{"id":"https://openalex.org/W7152087690","doi":"https://doi.org/10.48550/arxiv.2604.05042","title":"Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization","display_name":"Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization","publication_year":2026,"publication_date":"2026-04-06","ids":{"openalex":"https://openalex.org/W7152087690","doi":"https://doi.org/10.48550/arxiv.2604.05042"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.05042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05042","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.05042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016600664","display_name":"Arthur N. Montanari","orcid":"https://orcid.org/0000-0002-4866-3888"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Montanari, Arthur N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5097671358","display_name":"Francesco Bullo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bullo, Francesco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133214464","display_name":"Dmitry Krotov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krotov, Dmitry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031220186","display_name":"Adilson E. Motter","orcid":"https://orcid.org/0000-0003-1794-4828"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Motter, Adilson E.","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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.28450000286102295,"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"}},"topics":[{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.28450000286102295,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.11460000276565552,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.06840000301599503,"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/bridging","display_name":"Bridging (networking)","score":0.5835000276565552},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5236999988555908},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46540001034736633},{"id":"https://openalex.org/keywords/hopfield-network","display_name":"Hopfield network","score":0.45509999990463257},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.45170000195503235},{"id":"https://openalex.org/keywords/boltzmann-machine","display_name":"Boltzmann machine","score":0.42289999127388},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4000999927520752},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.3962000012397766},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.3635999858379364}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7188000082969666},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.5835000276565552},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5236999988555908},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4887000024318695},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46540001034736633},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.45509999990463257},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.45170000195503235},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.42289999127388},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.3962000012397766},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32359999418258667},{"id":"https://openalex.org/C2776184637","wikidata":"https://www.wikidata.org/wiki/Q6506039","display_name":"Living systems","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.29260000586509705},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C19273510","wikidata":"https://www.wikidata.org/wiki/Q263847","display_name":"Artificial life","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.2782000005245209},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.26980000734329224},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.262800008058548}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.05042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05042","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.05042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05042","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":"Preprint"},"sustainable_development_goals":[{"score":0.8690897226333618,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Recent":[0],"advances":[1,23],"at":[2],"the":[3,68,109,144,151],"intersection":[4],"of":[5,28,146],"control":[6],"theory,":[7],"neuroscience,":[8],"and":[9,31,39,45,61,72,89,103,106,128,133,156],"machine":[10],"learning":[11,38],"have":[12],"revealed":[13],"novel":[14],"mechanisms":[15],"by":[16,94],"which":[17],"dynamical":[18,81],"systems":[19],"perform":[20],"computation.":[21],"These":[22,114],"encompass":[24],"a":[25],"wide":[26],"range":[27],"conceptual,":[29],"mathematical,":[30],"computational":[32],"ideas,":[33],"with":[34],"applications":[35],"for":[36,120,125,131],"model":[37],"training,":[40],"memory":[41,118],"retrieval,":[42],"data-driven":[43],"control,":[44],"optimization.":[46],"This":[47],"tutorial":[48,137],"focuses":[49],"on":[50,79],"neuro-inspired":[51],"approaches":[52,158],"to":[53,57,111,159],"computation":[54],"that":[55,83],"aim":[56],"improve":[58],"scalability,":[59],"robustness,":[60],"energy":[62,90],"efficiency":[63],"across":[64],"such":[65,98],"tasks,":[66],"bridging":[67],"gap":[69],"between":[70],"artificial":[71,160],"biological":[73],"systems.":[74],"Particular":[75],"emphasis":[76],"is":[77],"placed":[78],"energy-based":[80],"models":[82,119],"encode":[84],"information":[85],"through":[86],"gradient":[87],"flows":[88],"landscapes.":[91],"We":[92],"begin":[93],"reviewing":[95],"classical":[96],"formulations,":[97],"as":[99],"continuous-time":[100],"Hopfield":[101],"networks":[102,124],"Boltzmann":[104],"machines,":[105],"then":[107],"extend":[108],"framework":[110],"modern":[112],"developments.":[113],"include":[115],"dense":[116],"associative":[117],"high-capacity":[121],"storage,":[122],"oscillator-based":[123],"large-scale":[126],"optimization,":[127],"proximal-descent":[129],"dynamics":[130],"composite":[132],"constrained":[134],"reconstruction.":[135],"The":[136],"demonstrates":[138],"how":[139],"control-theoretic":[140],"principles":[141],"can":[142],"guide":[143],"design":[145],"next-generation":[147],"neurocomputing":[148],"systems,":[149],"steering":[150],"discussion":[152],"beyond":[153],"conventional":[154],"feedforward":[155],"backpropagation-based":[157],"intelligence.":[161]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-09T00:00:00"}