{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T08:26:44Z","timestamp":1776155204328,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T00:00:00Z","timestamp":1540512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100004412","name":"Human Frontier Science Program","doi-asserted-by":"publisher","award":["RGP0057\/2016"],"award-info":[{"award-number":["RGP0057\/2016"]}],"id":[{"id":"10.13039\/100004412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through \u201cfactors\u201d that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a dataset of nouns. We find that such correlations reduce the storage capacity of a Potts network to a limited extent, so that the number of concepts that can be stored and retrieved in a large, human-scale cortical network may still be of order 107, as originally estimated without correlations. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving\u2019s remember\/know paradigms.<\/jats:p>","DOI":"10.3390\/e20110824","type":"journal-article","created":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T10:51:01Z","timestamp":1540551061000},"page":"824","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["The Capacity for Correlated Semantic Memories in the Cortex"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2476-8714","authenticated-orcid":false,"given":"Vezha","family":"Boboeva","sequence":"first","affiliation":[{"name":"Cognitive Neuroscience, SISSA\u2014International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8580-2173","authenticated-orcid":false,"given":"Romain","family":"Brasselet","sequence":"additional","affiliation":[{"name":"Cognitive Neuroscience, SISSA\u2014International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7246-5673","authenticated-orcid":false,"given":"Alessandro","family":"Treves","sequence":"additional","affiliation":[{"name":"Cognitive Neuroscience, SISSA\u2014International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy"},{"name":"Kavli Institute for Systems Neuroscience\/Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1006\/jmla.2002.2864","article-title":"The nature of recollection and familiarity: A review of 30 years of research","volume":"46","author":"Yonelinas","year":"2002","journal-title":"J. Mem. Lang."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1002\/hipo.450020209","article-title":"Computational constraints suggest the need for two distinct input systems to the hippocampal CA3 network","volume":"2","author":"Treves","year":"1992","journal-title":"Hippocampus"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"18428","DOI":"10.1073\/pnas.1421056111","article-title":"Place cells in the hippocampus: Eleven maps for eleven rooms","volume":"111","author":"Alme","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2702","DOI":"10.1111\/j.1460-9568.2007.05881.x","article-title":"Differential impact of brain damage on the access mode to memory representations: An information theoretic approach","volume":"26","author":"Ciaramelli","year":"2007","journal-title":"Eur. J. Neurosci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1016\/j.neuron.2012.10.014","article-title":"A continuous semantic space describes the representation of thousands of object and action categories across the human brain","volume":"76","author":"Huth","year":"2012","journal-title":"Neuron"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1038\/nature17637","article-title":"Natural speech reveals the semantic maps that tile human cerebral cortex","volume":"532","author":"Huth","year":"2016","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1126\/science.1152876","article-title":"Predicting human brain activity associated with the meanings of nouns","volume":"320","author":"Mitchell","year":"2008","journal-title":"Science"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/S0022-5371(69)80069-1","article-title":"Retrieval time from semantic memory","volume":"8","author":"Collins","year":"1969","journal-title":"J. Verbal Learn. Verbal Behav."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1080\/14640747508400525","article-title":"The selective impairment of semantic memory","volume":"27","author":"Warrington","year":"1975","journal-title":"Q. J. Exp. Psychol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0303-2647(96)01645-0","article-title":"On the perceptual structure of face space","volume":"40","author":"Treves","year":"1997","journal-title":"BioSystems"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1857","DOI":"10.1051\/jphys:0198600470110185700","article-title":"The ultrametric organization of memories in a neural network","volume":"47","author":"Parga","year":"1986","journal-title":"J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1103\/PhysRevA.37.570","article-title":"Neural networks with hierarchically correlated patterns","volume":"37","author":"Gutfreund","year":"1988","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1051\/jphys:01990005105038700","article-title":"Prosopagnosia in high capacity neural networks storing uncorrelated classes","volume":"51","author":"Franz","year":"1990","journal-title":"J. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0370-1573(89)90050-1","article-title":"Categorization in neural networks and prosopagnosia","volume":"184","author":"Virasoro","year":"1989","journal-title":"Phys. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Brasselet, R., and Arleo, A. (2018). Category Structure and Categorical Perception Jointly Explained by Similarity-Based Information Theory. Entropy, 20.","DOI":"10.3390\/e20070527"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shallice, T., and Cooper, R. (2011). The Organisation of Mind, Oxford University Press.","DOI":"10.1093\/acprof:osobl\/9780199579242.001.0001"},{"key":"ref_17","first-page":"45","article-title":"A general framework for parallel distributed processing","volume":"1","author":"Rumelhart","year":"1986","journal-title":"Parallel Distrib. Process. Explor. Microstruct. Cognit."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1037\/0096-3445.120.4.339","article-title":"A computational model of semantic memory impairment: Modality specificity and emergent category specificity","volume":"120","author":"Farah","year":"1991","journal-title":"J. Exp. Psychol. Gen."