{"id":"https://openalex.org/W7138333347","doi":"https://doi.org/10.48550/arxiv.2603.15494","title":"A practical randomized trust-region method to escape saddle points in high dimension","display_name":"A practical randomized trust-region method to escape saddle points in high dimension","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7138333347","doi":"https://doi.org/10.48550/arxiv.2603.15494"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.15494","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.15494","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.2603.15494","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052668617","display_name":"Radu-Alexandru Dragomir","orcid":"https://orcid.org/0000-0002-4600-7748"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dragomir, Radu-Alexandru","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021783986","display_name":"Xiaowen Jiang","orcid":"https://orcid.org/0000-0002-6283-2262"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Xiaowen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129706869","display_name":"Bonan Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Bonan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085231507","display_name":"Nicolas Boumal","orcid":"https://orcid.org/0000-0002-1322-958X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boumal, Nicolas","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9882000088691711,"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":0.9882000088691711,"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":0.00419999985024333,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/initialization","display_name":"Initialization","score":0.8445000052452087},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6607999801635742},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6366999745368958},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6204000115394592},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6129000186920166},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5214999914169312},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5110999941825867},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.5047000050544739}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.8445000052452087},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6607999801635742},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6366999745368958},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6204000115394592},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6129000186920166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5914000272750854},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5214999914169312},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5110999941825867},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47510001063346863},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4180999994277954},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4065000116825104},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3788999915122986},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.29789999127388},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26649999618530273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26440000534057617},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.2554999887943268}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.15494","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.15494","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.2603.15494","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.15494","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Without":[0],"randomization,":[1,26],"escaping":[2],"the":[3,88,100,114,150],"saddle":[4,55],"points":[5],"of":[6,17,102,153],"$f":[7],"\\colon":[8],"\\mathbb{R}^d":[9],"\\to":[10],"\\mathbb{R}$":[11],"requires":[12,70],"at":[13],"least":[14],"$\u03a9(d)$":[15],"pieces":[16],"information":[18],"about":[19],"$f$":[20],"(values,":[21],"gradients,":[22],"Hessian-vector":[23],"products).":[24],"With":[25],"this":[27],"can":[28],"be":[29],"reduced":[30],"to":[31,40],"a":[32,78,160],"polylogarithmic":[33],"dependence":[34],"in":[35],"$d$.":[36],"The":[37,142],"prototypical":[38],"algorithm":[39,144],"that":[41,110],"effect":[42],"is":[43,63,67,137,145],"perturbed":[44],"gradient":[45],"descent":[46],"(PGD):":[47],"through":[48],"sustained":[49],"jitter,":[50],"it":[51,58,122,147],"reliably":[52],"escapes":[53],"strict":[54],"points.":[56],"However,":[57],"also":[59],"never":[60],"settles:":[61],"there":[62],"no":[64],"convergence.":[65],"What":[66],"more,":[68],"PGD":[69],"precise":[71],"tuning":[72],"based":[73],"on":[74,84],"Lipschitz":[75],"constants":[76],"and":[77,107,120,159,172],"preset":[79],"target":[80],"accuracy.":[81],"To":[82],"improve":[83],"this,":[85],"we":[86,98,108],"modify":[87],"time-tested":[89],"trust-region":[90],"method":[91],"with":[92,139,155],"truncated":[93],"conjugate":[94],"gradients":[95],"(TR-tCG).":[96],"Specifically,":[97],"randomize":[99],"initialization":[101],"tCG":[103,111],"(the":[104,164],"subproblem":[105],"solver),":[106],"prove":[109],"automatically":[112],"amplifies":[113],"randomization":[115],"near":[116,123],"saddles":[117],"(to":[118,126],"escape)":[119],"absorbs":[121],"local":[124],"minimizers":[125],"converge).":[127],"Saddle":[128],"escape":[129],"happens":[130],"over":[131],"several":[132,140],"iterations.":[133],"Accordingly,":[134],"our":[135],"analysis":[136],"multi-step,":[138],"novelties.":[141],"proposed":[143],"practical:":[146],"essentially":[148],"tracks":[149],"good":[151],"behavior":[152],"TR-tCG,":[154],"three":[156],"minute":[157],"modifications":[158],"single":[161],"new":[162],"hyperparameter":[163],"noise":[165],"scale":[166],"$\u03c3$).":[167],"We":[168],"provide":[169],"an":[170],"implementation":[171],"numerical":[173],"experiments.":[174]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-18T00:00:00"}