{"id":"https://openalex.org/W7164878325","doi":"https://doi.org/10.48550/arxiv.2606.16768","title":"Taming Curvature: Architecture Warm-Up for Stable Transformer Training","display_name":"Taming Curvature: Architecture Warm-Up for Stable Transformer Training","publication_year":2026,"publication_date":"2026-06-15","ids":{"openalex":"https://openalex.org/W7164878325","doi":"https://doi.org/10.48550/arxiv.2606.16768"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.16768","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16768","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.16768","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138747010","display_name":"Sameera Ramasinghe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ramasinghe, Sameera","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138718886","display_name":"Ajanthan Thalaiyasingam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thalaiyasingam, Ajanthan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024380002","display_name":"Hadi M. Dolatabadi","orcid":"https://orcid.org/0000-0001-9418-1487"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dolatabadi, Hadi Mohaghegh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075325374","display_name":"Chamin Hewa Koneputugodage","orcid":"https://orcid.org/0009-0000-1333-5967"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koneputugodage, Chamin Hewa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136948014","display_name":"Gil Avraham","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avraham, Gil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015805464","display_name":"Violetta Shevchenko","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shevchenko, Violetta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101436506","display_name":"Yan Zuo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo, Yan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038823661","display_name":"Karol Paj\u0105k","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pajak, Karol","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128196329","display_name":"Alexander Long","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Long, Alexander","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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.17399999499320984,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.17399999499320984,"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":0.155799999833107,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.09759999811649323,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/hessian-matrix","display_name":"Hessian matrix","score":0.7820000052452087},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6730999946594238},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.5638999938964844},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4575999975204468},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.39910000562667847},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.38830000162124634},{"id":"https://openalex.org/keywords/state-estimator","display_name":"State estimator","score":0.3310999870300293}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7820000052452087},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6730999946594238},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.5638999938964844},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4575999975204468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43160000443458557},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33799999952316284},{"id":"https://openalex.org/C2984536560","wikidata":"https://www.wikidata.org/wiki/Q818544","display_name":"State estimator","level":3,"score":0.3310999870300293},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32989999651908875},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.30329999327659607},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C2780719617","wikidata":"https://www.wikidata.org/wiki/Q1030752","display_name":"Salient","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2615000009536743},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.16768","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16768","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":"doi:10.48550/arxiv.2606.16768","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16768","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":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Training":[0],"billion-parameter":[1],"Transformers":[2,155],"is":[3],"often":[4],"brittle,":[5],"with":[6,85,120,129],"transient":[7],"loss":[8],"spikes":[9],"and":[10,31,91,125,149,164],"divergence":[11],"that":[12,94,116,126,157],"waste":[13],"compute.":[14],"Even":[15],"though":[16],"the":[17,33,39,54,70,95,146],"recently":[18],"developed":[19],"Edge":[20],"of":[21,35,56,69],"Stability":[22],"(EoS)":[23],"theory":[24],"provides":[25],"a":[26,65,79],"powerful":[27],"tool":[28],"to":[29,53,143,168],"understand":[30],"control":[32,145],"stability":[34],"optimization":[36],"methods":[37,44],"via":[38],"(preconditioned)":[40,72],"curvature,":[41],"these":[42,133],"curvature-controlling":[43],"are":[45],"not":[46],"popular":[47],"in":[48,122],"large-scale":[49],"Transformer":[50],"training":[51,117],"due":[52],"complexity":[55],"curvature":[57,100,124,127,162],"estimation.":[58],"To":[59],"this":[60,112],"end,":[61],"we":[62,114,135],"first":[63],"introduce":[64],"fast":[66],"online":[67],"estimator":[68],"largest":[71],"Hessian":[73,148],"eigenvalue":[74],"(i.e.,":[75],"curvature)":[76],"based":[77],"on":[78,153],"warm-started":[80],"variant":[81],"for":[82],"power":[83],"iteration":[84],"Hessian-vector":[86],"products.":[87],"We":[88],"show":[89],"theoretically,":[90],"verify":[92],"empirically,":[93],"proposed":[96],"method":[97],"makes":[98],"per-iteration":[99],"tracking":[101,163],"feasible":[102],"at":[103],"billion":[104],"parameter":[105],"scale":[106],"while":[107],"being":[108],"more":[109],"accurate.":[110],"Using":[111],"tool,":[113],"find":[115],"instabilities":[118,166],"coincide":[119],"surges":[121],"preconditioned":[123,147],"grows":[128],"depth.":[130],"Motivated":[131],"by":[132],"observations,":[134],"propose":[136],"architecture":[137],"warm-up:":[138],"progressively":[139],"growing":[140],"network":[141],"depth":[142],"carefully":[144],"stabilize":[150],"training.":[151],"Experiments":[152],"large":[154],"validate":[156],"our":[158],"approach":[159],"enables":[160],"efficient":[161],"reduces":[165],"compared":[167],"existing":[169],"state-of-the-art":[170],"stabilization":[171],"techniques":[172],"without":[173],"slowing":[174],"down":[175],"convergence.":[176]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-17T00:00:00"}
