{"id":"https://openalex.org/W7142294399","doi":"https://doi.org/10.1016/j.neucom.2026.133472","title":"Self-orthogonalizing attractor neural networks emerging from the free energy principle","display_name":"Self-orthogonalizing attractor neural networks emerging from the free energy principle","publication_year":2026,"publication_date":"2026-03-28","ids":{"openalex":"https://openalex.org/W7142294399","doi":"https://doi.org/10.1016/j.neucom.2026.133472"},"language":"en","primary_location":{"id":"doi:10.1016/j.neucom.2026.133472","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.neucom.2026.133472","pdf_url":null,"source":{"id":"https://openalex.org/S45693802","display_name":"Neurocomputing","issn_l":"0925-2312","issn":["0925-2312","1872-8286"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neurocomputing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.neucom.2026.133472","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043472063","display_name":"Tam\u00e1s Spis\u00e1k","orcid":"https://orcid.org/0000-0002-2942-0821"},"institutions":[{"id":"https://openalex.org/I4210119759","display_name":"Essen University Hospital","ror":"https://ror.org/02na8dn90","country_code":"DE","type":"funder","lineage":["https://openalex.org/I4210119759"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tamas Spisak","raw_affiliation_strings":["Center for Translational Neuro- and Behavioral Sciences (C-TNBS), University Medicine Essen, Essen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2942-0821","affiliations":[{"raw_affiliation_string":"Center for Translational Neuro- and Behavioral Sciences (C-TNBS), University Medicine Essen, Essen, Germany","institution_ids":["https://openalex.org/I4210119759"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130823892","display_name":"Karl Friston","orcid":null},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Karl Friston","raw_affiliation_strings":["Queen Square Institute of Neurology, University College London, WC1N 3AR, UK VERSES, Los Angeles, CA 90067, USA"],"raw_orcid":"https://orcid.org/0000-0001-7984-8909","affiliations":[{"raw_affiliation_string":"Queen Square Institute of Neurology, University College London, WC1N 3AR, UK VERSES, Los Angeles, CA 90067, USA","institution_ids":["https://openalex.org/I45129253","https://openalex.org/I166337079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043472063"],"corresponding_institution_ids":["https://openalex.org/I4210119759"],"apc_list":{"value":2470,"currency":"USD","value_usd":2470},"apc_paid":{"value":2470,"currency":"USD","value_usd":2470},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.65204541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"682","issue":null,"first_page":"133472","last_page":"133472"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.3864000141620636,"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/T11883","display_name":"Embodied and Extended Cognition","score":0.3864000141620636,"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/T10581","display_name":"Neural dynamics and brain function","score":0.17249999940395355,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.09700000286102295,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7843000292778015},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6430000066757202},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6047999858856201},{"id":"https://openalex.org/keywords/free-energy-principle","display_name":"Free energy principle","score":0.5358999967575073},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.4814999997615814},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.453000009059906},{"id":"https://openalex.org/keywords/dynamic-bayesian-network","display_name":"Dynamic Bayesian network","score":0.4410000145435333},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4228000044822693},{"id":"https://openalex.org/keywords/boltzmann-machine","display_name":"Boltzmann machine","score":0.3887999951839447}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7843000292778015},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6430000066757202},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6047999858856201},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5976999998092651},{"id":"https://openalex.org/C33553690","wikidata":"https://www.wikidata.org/wiki/Q17014702","display_name":"Free energy principle","level":2,"score":0.5358999967575073},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5149999856948853},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.4814999997615814},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C82142266","wikidata":"https://www.wikidata.org/wiki/Q3456604","display_name":"Dynamic Bayesian network","level":3,"score":0.4410000145435333},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.3887999951839447},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C2779377595","wikidata":"https://www.wikidata.org/wiki/Q21045424","display_name":"Approximate Bayesian computation","level":3,"score":0.336899995803833},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3325999975204468},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.33090001344680786},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3179999887943268},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3098999857902527},{"id":"https://openalex.org/C192872217","wikidata":"https://www.wikidata.org/wiki/Q720574","display_name":"R\u00f6ssler attractor","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30000001192092896},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.2976999878883362},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C123757187","wikidata":"https://www.wikidata.org/wiki/Q9195957","display_name":"Network dynamics","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.267300009727478},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C2779127903","wikidata":"https://www.wikidata.org/wiki/Q6510194","display_name":"Learning