{"id":"https://openalex.org/W7153119699","doi":"https://doi.org/10.48550/arxiv.2604.07401","title":"Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory","display_name":"Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory","publication_year":2026,"publication_date":"2026-04-08","ids":{"openalex":"https://openalex.org/W7153119699","doi":"https://doi.org/10.48550/arxiv.2604.07401"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07401","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07401","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.07401","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080510384","display_name":"Tatiana V. Petrova","orcid":"https://orcid.org/0000-0002-0563-6521"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Petrova, Tatiana","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122913706","display_name":"Evgeny V. Polyachenko","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Polyachenko, Evgeny","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069228908","display_name":"Radu State","orcid":"https://orcid.org/0000-0002-4751-9577"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"State, Radu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080510384"],"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/T10320","display_name":"Neural Networks and Applications","score":0.5516999959945679,"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/T10320","display_name":"Neural Networks and Applications","score":0.5516999959945679,"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/T10581","display_name":"Neural dynamics and brain function","score":0.12110000103712082,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.019999999552965164,"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/spurious-relationship","display_name":"Spurious relationship","score":0.8391000032424927},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.7289999723434448},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5679000020027161},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4927000105381012},{"id":"https://openalex.org/keywords/bidirectional-associative-memory","display_name":"Bidirectional associative memory","score":0.44339999556541443},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.429500013589859},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.4253999888896942},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.39160001277923584},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.3767000138759613}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.8391000032424927},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.7289999723434448},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5679000020027161},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4927000105381012},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47760000824928284},{"id":"https://openalex.org/C120620853","wikidata":"https://www.wikidata.org/wiki/Q506355","display_name":"Bidirectional associative memory","level":4,"score":0.44339999556541443},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42579999566078186},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.4253999888896942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39250001311302185},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.39160001277923584},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.326200008392334},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.31700000166893005},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C111437709","wikidata":"https://www.wikidata.org/wiki/Q1277874","display_name":"Hebbian theory","level":3,"score":0.2881999909877777},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.28189998865127563},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26579999923706055},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26249998807907104},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.2572000026702881}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07401","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07401","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.07401","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07401","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":"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":{"We":[0,27],"study":[1],"the":[2,56,62,66,69,72,116,130,148],"thermodynamic":[3,29],"memory":[4,153,164],"capacity":[5,39,75],"of":[6,23,150,158],"modern":[7,162],"Hopfield":[8],"networks":[9,36],"(Dense":[10],"Associative":[11,34],"Memory":[12,35],"models)":[13],"with":[14,37],"continuous":[15,51],"states":[16],"under":[17],"geometric":[18,57],"constraints,":[19],"extending":[20],"classical":[21],"analyses":[22],"pairwise":[24],"associative":[25,152],"memory.":[26],"derive":[28],"phase":[30,100],"boundaries":[31],"for":[32,103],"Dense":[33],"exponential":[38],"$M":[40],"=":[41],"e^{\u03b1N}$,":[42],"comparing":[43],"Gaussian":[44],"(LSE)":[45],"and":[46,133,154],"Epanechnikov":[47],"(LSR)":[48],"kernels.":[49],"For":[50,114],"neurons":[52],"on":[53,61],"an":[54],"$N$-sphere,":[55],"entropy":[58],"depends":[59],"solely":[60],"spherical":[63],"geometry,":[64],"not":[65],"kernel.":[67],"In":[68],"sharp-kernel":[70],"regime,":[71],"maximum":[73],"theoretical":[74],"$\u03b1=":[76],"0.5$":[77],"is":[78,140],"achieved":[79],"at":[80,109,142],"zero":[81],"temperature;":[82],"below":[83,123],"this":[84],"threshold,":[85],"a":[86,105,120],"critical":[87,106,135],"line":[88,107,136],"separates":[89],"retrieval":[90,139,159],"from":[91],"non-retrieval.":[92],"The":[93],"two":[94],"kernels":[95],"differ":[96],"qualitatively":[97],"in":[98,161],"their":[99],"boundary":[101],"structure:":[102],"LSE,":[104],"exists":[108,137],"all":[110],"loads":[111],"$\u03b1>":[112],"0$.":[113],"LSR,":[115],"finite":[117],"support":[118],"introduces":[119],"threshold":[121],"$\u03b1_{\\text{th}}$":[122],"which":[124],"no":[125,134],"spurious":[126],"patterns":[127],"contribute":[128],"to":[129],"noise":[131],"floor,":[132],"--":[138],"perfect":[141],"any":[143],"temperature.":[144],"These":[145],"results":[146],"advance":[147],"theory":[149],"high-capacity":[151],"clarify":[155],"fundamental":[156],"limits":[157],"robustness":[160],"attention-like":[163],"architectures.":[165]},"counts_by_year":[],"updated_date":"2026-05-08T13:12:06.581006","created_date":"2026-04-11T00:00:00"}