,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.20360000431537628,"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/T12676","display_name":"Machine Learning and ELM","score":0.1306000053882599,"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/T10057","display_name":"Face and Expression Recognition","score":0.11159999668598175,"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/generalization","display_name":"Generalization","score":0.7164999842643738},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7024000287055969},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5170000195503235},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.512499988079071},{"id":"https://openalex.org/keywords/imperfect","display_name":"Imperfect","score":0.4754999876022339},{"id":"https://openalex.org/keywords/generalization-error","display_name":"Generalization error","score":0.44530001282691956},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.41850000619888306},{"id":"https://openalex.org/keywords/scaling-law","display_name":"Scaling law","score":0.3790999948978424},{"id":"https://openalex.org/keywords/test","display_name":"Test (biology)","score":0.3767000138759613}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7164999842643738},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7024000287055969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5408999919891357},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5170000195503235},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.512499988079071},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.4754999876022339},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.44530001282691956},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42739999294281006},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.336899995803833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3310000002384186},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C16910744","wikidata":"https://www.wikidata.org/wiki/Q7705759","display_name":"Test data","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C40969351","wikidata":"https://www.wikidata.org/wiki/Q3516228","display_name":"Word error rate","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2784999907016754},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2709999978542328},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.2578999996185303},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.05691","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.2603.05691","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.05691","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.2603.05691","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5075909495353699},{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.40742987394332886}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"It":[0],"is":[1,39,67,100],"increasingly":[2],"common":[3],"in":[4,69,129,151,174],"machine":[5],"learning":[6],"to":[7,11,19,101],"use":[8],"learned":[9],"models":[10],"label":[12],"data":[13,18],"and":[14,49,87,153],"then":[15,126],"employ":[16],"such":[17],"train":[20],"more":[21],"capable":[22],"models.":[23],"The":[24],"phenomenon":[25],"of":[26,32,111,134,140,166,170,180],"weak-to-strong":[27],"generalization":[28],"exemplifies":[29],"the":[30,51,55,64,70,75,80,107,112,119,131,135,141,145,157,161,167,171,177,181,188],"advantage":[31],"this":[33,59,122],"two-stage":[34],"procedure:":[35],"a":[36,46,103],"strong":[37,52],"student":[38,53,113,136,158],"trained":[40,89,114],"on":[41,115],"imperfect":[42],"labels":[43,116],"obtained":[44,117],"from":[45],"weak":[47,56],"teacher,":[48,142],"yet":[50],"outperforms":[54],"teacher.":[57,120],"In":[58],"paper,":[60],"we":[61,84,125],"show":[62],"that":[63,72,139,144],"potential":[65],"improvement":[66,146],"substantial,":[68],"sense":[71],"it":[73],"affects":[74],"scaling":[76,132,168],"law":[77,133,169],"followed":[78],"by":[79],"test":[81,109,178],"error.":[82],"Specifically,":[83],"consider":[85],"students":[86],"teachers":[88],"via":[90,118],"random":[91],"feature":[92],"ridge":[93],"regression":[94],"(RFRR).":[95],"Our":[96],"main":[97],"technical":[98],"contribution":[99],"derive":[102],"deterministic":[104,123],"equivalent":[105],"for":[106],"excess":[108],"error":[110,179],"Via":[121],"equivalent,":[124],"identify":[127],"regimes":[128],"which":[130],"improves":[137],"upon":[138],"unveiling":[143],"can":[147],"be":[148],"achieved":[149],"both":[150],"bias-dominated":[152],"variance-dominated":[154],"settings.":[155],"Strikingly,":[156],"may":[159],"attain":[160],"minimax":[162],"optimal":[163],"rate":[164],"regardless":[165],"teacher":[172,182],"--":[173],"fact,":[175],"when":[176],"does":[183],"not":[184],"even":[185],"decay":[186],"with":[187],"sample":[189],"size.":[190]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-10T00:00:00"}