{"id":"https://openalex.org/W7139007123","doi":"https://doi.org/10.48550/arxiv.2603.16850","title":"Unifying Optimization and Dynamics to Parallelize Sequential Computation: A Guide to Parallel Newton Methods for Breaking Sequential Bottlenecks","display_name":"Unifying Optimization and Dynamics to Parallelize Sequential Computation: A Guide to Parallel Newton Methods for Breaking Sequential Bottlenecks","publication_year":2026,"publication_date":"2026-03-17","ids":{"openalex":"https://openalex.org/W7139007123","doi":"https://doi.org/10.48550/arxiv.2603.16850"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.16850","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.16850","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.2603.16850","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129906529","display_name":"Xavier Gonzalez","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gonzalez, Xavier","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5129906529"],"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":0.25519999861717224,"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":0.25519999861717224,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.09690000116825104,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.07859999686479568,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.614799976348877},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5788000226020813},{"id":"https://openalex.org/keywords/massively-parallel","display_name":"Massively parallel","score":0.5712000131607056},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.45980000495910645},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.4564000070095062},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.44269999861717224},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4399000108242035},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.42890000343322754},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41850000619888306}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7594000101089478},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.614799976348877},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5788000226020813},{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.5712000131607056},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.45980000495910645},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.4564000070095062},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44269999861717224},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38940000534057617},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.3749000132083893},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.36469998955726624},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.36090001463890076},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C106515295","wikidata":"https://www.wikidata.org/wiki/Q26806595","display_name":"Parallel processing","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3149000108242035},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2851000130176544},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.28380000591278076},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C2778319340","wikidata":"https://www.wikidata.org/wiki/Q776861","display_name":"Transputer","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26269999146461487}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.16850","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.16850","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.2603.16850","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.16850","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Massively":[0],"parallel":[1,10,71,76,110,144,209,250],"hardware":[2],"(GPUs)":[3],"and":[4,25,85,97,108,116,124,149,168,189,220,227,238],"long":[5],"sequence":[6,50],"data":[7],"have":[8],"made":[9],"algorithms":[11],"essential":[12],"for":[13,158,223,233,253],"machine":[14],"learning":[15],"at":[16],"scale.":[17],"Yet":[18],"dynamical":[19,41,178,187,203],"systems,":[20],"like":[21],"recurrent":[22],"neural":[23],"networks":[24],"Markov":[26],"chain":[27],"Monte":[28],"Carlo,":[29],"were":[30],"thought":[31],"to":[32,249,257],"suffer":[33],"from":[34,102],"sequential":[35,225],"bottlenecks.":[36],"Recent":[37],"work":[38],"showed":[39],"that":[40,161,180],"systems":[42],"can":[43,63],"in":[44,177,262],"fact":[45],"be":[46,64],"parallelized":[47],"across":[48],"the":[49,129,164,194,197,259],"length":[51],"by":[52],"reframing":[53],"their":[54],"evaluation":[55],"as":[56,246],"a":[57,70,154,173,186,202,229,247],"system":[58,188,204],"of":[59,87,196,201],"nonlinear":[60],"equations,":[61],"which":[62],"solved":[65],"with":[66,80,95],"Newton's":[67],"method":[68],"using":[69],"associative":[72],"scan.":[73],"However,":[74],"these":[75,93,159],"Newton":[77,111,145,210,251],"methods":[78,121,141,211,222,252],"struggled":[79],"limitations,":[81],"primarily":[82],"inefficiency,":[83],"instability,":[84],"lack":[86],"convergence":[88,156],"guarantees.":[89],"This":[90,242],"thesis":[91,217,243],"addresses":[92],"limitations":[94],"methodological":[96],"theoretical":[98,231],"contributions,":[99],"drawing":[100],"particularly":[101],"optimization.":[103],"Methodologically,":[104],"we":[105,137,171],"develop":[106],"scalable":[107,219],"stable":[109,221],"methods,":[112],"based":[113],"on":[114,163],"quasi-Newton":[115,120],"trust-region":[117,130],"approaches.":[118],"The":[119],"are":[122,132],"faster":[123],"more":[125,134],"memory":[126],"efficient,":[127],"while":[128],"approaches":[131],"significantly":[133],"stable.":[135],"Theoretically,":[136],"unify":[138],"many":[139],"fixed-point":[140],"into":[142],"our":[143],"framework,":[146],"including":[147],"Picard":[148],"Jacobi":[150],"iterations.":[151],"We":[152],"establish":[153],"linear":[155],"rate":[157],"techniques":[160,236],"depends":[162],"method's":[165],"approximation":[166],"accuracy":[167],"stability.":[169],"Moreover,":[170],"give":[172],"precise":[174],"condition,":[175],"rooted":[176],"stability,":[179],"characterizes":[181],"when":[182,190,234],"parallelization":[183],"provably":[184],"accelerates":[185],"it":[191],"cannot.":[192],"Specifically,":[193],"sign":[195],"Largest":[198],"Lyapunov":[199],"Exponent":[200],"determines":[205],"whether":[206],"or":[207],"not":[208,240],"converge":[212],"quickly.":[213],"In":[214],"sum,":[215],"this":[216,263],"unlocks":[218],"parallelizing":[224],"computation,":[226],"provides":[228],"firm":[230],"basis":[232],"such":[235],"will":[237,239],"work.":[241],"also":[244],"serves":[245],"guide":[248],"researchers":[254],"who":[255],"want":[256],"write":[258],"next":[260],"chapter":[261],"ongoing":[264],"story.":[265]},"counts_by_year":[],"updated_date":"2026-03-20T20:54:20.808490","created_date":"2026-03-20T00:00:00"}