{"id":"https://openalex.org/W4415198629","doi":"https://doi.org/10.48550/arxiv.2505.09816","title":"Slow Transition to Low-Dimensional Chaos in Heavy-Tailed Recurrent Neural Networks","display_name":"Slow Transition to Low-Dimensional Chaos in Heavy-Tailed Recurrent Neural Networks","publication_year":2025,"publication_date":"2025-05-14","ids":{"openalex":"https://openalex.org/W4415198629","doi":"https://doi.org/10.48550/arxiv.2505.09816"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.09816","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.09816","pdf_url":"https://arxiv.org/pdf/2505.09816","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":"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/2505.09816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110379120","display_name":"Yi Xie","orcid":"https://orcid.org/0009-0009-6048-7491","observed_orcids":["https://orcid.org/0009-0009-6048-7491","https://orcid.org/0000-0002-9471-9133"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072126704","display_name":"\u015etefan Mihala\u015f","orcid":"https://orcid.org/0000-0002-2629-7100","observed_orcids":["https://orcid.org/0000-0002-2629-7100"]},"institutions":[{"id":"https://openalex.org/I4210140341","display_name":"Allen Institute","ror":"https://ror.org/03cpe7c52","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210140341"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mihalas, Stefan","raw_affiliation_strings":["Allen Institute , Seattle , WA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Allen Institute , Seattle , WA , USA","institution_ids":["https://openalex.org/I4210140341"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051558700","display_name":"\u0141ukasz Ku\u015bmierz","orcid":"https://orcid.org/0000-0003-3090-2550","observed_orcids":["https://orcid.org/0000-0003-3090-2550"]},"institutions":[{"id":"https://openalex.org/I4210140341","display_name":"Allen Institute","ror":"https://ror.org/03cpe7c52","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210140341"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ku\u015bmierz, \u0141ukasz","raw_affiliation_strings":["Allen Institute , Seattle , WA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Allen Institute , Seattle , WA , USA","institution_ids":["https://openalex.org/I4210140341"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T10581","display_name":"Neural dynamics and brain function","score":0.6234999895095825,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.6234999895095825,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.21629999577999115,"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/T10244","display_name":"Chaos control and synchronization","score":0.040699999779462814,"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":0.925000011920929},{"id":"https://openalex.org/keywords/heavy-tailed-distributions","display_name":"heavy-tailed distributions","score":0.9729999899864197},{"id":"https://openalex.org/keywords/chaos","display_name":"chaos","score":0.4180000126361847},{"id":"https://openalex.org/keywords/edge-of-chaos","display_name":"edge of chaos","score":0.8600000143051147},{"id":"https://openalex.org/keywords/finite-size-effects","display_name":"finite-size effects","score":0.7480000257492065},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"mean-field theory","score":0.8939999938011169},{"id":"https://openalex.org/keywords/lyapunov-dimension","display_name":"Lyapunov dimension","score":0.9700000286102295},{"id":"https://openalex.org/keywords/synaptic-weight-distribution","display_name":"synaptic weight distribution","score":0.6430000066757202},{"id":"https://openalex.org/keywords/low-dimensional-chaos","display_name":"low-dimensional chaos","score":0.5950000286102295}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7009999752044678},{"id":"https://openalex.org/C2780713532","wikidata":"https://www.wikidata.org/wiki/Q93158","display_name":"Edge of chaos","level":2,"score":0.6556000113487244},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6394000053405762},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.6262000203132629},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5889999866485596},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5131999850273132},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5120000243186951},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4059000015258789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39980000257492065},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3361000120639801},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3328000009059906},{"id":"https://openalex.org/C92866567","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaos theory","level":3,"score":0.3109000027179718},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.3059999942779541},{"id":"https://openalex.org/C168907044","wikidata":"https://www.wikidata.org/wiki/Q7834431","display_name":"Transition point","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.29589998722076416},{"id":"https://openalex.org/C2986949344","wikidata":"https://www.wikidata.org/wiki/Q9404","display_name":"Neural system","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C39630112","wikidata":"https://www.wikidata.org/wiki/Q5178018","display_name":"Coupled map lattice","level":5,"score":0.28139999508857727},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C110601934","wikidata":"https://www.wikidata.org/wiki/Q5172849","display_name":"Correlation dimension","level":4,"score":0.2720000147819519},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C194232998","wikidata":"https://www.wikidata.org/wiki/Q1606712","display_name":"Transition (genetics)","level":3,"score":0.26510000228881836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26249998807907104},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.25540000200271606},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2505.09816","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.09816","pdf_url":"https://arxiv.org/pdf/2505.09816","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:europepmc.org:11440975","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12633624","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"doi:10.48550/arxiv.2505.09816","doi":"https://doi.org/10.48550/arxiv.2505.09816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.09816","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:2505.09816","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.09816","pdf_url":"https://arxiv.org/pdf/2505.09816","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415198629.pdf","grobid_xml":"https://content.openalex.org/works/W4415198629.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2766678531","https://openalex.org/W4225854487","https://openalex.org/W4364382896","https://openalex.org/W4382986740"],"related_works":["https://openalex.org/W3042081969","https://openalex.org/W2979635115","https://openalex.org/W7139931768","https://openalex.org/W2110804722","https://openalex.org/W2059874507","https://openalex.org/W2061609673","https://openalex.org/W7095423578","https://openalex.org/W7223343928","https://openalex.org/W1950611080","https://openalex.org/W4322097020"],"abstract_inverted_index":{"Growing":[0],"evidence":[1],"suggests":[2],"that":[3,49],"synaptic":[4],"weights":[5,33],"in":[6,165,183],"the":[7,27,45,50,76,80,105,125,129,143,148,153,162],"brain":[8],"follow":[9],"heavy-tailed":[10,97,186],"distributions,":[11],"yet":[12],"most":[13],"theoretical":[14],"analyses":[15],"of":[16,29,107,128,145,150,155],"recurrent":[17],"neural":[18,157,187],"networks":[19,167],"(RNNs)":[20],"assume":[21],"Gaussian":[22,95],"connectivity.":[23],"We":[24,73],"systematically":[25],"study":[26],"activity":[28],"RNNs":[30,98],"with":[31,119],"random":[32],"drawn":[34],"from":[35,83],"biologically":[36,139],"plausible":[37],"L\u00e9vy":[38],"alpha-stable":[39],"distributions.":[40],"While":[41],"mean-field":[42,170],"theory":[43,171],"for":[44,180],"infinite":[46],"system":[47,81],"predicts":[48],"quiescent":[51,69,84],"state":[52],"is":[53],"always":[54],"unstable":[55],"--":[56,60,168,174],"implying":[57],"ubiquitous":[58],"chaos":[59,151],"our":[61],"finite-size":[62,166],"analysis":[63],"reveals":[64],"a":[65,100,110,120,138,177],"sharp":[66],"transition":[67,112,163],"between":[68,142],"and":[70,88,152],"chaotic":[71,86],"dynamics.":[72],"theoretically":[74],"predict":[75],"gain":[77],"at":[78],"which":[79],"transitions":[82],"to":[85,94,113],"dynamics,":[87],"validate":[89],"it":[90],"through":[91],"simulations.":[92],"Compared":[93],"networks,":[96],"exhibit":[99],"broader":[101],"parameter":[102],"regime":[103],"near":[104,147],"edge":[106,149],"chaos,":[108],"namely":[109],"slow":[111],"chaos.":[114],"However,":[115],"this":[116],"robustness":[117,144],"comes":[118],"tradeoff:":[121],"heavier":[122],"tails":[123],"reduce":[124],"Lyapunov":[126],"dimension":[127],"attractor,":[130],"indicating":[131],"lower":[132],"effective":[133],"dimensionality.":[134],"Our":[135],"results":[136],"reveal":[137],"aligned":[140],"tradeoff":[141],"dynamics":[146,182],"richness":[154],"high-dimensional":[156],"activity.":[158],"By":[159],"analytically":[160],"characterizing":[161],"point":[164],"where":[169],"breaks":[172],"down":[173],"we":[175],"provide":[176],"tractable":[178],"framework":[179],"understanding":[181],"realistically":[184],"sized,":[185],"circuits.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-15T00:00:00"}