rule","level":3,"score":0.2565999925136566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.neucom.2026.133472","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.neucom.2026.133472","pdf_url":null,"source":{"id":"https://openalex.org/S45693802","display_name":"Neurocomputing","issn_l":"0925-2312","issn":["0925-2312","1872-8286"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neurocomputing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.neucom.2026.133472","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.neucom.2026.133472","pdf_url":null,"source":{"id":"https://openalex.org/S45693802","display_name":"Neurocomputing","issn_l":"0925-2312","issn":["0925-2312","1872-8286"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neurocomputing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.5721098780632019,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311904","display_name":"Wellcome Trust","ror":"https://ror.org/029chgv08"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W1884390770","https://openalex.org/W1971366718","https://openalex.org/W1971715144","https://openalex.org/W1986767000","https://openalex.org/W1990390131","https://openalex.org/W1995114494","https://openalex.org/W2018360451","https://openalex.org/W2027063265","https://openalex.org/W2029182425","https://openalex.org/W2051137788","https://openalex.org/W2051682114","https://openalex.org/W2059238825","https://openalex.org/W2059994748","https://openalex.org/W2062009383","https://openalex.org/W2064675550","https://openalex.org/W2065683694","https://openalex.org/W2106884367","https://openalex.org/W2107433900","https://openalex.org/W2115900486","https://openalex.org/W2116064496","https://openalex.org/W2119885245","https://openalex.org/W2128084896","https://openalex.org/W2131329059","https://openalex.org/W2137411342","https://openalex.org/W2138351621","https://openalex.org/W2148534890","https://openalex.org/W2148764920","https://openalex.org/W2157169496","https://openalex.org/W2165443127","https://openalex.org/W2463330366","https://openalex.org/W2530046647","https://openalex.org/W2590144118","https://openalex.org/W2743911451","https://openalex.org/W2775655637","https://openalex.org/W2950462296","https://openalex.org/W2963208784","https://openalex.org/W2989729815","https://openalex.org/W3040940214","https://openalex.org/W3121698465","https://openalex.org/W3133036396","https://openalex.org/W4206476507","https://openalex.org/W4210357113","https://openalex.org/W4220703647","https://openalex.org/W4245635145","https://openalex.org/W4308294084","https://openalex.org/W4324092353","https://openalex.org/W4365515296","https://openalex.org/W4385338481","https://openalex.org/W4386027963","https://openalex.org/W4388591883","https://openalex.org/W4389952311","https://openalex.org/W4390572244","https://openalex.org/W4393392404","https://openalex.org/W4396780139","https://openalex.org/W4399800561","https://openalex.org/W4402666946","https://openalex.org/W4406090208","https://openalex.org/W4407792652","https://openalex.org/W4409653047"],"related_works":[],"abstract_inverted_index":{"Attractor":[0,210],"dynamics":[1,16,81],"are":[2,212],"a":[3,51,89,135,185,195,222,241],"hallmark":[4],"of":[5,27,33,54,137,188,198,225],"many":[6],"complex":[7],"systems,":[8],"including":[9],"the":[10,31,45,61,98,127,149,155,215],"brain.":[11],"Understanding":[12],"how":[13,40],"such":[14,83],"self-organizing":[15,84,199],"emerge":[17,43],"from":[18,44,214],"first":[19],"principles":[20],"is":[21],"crucial":[22],"for":[23,63,82,205],"advancing":[24],"our":[25],"understanding":[26],"neuronal":[28],"computations":[29],"and":[30,67,70,75,79,112,121,142,154,161,172,180,207,237,258,269,287],"design":[32],"artificial":[34],"intelligence":[35],"systems.":[36,57,85,228],"Here":[37],"we":[38,124],"formalize":[39],"attractor":[41,133,200,253],"networks":[42,129,211,249],"free":[46,99],"energy":[47,100],"principle":[48],"applied":[49,220],"to":[50,116,170,221,266,289],"universal":[52,223],"partitioning":[53,224],"random":[55,166,226],"dynamical":[56,227],"Our":[58,192],"approach":[59,231],"obviates":[60],"need":[62],"explicitly":[64],"imposed":[65],"learning":[66,80,113,238],"inference":[68,78,94,105,236,245],"rules":[69],"identifies":[71],"emergent,":[72,233],"but":[73],"efficient":[74],"biologically":[76,234],"plausible":[77,235],"These":[86,145],"result":[87],"in":[88],"collective,":[90],"multi-level":[91,242],"Bayesian":[92,243],"active":[93,244],"process.":[95,246],"Attractors":[96],"on":[97],"landscape":[101],"encode":[102],"prior":[103],"beliefs;":[104,111],"integrates":[106],"sensory":[107],"data":[108,167,176,263],"into":[109],"posterior":[110],"fine-tunes":[114],"couplings":[115,179,268],"minimize":[117],"long-term":[118],"surprise.":[119],"Analytically":[120],"via":[122],"simulations,":[123],"establish":[125],"that":[126],"proposed":[128],"favor":[130,250],"approximately":[131,251],"orthogonalized":[132,252],"representations,":[134,254],"consequence":[136],"simultaneously":[138],"optimizing":[139,255],"predictive":[140,256],"accuracy":[141,257],"model":[143,259],"complexity.":[144,260],"attractors":[146],"efficiently":[147],"span":[148],"input":[150],"subspace,":[151],"enhancing":[152],"generalization":[153,187],"mutual":[156],"information":[157],"between":[158],"hidden":[159],"causes":[160],"observable":[162],"effects.":[163],"Furthermore,":[164],"while":[165],"presentation":[168,264],"leads":[169,265],"symmetric":[171],"sparse":[173],"couplings,":[174],"sequential":[175],"fosters":[177],"asymmetric":[178,267],"non-equilibrium":[181,270],"steady-state":[182,271],"dynamics,":[183,239,272],"offering":[184],"natural":[186],"conventional":[189,274],"Boltzmann":[190,275],"Machines.":[191,276],"findings":[193],"offer":[194],"unifying":[196],"theory":[197],"networks,":[201],"providing":[202],"novel":[203],"insights":[204],"AI":[206],"neuroscience.":[208],"\u2022":[209,229,247,261,277],"derived":[213],"Free":[216],"Energy":[217],"Principle":[218],"(FEP)":[219],"This":[230],"yields":[232],"forming":[240],"The":[248],"Sequential":[262],"generalizing":[273],"Simulations":[278],"demonstrate":[279],"orthogonal":[280],"basis":[281],"formation,":[282],"generalization,":[283],"sequence":[284],"learning,":[285],"scalability":[286],"resistance":[288],"catastrophic":[290],"forgetting.":[291]},"counts_by_year":[],"updated_date":"2026-04-02T13:48:15.688549","created_date":"2026-03-29T00:00:00"}
