{"id":"https://openalex.org/W7223343928","doi":"https://doi.org/10.48550/arxiv.2610.31575","title":"Dynamics of random recurrent neural networks: colored noise and sublinear activations","display_name":"Dynamics of random recurrent neural networks: colored noise and sublinear activations","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223343928","doi":"https://doi.org/10.48550/arxiv.2610.31575"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.31575","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31575","pdf_url":"https://arxiv.org/pdf/2610.31575","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.31575","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076964917","display_name":"Germ\u00e1n Mato","orcid":"https://orcid.org/0000-0003-3106-1423","observed_orcids":["https://orcid.org/0000-0003-3106-1423"]},"institutions":[{"id":"https://openalex.org/I2802473995","display_name":"Balseiro Institute","ror":"https://ror.org/00sx0cd23","country_code":"AR","type":"education","lineage":["https://openalex.org/I2802473995","https://openalex.org/I9340077"]},{"id":"https://openalex.org/I2883434090","display_name":"Bariloche Atomic Centre","ror":"https://ror.org/05m802881","country_code":"AR","type":"facility","lineage":["https://openalex.org/I2883434090","https://openalex.org/I9340077"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Mato, German","raw_affiliation_strings":["Centro At\u00f3mico Bariloche and","Instituto Balseiro , UNCuyo and CNEA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro At\u00f3mico Bariloche and","institution_ids":["https://openalex.org/I2883434090"]},{"raw_affiliation_string":"Instituto Balseiro , UNCuyo and CNEA","institution_ids":["https://openalex.org/I2802473995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120163210","display_name":"Facundo Rigatuso","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rigatuso, Facundo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159362300","display_name":"Gonzalo Torroba","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2802473995","display_name":"Balseiro Institute","ror":"https://ror.org/00sx0cd23","country_code":"AR","type":"education","lineage":["https://openalex.org/I2802473995","https://openalex.org/I9340077"]},{"id":"https://openalex.org/I2883434090","display_name":"Bariloche Atomic Centre","ror":"https://ror.org/05m802881","country_code":"AR","type":"facility","lineage":["https://openalex.org/I2883434090","https://openalex.org/I9340077"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Torroba, Gonzalo","raw_affiliation_strings":["Centro At\u00f3mico Bariloche and","Instituto Balseiro , UNCuyo and CNEA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro At\u00f3mico Bariloche and","institution_ids":["https://openalex.org/I2883434090"]},{"raw_affiliation_string":"Instituto Balseiro , UNCuyo and CNEA","institution_ids":["https://openalex.org/I2802473995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.4652999937534332,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.4652999937534332,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.1550000011920929,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.09160000085830688,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/recurrent-neural-networks","display_name":"recurrent neural networks","score":0.8479999899864197},{"id":"https://openalex.org/keywords/random-couplings","display_name":"random couplings","score":0.953000009059906},{"id":"https://openalex.org/keywords/colored-noise","display_name":"colored noise","score":0.8669999837875366},{"id":"https://openalex.org/keywords/temporally-correlated-noise","display_name":"temporally correlated noise","score":0.8309999704360962},{"id":"https://openalex.org/keywords/edge-of-chaos","display_name":"edge of chaos","score":0.621999979019165},{"id":"https://openalex.org/keywords/lyapunov-exponents","display_name":"Lyapunov exponents","score":0.9049999713897705},{"id":"https://openalex.org/keywords/local-stability","display_name":"local stability","score":0.5220000147819519},{"id":"https://openalex.org/keywords/correlation-time","display_name":"correlation time","score":0.7390000224113464},{"id":"https://openalex.org/keywords/four-point-correlation-functions","display_name":"four-point functions","score":0.8289999961853027},{"id":"https://openalex.org/keywords/finite-size-effects","display_name":"finite-size effects","score":0.7670000195503235}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.7724000215530396},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6611999869346619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6492999792098999},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5771999955177307},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.576200008392334},{"id":"https://openalex.org/C114996537","wikidata":"https://www.wikidata.org/wiki/Q4854529","display_name":"Colors of noise","level":3,"score":0.5728999972343445},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4966000020503998},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4941999912261963},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.47920000553131104},{"id":"https://openalex.org/C110601934","wikidata":"https://www.wikidata.org/wiki/Q5172849","display_name":"Correlation