{"id":"https://openalex.org/W7160381331","doi":"https://doi.org/10.48550/arxiv.2605.02968","title":"Finite-Size Gradient Transport in Large Language Model Pretraining: From Cascade Size to Intensive Transport Efficiency","display_name":"Finite-Size Gradient Transport in Large Language Model Pretraining: From Cascade Size to Intensive Transport Efficiency","publication_year":2026,"publication_date":"2026-05-03","ids":{"openalex":"https://openalex.org/W7160381331","doi":"https://doi.org/10.48550/arxiv.2605.02968"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02968","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02968","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135439929","display_name":"Ping Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Ping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135482969","display_name":"Yan-Qi Du","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Du, Yan-Qi","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":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/T10036","display_name":"Advanced Neural Network Applications","score":0.15940000116825104,"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"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.15940000116825104,"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"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.15559999644756317,"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":0.13910000026226044,"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/cascade","display_name":"Cascade","score":0.8184999823570251},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7526999711990356},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.715499997138977},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.6380000114440918},{"id":"https://openalex.org/keywords/null-model","display_name":"Null model","score":0.5708000063896179},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4717000126838684},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.4341000020503998},{"id":"https://openalex.org/keywords/duration","display_name":"Duration (music)","score":0.42570000886917114},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41499999165534973}],"concepts":[{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.8184999823570251},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7526999711990356},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.715499997138977},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.6380000114440918},{"id":"https://openalex.org/C36382193","wikidata":"https://www.wikidata.org/wiki/Q7068966","display_name":"Null model","level":2,"score":0.5708000063896179},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5351999998092651},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5105999708175659},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.4341000020503998},{"id":"https://openalex.org/C112758219","wikidata":"https://www.wikidata.org/wiki/Q16038819","display_name":"Duration (music)","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.36309999227523804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.362199991941452},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C125611927","wikidata":"https://www.wikidata.org/wiki/Q17008131","display_name":"Criticality","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.33649998903274536},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3249000012874603},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C115051666","wikidata":"https://www.wikidata.org/wiki/Q6522493","display_name":"Ranging","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2948000133037567},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.29109999537467957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2793999910354614},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2662999927997589}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02968","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02968","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":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"We":[0,26],"introduce":[1],"a":[2,42,65,120,177,182,190,197,202],"finite-size":[3],"gradient-transport":[4],"framework":[5,194],"for":[6],"real":[7,117],"language-model":[8],"training,":[9],"based":[10],"on":[11],"five":[12],"observables":[13],"$(D,z,\u03b2,\u03b4,v_{\\mathrm{rel}})$":[14],"that":[15,112],"separate":[16],"cascade":[17,171],"size,":[18],"duration,":[19,172],"absolute":[20],"transport,":[21],"and":[22,36,62,80,108,141,169],"intensive":[23,107],"transport":[24,73,192],"efficiency.":[25],"analyze":[27],"direct":[28],"raw-gradient":[29],"measurements":[30],"from":[31,48,119],"Pico-LM":[32,75,137],"across":[33],"four":[34],"scales":[35],"125":[37],"aligned":[38,50],"steps,":[39],"together":[40],"with":[41,91],"five-scale":[43],"Pythia":[44,85,146],"companion":[45],"dataset":[46],"built":[47],"153":[49],"checkpoint-difference":[51],"update":[52],"fields.":[53],"The":[54,129],"same":[55],"algebraic":[56],"closure":[57],"holds":[58],"in":[59,105,133,156],"both":[60,63],"families,":[61],"share":[64],"near-unity":[66],"cascade-size":[67],"backbone,":[68],"but":[69,151],"they":[70],"occupy":[71],"distinct":[72],"regimes:":[74],"shows":[76,152],"positive":[77,94],"duration":[78,109,140],"scaling":[79,207],"negative":[81],"intensive-efficiency":[82],"scaling,":[83],"whereas":[84,145],"remains":[86],"near":[87],"the":[88,106,113,148],"$D=1$":[89],"baseline":[90],"only":[92],"weak":[93],"efficiency":[95,142],"scale":[96],"dependence.":[97],"Randomized-field":[98],"controls":[99],"give":[100],"nearly":[101],"matched":[102],"null":[103,122,127],"floors":[104],"channels,":[110],"indicating":[111],"contrast":[114],"reflects":[115],"different":[116,126],"departures":[118],"shared":[121,178],"skeleton":[123],"rather":[124],"than":[125],"calibrations.":[128],"families":[130],"also":[131],"differ":[132],"stepwise":[134],"power-law":[135],"compressibility:":[136],"retains":[138],"clean":[139],"power":[143],"laws,":[144],"preserves":[147],"size":[149,179],"backbone":[150,180],"weaker":[153],"one-slope":[154],"compressibility":[155],"those":[157],"channels.":[158],"External":[159],"performance":[160,185],"associations":[161],"are":[162],"correspondingly":[163],"channel-level,":[164],"carried":[165],"mainly":[166],"by":[167],"$v_{\\mathrm{rel}}$":[168],"normalized":[170],"while":[173],"$D(t)$":[174],"acts":[175],"as":[176],"without":[181,195],"significant":[183],"exponent-level":[184],"association.":[186],"These":[187],"results":[188],"support":[189],"reusable":[191],"measurement":[193],"claiming":[196],"universal":[198],"fixed":[199],"point":[200],"or":[201],"first-principles":[203],"derivation":[204],"of":[205],"neural":[206],"laws.":[208]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-07T00:00:00"}
