{"id":"https://openalex.org/W7130409002","doi":"https://doi.org/10.48550/arxiv.2602.15327","title":"Prescriptive Scaling Reveals the Evolution of Language Model Capabilities","display_name":"Prescriptive Scaling Reveals the Evolution of Language Model Capabilities","publication_year":2026,"publication_date":"2026-02-17","ids":{"openalex":"https://openalex.org/W7130409002","doi":"https://doi.org/10.48550/arxiv.2602.15327"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.15327","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15327","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.2602.15327","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126299069","display_name":"Hanlin Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhang, Hanlin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126302369","display_name":"Jikai Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Jikai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112443698","display_name":"Vasilis Syrgkanis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Syrgkanis, Vasilis","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022501668","display_name":"Sham Kakade","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kakade, Sham","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5126299069"],"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/T10028","display_name":"Topic Modeling","score":0.3005000054836273,"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/T10028","display_name":"Topic Modeling","score":0.3005000054836273,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.15369999408721924,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0478999987244606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5702000260353088},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5339000225067139},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4902999997138977},{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.474700003862381},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47350001335144043},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44339999556541443},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4406000077724457},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4350000023841858},{"id":"https://openalex.org/keywords/conditional-random-field","display_name":"Conditional random field","score":0.43070000410079956},{"id":"https://openalex.org/keywords/quantile-regression","display_name":"Quantile regression","score":0.40459999442100525}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5702000260353088},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5665000081062317},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5339000225067139},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4902999997138977},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.474700003862381},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47350001335144043},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4350000023841858},{"id":"https://openalex.org/C152565575","wikidata":"https://www.wikidata.org/wiki/Q1124538","display_name":"Conditional random field","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.42100000381469727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4068000018596649},{"id":"https://openalex.org/C63817138","wikidata":"https://www.wikidata.org/wiki/Q3455889","display_name":"Quantile regression","level":2,"score":0.40459999442100525},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3776000142097473},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C23131810","wikidata":"https://www.wikidata.org/wiki/Q818574","display_name":"Observational study","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32600000500679016},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.3188000023365021},{"id":"https://openalex.org/C22029948","wikidata":"https://www.wikidata.org/wiki/Q45089","display_name":"Dice","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C146849305","wikidata":"https://www.wikidata.org/wiki/Q370766","display_name":"Ground truth","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2775000035762787},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C2780148112","wikidata":"https://www.wikidata.org/wiki/Q1432581","display_name":"Proxy (statistics)","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C47121976","wikidata":"https://www.wikidata.org/wiki/Q3489473","display_name":"Quantile function","level":4,"score":0.2587999999523163},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2565000057220459},{"id":"https://openalex.org/C197640229","wikidata":"https://www.wikidata.org/wiki/Q2534066","display_name":"Predictability","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.15327","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15327","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.2602.15327","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15327","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":[{"display_name":"Quality Education","score":0.43018126487731934,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"deploying":[1],"foundation":[2],"models,":[3],"practitioners":[4],"increasingly":[5],"need":[6],"prescriptive":[7],"scaling":[8],"laws:":[9],"given":[10],"a":[11,63,75,113,172],"pre":[12,67],"training":[13,24,68],"compute":[14,177],"budget,":[15],"what":[16],"downstream":[17],"accuracy":[18],"is":[19,29],"attainable":[20],"with":[21,41,74,105],"contemporary":[22],"post":[23],"practice,":[25],"and":[26,44,91,129,170,183],"how":[27],"stable":[28],"that":[30,111,145],"mapping":[31],"as":[32,62],"the":[33,82,99,106,161,164],"field":[34],"evolves?":[35],"Using":[36],"large":[37],"scale":[38],"observational":[39,43],"evaluations":[40],"5k":[42],"2k":[45],"newly":[46],"sampled":[47],"data":[48,149],"on":[49,87,93,135],"model":[50,89,166],"performance,":[51],"we":[52,140],"estimate":[53],"capability":[54,187],"boundaries,":[55],"high":[56],"conditional":[57],"quantiles":[58],"of":[59,65,108,154],"benchmark":[60],"scores":[61],"function":[64],"log":[66],"FLOPs,":[69],"via":[70],"smoothed":[71],"quantile":[72],"regression":[73],"monotone,":[76],"saturating":[77],"sigmoid":[78],"parameterization.":[79],"We":[80,119],"validate":[81],"temporal":[83],"reliability":[84],"by":[85],"fitting":[86],"earlier":[88],"generations":[90],"evaluating":[92],"later":[94],"releases.":[95],"Across":[96],"various":[97],"tasks,":[98],"estimated":[100],"boundaries":[101,188],"are":[102],"mostly":[103],"stable,":[104],"exception":[107],"math":[109,136],"reasoning":[110,137],"exhibits":[112],"consistently":[114],"advancing":[115],"boundary":[116],"over":[117],"time.":[118,191],"then":[120],"extend":[121],"our":[122,158],"approach":[123],"to":[124,130],"analyze":[125],"task":[126],"dependent":[127],"saturation":[128],"probe":[131],"contamination":[132],"related":[133],"shifts":[134],"tasks.":[138],"Finally,":[139],"introduce":[141],"an":[142],"efficient":[143],"algorithm":[144],"recovers":[146],"near":[147],"full":[148],"frontiers":[150],"using":[151],"roughly":[152],"20%":[153],"evaluation":[155,168],"budget.":[156],"Together,":[157],"work":[159],"releases":[160],"Proteus":[162],"2k,":[163],"latest":[165],"performance":[167,181],"dataset,":[169],"introduces":[171],"practical":[173],"methodology":[174],"for":[175,184],"translating":[176],"budgets":[178],"into":[179],"reliable":[180],"expectations":[182],"monitoring":[185],"when":[186],"shift":[189],"across":[190]},"counts_by_year":[],"updated_date":"2026-02-19T06:31:58.851227","created_date":"2026-02-19T00:00:00"}