dimension","level":4,"score":0.4602000117301941},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4560000002384186},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.44029998779296875},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.398499995470047},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3806999921798706},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3271999955177307},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31049999594688416},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2632000148296356},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.26100000739097595},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C186659197","wikidata":"https://www.wikidata.org/wiki/Q5452195","display_name":"First-hitting-time model","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2540999948978424},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.31575","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31575","pdf_url":"https://arxiv.org/pdf/2610.31575","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.31575","doi":"https://doi.org/10.48550/arxiv.2610.31575","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.31575","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.31575","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31575","pdf_url":"https://arxiv.org/pdf/2610.31575","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G367014277","display_name":null,"funder_award_id":"112202101 00114CO","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G6085355593","display_name":null,"funder_award_id":"11220200101008CO","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"}],"funders":[{"id":"https://openalex.org/F4320321583","display_name":"Comisi\u00f3n Nacional de Energ\u00eda At\u00f3mica, Gobierno de Argentina","ror":"https://ror.org/01xz39a70"},{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320323547","display_name":"Universidad Nacional de Cuyo","ror":"https://ror.org/05sn8wf81"},{"id":"https://openalex.org/F4320335724","display_name":"Instituto Balseiro, Universidad Nacional de Cuyo","ror":"https://ror.org/00sx0cd23"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223343928.pdf","grobid_xml":"https://content.openalex.org/works/W7223343928.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1598796236","https://openalex.org/W2010242617","https://openalex.org/W2027802883","https://openalex.org/W2057755457","https://openalex.org/W2162515722","https://openalex.org/W2331219843","https://openalex.org/W2759132499","https://openalex.org/W2773966064","https://openalex.org/W2890473586","https://openalex.org/W2913967256","https://openalex.org/W2944851425","https://openalex.org/W3157560649","https://openalex.org/W3204510764","https://openalex.org/W6947889615","https://openalex.org/W7156713044","https://openalex.org/W7169008678"],"related_works":["https://openalex.org/W7099321151","https://openalex.org/W7169008678","https://openalex.org/W2108146311","https://openalex.org/W3210319373","https://openalex.org/W2429257368","https://openalex.org/W2110804722","https://openalex.org/W6979255972","https://openalex.org/W7095423578","https://openalex.org/W3032975493","https://openalex.org/W3105747146"],"abstract_inverted_index":{"We":[0,83,136],"study":[1],"the":[2,29,36,71,76,80,95,98,105,120,139,155,159,168,175],"dynamics":[3],"of":[4,31,38,79,97,107,158],"recurrent":[5],"neural":[6],"networks":[7],"with":[8,58,88],"random":[9,125],"couplings,":[10],"sublinear":[11],"odd":[12],"activation":[13,81],"functions,":[14],"and":[15,27,75,131,178],"temporally":[16],"correlated":[17],"noise.":[18],"Using":[19],"large":[20],"N":[21],"methods,":[22],"we":[23],"determine":[24],"stationary":[25],"correlations":[26],"distinguish":[28],"loss":[30],"local":[32,55],"linear":[33],"stability":[34,60],"from":[35,143],"onset":[37],"chaos,":[39],"characterized":[40],"by":[41],"a":[42,62,111,132,144,164],"positive":[43],"largest":[44],"Lyapunov":[45],"exponent.":[46],"These":[47],"thresholds":[48,130],"delimit":[49],"an":[50],"intermediate":[51],"regime":[52],"in":[53],"which":[54],"instability":[56],"coexists":[57],"asymptotic":[59,77],"under":[61],"common":[63],"noise":[64,72,87,122],"history.":[65],"Their":[66],"separation":[67],"depends":[68],"on":[69],"both":[70],"correlation":[73,91,101,134,146,161],"time":[74,92,102],"growth":[78],"function.":[82,147],"show":[84],"that":[85],"internal":[86],"any":[89],"finite":[90],"cuts":[93],"off":[94],"divergence":[96],"network's":[99],"intrinsic":[100],"tau_corr":[103],"at":[104,167],"edge":[106],"chaos;":[108],"it":[109],"exhibits":[110],"critical":[112],"scaling":[113],"tau_{corr,max}":[114],"propto":[115],"1/sqrt{D_0},":[116],"where":[117],"D_0":[118],"is":[119,151],"integrated":[121],"strength.":[123],"Static":[124],"input":[126],"instead":[127],"produces":[128],"coincident":[129],"divergent":[133],"time.":[135],"also":[137],"calculate":[138],"frequency-dependent":[140],"participation":[141],"dimension":[142],"four-point":[145],"Its":[148],"zero-frequency":[149],"value":[150],"inversely":[152],"proportional":[153],"to":[154],"fourth":[156],"power":[157],"network":[160],"time,":[162],"predicting":[163],"smooth":[165],"minimum":[166],"weak-noise":[169],"chaos":[170],"threshold.":[171],"Numerical":[172],"simulations":[173],"support":[174],"large-network":[176],"predictions":[177],"reveal":[179],"appreciable":[180],"finite-size":[181],"effects.":[182]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}
