{"id":"https://openalex.org/W7134939736","doi":"https://doi.org/10.48550/arxiv.2603.09600","title":"A Variational Latent Equilibrium for Learning in Neuronal Circuits","display_name":"A Variational Latent Equilibrium for Learning in Neuronal Circuits","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134939736","doi":"https://doi.org/10.48550/arxiv.2603.09600"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.09600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09600","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.2603.09600","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005457342","display_name":"Simon D. Brandt","orcid":"https://orcid.org/0000-0001-8632-5372"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brandt, Simon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045119130","display_name":"Paul Haider","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haider, Paul","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128760504","display_name":"Walter Senn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Senn, Walter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053538096","display_name":"Federico Benitez","orcid":"https://orcid.org/0000-0001-7978-970X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benitez, Federico","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128707313","display_name":"Mihai A. Petrovici","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petrovici, Mihai A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5005457342"],"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/T10581","display_name":"Neural dynamics and brain function","score":0.7336000204086304,"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":0.7336000204086304,"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/T10241","display_name":"Functional Brain Connectivity Studies","score":0.08030000329017639,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.044199999421834946,"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/backpropagation","display_name":"Backpropagation","score":0.4203999936580658},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.41839998960494995},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3871000111103058},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.35010001063346863},{"id":"https://openalex.org/keywords/hebbian-theory","display_name":"Hebbian theory","score":0.3449999988079071},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.3269999921321869},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3237999975681305},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.3034999966621399}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5638999938964844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5515000224113464},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.4203999936580658},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3871000111103058},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.35010001063346863},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34610000252723694},{"id":"https://openalex.org/C111437709","wikidata":"https://www.wikidata.org/wiki/Q1277874","display_name":"Hebbian theory","level":3,"score":0.3449999988079071},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31949999928474426},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30230000615119934},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.28949999809265137},{"id":"https://openalex.org/C2779127903","wikidata":"https://www.wikidata.org/wiki/Q6510194","display_name":"Learning rule","level":3,"score":0.28600001335144043},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C33553690","wikidata":"https://www.wikidata.org/wiki/Q17014702","display_name":"Free energy principle","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C92393732","wikidata":"https://www.wikidata.org/wiki/Q1790374","display_name":"Learning theory","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C118403218","wikidata":"https://www.wikidata.org/wiki/Q43283","display_name":"Biological neural network","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.09600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09600","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.2603.09600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09600","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":{"Brains":[0],"remain":[1,26],"unrivaled":[2],"in":[3,68,180],"their":[4],"ability":[5],"to":[6,17,65,84,144],"recognize":[7],"and":[8,37,79,97,130,160,167,200],"generate":[9],"complex":[10,54],"spatiotemporal":[11,88,177],"patterns.":[12],"While":[13],"AI":[14],"is":[15,40,103],"able":[16],"reproduce":[18],"some":[19],"of":[20,34,94,108,133,163,192],"these":[21,195],"capabilities,":[22],"deep":[23,178],"learning":[24,53,179],"algorithms":[25],"largely":[27],"at":[28],"odds":[29],"with":[30],"our":[31],"current":[32],"understanding":[33],"brain":[35],"circuitry":[36],"dynamics.":[38,169],"This":[39],"prominently":[41],"the":[42,49,123,134,141,181,202],"case":[43],"for":[44,52,118,138,165,176,188],"backpropagation":[45],"through":[46],"time":[47],"(BPTT),":[48],"go-to":[50],"algorithm":[51],"temporal":[55],"dependencies.":[56],"In":[57,122],"this":[58,126,153],"work":[59],"we":[60,113,150],"propose":[61],"a":[62,69,104,128,147,155,173,186],"general":[63,124],"formalism":[64],"approximate":[66],"BPTT":[67],"controlled,":[70],"biologically":[71],"plausible":[72],"manner.":[73],"Our":[74,100,170],"approach":[75],"builds":[76],"on,":[77],"unifies":[78],"extends":[80],"several":[81],"previous":[82],"approaches":[83],"local,":[85],"time-continuous,":[86],"phase-free":[87],"credit":[89],"assignment":[90],"based":[91],"on":[92],"principles":[93],"energy":[95,106],"conservation":[96],"extremal":[98],"action.":[99],"starting":[101],"point":[102],"prospective":[105],"function":[107],"neuronal":[109,120,139],"states,":[110],"from":[111],"which":[112],"calculate":[114],"real-time":[115],"error":[116],"dynamics":[117],"time-continuous":[119,142],"networks.":[121],"case,":[125],"provides":[127,172],"simple":[129],"straightforward":[131],"derivation":[132],"adjoint":[135],"method":[136],"result":[137],"networks,":[140],"equivalent":[143],"BPTT.":[145],"With":[146],"few":[148],"modifications,":[149],"can":[151],"turn":[152],"into":[154],"fully":[156],"local":[157],"(in":[158],"space":[159],"time)":[161],"set":[162],"equations":[164],"neuron":[166],"synapse":[168],"theory":[171],"rigorous":[174],"framework":[175],"brain,":[182],"while":[183],"simultaneously":[184],"suggesting":[185],"blueprint":[187],"physical":[189],"circuits":[190],"capable":[191],"carrying":[193],"out":[194],"computations.":[196],"These":[197],"results":[198],"reframe":[199],"extend":[201],"recently":[203],"proposed":[204],"Generalized":[205],"Latent":[206],"Equilibrium":[207],"(GLE)":[208],"model.":[209]},"counts_by_year":[],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2026-03-12T00:00:00"}
