{"id":"https://openalex.org/W7161031680","doi":"https://doi.org/10.48550/arxiv.2605.12049","title":"Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons","display_name":"Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons","publication_year":2026,"publication_date":"2026-05-12","ids":{"openalex":"https://openalex.org/W7161031680","doi":"https://doi.org/10.48550/arxiv.2605.12049"},"language":null,"primary_location":{"id":"pmh:oai:pure.mpg.de:item_3715587","is_oa":false,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-341F-F","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"info:eu-repo/semantics/preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.12049","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112950182","display_name":"Aaron Spieler","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Spieler, Aaron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001474340","display_name":"Georg Martius","orcid":"https://orcid.org/0000-0002-8963-7627"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martius, Georg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136024849","display_name":"Anna Levina","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Levina, Anna","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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.4699999988079071,"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"}},"topics":[{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.4699999988079071,"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"}},{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.16439999639987946,"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":0.1168999969959259,"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/scaling","display_name":"Scaling","score":0.5263000130653381},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4577000141143799},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.43389999866485596},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.4260999858379364},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.41659998893737793},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.3880000114440918},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.38510000705718994},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.37869998812675476}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6399000287055969},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5263000130653381},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4577000141143799},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.4260999858379364},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3865000009536743},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.37560001015663147},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3709000051021576},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3447999954223633},{"id":"https://openalex.org/C151927369","wikidata":"https://www.wikidata.org/wiki/Q1981312","display_name":"Neuromorphic engineering","level":3,"score":0.3402999937534332},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31679999828338623},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C126691448","wikidata":"https://www.wikidata.org/wiki/Q2028919","display_name":"Magnitude (astronomy)","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C203005215","wikidata":"https://www.wikidata.org/wiki/Q79798","display_name":"Machine translation","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.2646999955177307}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:pure.mpg.de:item_3715587","is_oa":false,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-341F-F","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2605.12049","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12049","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.12049","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12049","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":"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"},"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":{"Cortical":[0],"neurons":[1],"are":[2],"complex,":[3],"multi-timescale":[4],"processors":[5],"wired":[6],"into":[7],"recurrent":[8,98],"circuits,":[9],"shaped":[10],"by":[11,22],"long":[12],"evolutionary":[13],"pressure":[14],"under":[15],"stringent":[16],"biological":[17],"constraints.":[18],"Mainstream":[19],"machine":[20],"learning,":[21],"contrast,":[23],"predominantly":[24],"builds":[25],"models":[26],"from":[27,34,102],"extremely":[28],"simple":[29],"units,":[30],"a":[31,42,50,77,165,168,220,248],"default":[32,233],"inherited":[33],"early":[35],"neural-network":[36],"theory.":[37],"We":[38,135],"treat":[39],"this":[40,241],"as":[41],"normative":[43,249],"architectural":[44],"question.":[45],"How":[46],"should":[47],"one":[48],"split":[49],"fixed":[51,166],"parameter":[52],"budget":[53],"$P$":[54],"between":[55],"the":[56,71,94,137,145,160,195,226,231],"number":[57],"of":[58,87,113,131,159,214],"units":[59],"$N$,":[60,122],"per-unit":[61,66,81],"effective":[62],"complexity":[63,82],"$k_e$,":[64,123],"and":[65,89,124,126,149,176,182,193,205,246],"connectivity":[67],"$k_c$?":[68],"What":[69],"controls":[70],"optimal":[72,239],"allocation?":[73],"This":[74,228],"calls":[75],"for":[76,119],"model":[78,138,189],"in":[79,133,173,216,234],"which":[80],"can":[83],"be":[84],"tuned":[85],"independently":[86],"width":[88],"connectivity.":[90],"Accordingly,":[91],"we":[92],"introduce":[93],"ELM":[95],"Network,":[96],"whose":[97],"layer":[99],"is":[100,236,244],"built":[101],"Expressive":[103],"Leaky":[104],"Memory":[105],"(ELM)":[106],"neurons,":[107],"chosen":[108],"to":[109],"mirror":[110],"functional":[111],"components":[112],"cortical":[114],"neurons.":[115,185],"The":[116],"architecture":[117],"allows":[118],"individually":[120],"adjusting":[121],"$k_c$":[125],"trains":[127],"stably":[128],"across":[129],"orders":[130,213],"magnitude":[132,215],"scale.":[134],"evaluate":[136],"on":[139,251,254],"two":[140,199],"qualitatively":[141],"different":[142],"sequence":[143],"benchmarks:":[144],"neuromorphic":[146],"SHD-Adding":[147],"task":[148],"Enwik8":[150],"character-level":[151],"language":[152],"modeling.":[153],"Performance":[154],"improves":[155],"monotonically":[156],"along":[157],"each":[158],"three":[161,212],"axes":[162],"individually.":[163],"Under":[164],"budget,":[167],"clear":[169],"non-trivial":[170],"optimum":[171],"emerges":[172],"their":[174],"tradeoff,":[175],"larger":[177],"budgets":[178],"favor":[179],"both":[180],"more":[181,183],"complex":[184,255],"A":[186,208],"closed-form":[187],"information-theoretic":[188],"captures":[190],"these":[191],"tradeoffs":[192],"attributes":[194],"diminishing":[196],"returns":[197],"at":[198],"ends":[200],"to:":[201],"per-neuron":[202],"signal-to-noise":[203],"saturation":[204],"across-neuron":[206],"redundancy.":[207],"hyperparameter":[209],"sweep":[210],"spanning":[211],"trainable":[217],"parameters":[218],"traces":[219],"near-Pareto-frontier":[221],"scaling":[222],"law":[223],"consistent":[224],"with":[225],"framework.":[227],"suggests":[229],"that":[230],"simple-unit":[232],"ML":[235],"not":[237],"obviously":[238],"once":[240],"tradeoff":[242],"surface":[243],"probed,":[245],"offers":[247],"lens":[250],"cortex's":[252],"reliance":[253],"spatio-temporal":[256],"integrators.":[257]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-14T00:00:00"}