},{"key":"ref_19","unstructured":"Plaut, D.C. (1995, January 22\u201325). Semantic and associative priming in a distributed attractor network. Proceedings of the 17th Annual Conference of the Cognitive Science Society, Hillsdale, NJ, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1037\/0033-295X.111.1.205","article-title":"Structure and deterioration of semantic memory: A neuropsychological and computational investigation","volume":"111","author":"Rogers","year":"2004","journal-title":"Psychol. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/PL00007964","article-title":"A quantitative analysis of the local connectivity between pyramidal neurons in layers 2\/3 of the rat visual cortex","volume":"82","author":"Hellwig","year":"2000","journal-title":"Biol. Cybern."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"P07010","DOI":"10.1088\/1742-5468\/2004\/07\/P07010","article-title":"An associative network with spatially organized connectivity","volume":"2004","author":"Roudi","year":"2004","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1002\/(SICI)1096-9861(19961223)376:4<614::AID-CNE9>3.0.CO;2-4","article-title":"Patterns of intrinsic and associational circuitry in monkey prefrontal cortex","volume":"376","author":"Pucak","year":"1996","journal-title":"J. Comp. Neurol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Braitenberg, V., and Sch\u00fcz, A. (1991). Anatomy of the Cortex: Statistics and Geometry, Springer Science & Business Media.","DOI":"10.1007\/978-3-662-02728-8"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5055","DOI":"10.1088\/0305-4470\/25\/19\/018","article-title":"Short-and long-range connections in autoassociative memory","volume":"25","author":"Treves","year":"1992","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1088\/0954-898X_3_4_002","article-title":"Why the simplest notion of neocortex as an autoassociative memory would not work","volume":"3","author":"Treves","year":"1992","journal-title":"Netw. Comput. Neural Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0303-2647(98)00049-5","article-title":"Modeling neocortical areas with a modular neural network","volume":"48","author":"Mari","year":"1998","journal-title":"Biosystems"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/j.neucom.2005.12.002","article-title":"Attractor neural networks with patchy connectivity","volume":"69","author":"Johansson","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s10827-016-0590-z","article-title":"Storing structured sparse memories in a multi-modular cortical network model","volume":"40","author":"Dubreuil","year":"2016","journal-title":"J. Comput. Neurosci."},{"key":"ref_30","unstructured":"Sabour, S., Frosst, N., and Hinton, G.E. (2017, January 4\u20139). Dynamic routing between capsules. Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"043304","DOI":"10.1088\/1742-5468\/aab683","article-title":"Reducing a cortical network to a Potts model yields storage capacity estimates","volume":"2018","author":"Naim","year":"2018","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","article-title":"Neural networks and physical systems with emergent collective computational abilities","volume":"79","author":"Hopfield","year":"1982","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1209\/0295-5075\/6\/2\/002","article-title":"The enhanced storage capacity in neural networks with low activity level","volume":"6","author":"Tsodyks","year":"1988","journal-title":"EPL (Europhys. Lett.)"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"P08010","DOI":"10.1088\/1742-5468\/2005\/08\/P08010","article-title":"The storage capacity of Potts models for semantic memory retrieval","volume":"2005","author":"Kropff","year":"2005","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"M\u00e9zard, M., Parisi, G., and Virasoro, M.A. (1987). Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications, World Scientific Publishing Co Inc.","DOI":"10.1142\/0271"},{"key":"ref_36","unstructured":"Amit, D.J. (1992). Modeling Brain Function: The World of Attractor Neural Networks, Cambridge University Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1080\/02643290442000329","article-title":"Frontal latching networks: A possible neural basis for infinite recursion","volume":"22","author":"Treves","year":"2005","journal-title":"Cognit. Neuropsychol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1162\/089892904322926773","article-title":"Semantic relevance and semantic disorders","volume":"16","author":"Sartori","year":"2004","journal-title":"J. Cognit. Neurosci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1525\/aa.1964.66.3.02a00880","article-title":"Semantic differential technique in the comparative study of cultures","volume":"66","author":"Osgood","year":"1964","journal-title":"Am. Anthropol."},{"key":"ref_40","first-page":"1216","article-title":"On the storage capacity of Hopfield models with correlated patterns","volume":"8","year":"1998","journal-title":"Ann. Appl. Probab."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"L285","DOI":"10.1088\/0305-4470\/23\/6\/009","article-title":"Storage capacity for hierarchically correlated patterns","volume":"23","author":"Engel","year":"1990","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1103\/PhysRevE.48.867","article-title":"Self-consistent signal-to-noise analysis of the statistical behavior of analog neural networks and enhancement of the storage capacity","volume":"48","author":"Shiino","year":"1993","journal-title":"Phys. Rev. E"},{"key":"ref_43","first-page":"225","article-title":"Full solution for the storage of correlated memories in an autoassociative memory","volume":"2","author":"Kropff","year":"2009","journal-title":"Comput. Model. Behav. Neurosci. Closing Gap Neurophysiol. Behav."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/BF01020883","article-title":"Pair-correlated patterns in Hopfield model of neural networks","volume":"62","author":"Tamarit","year":"1991","journal-title":"J. Stat. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1037\/h0044417","article-title":"The discrimination of speech sounds within and across phoneme boundaries","volume":"54","author":"Liberman","year":"1957","journal-title":"J. Exp. Psychol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-5371(73)80056-8","article-title":"Semantic distance and the verification of semantic relations","volume":"12","author":"Rips","year":"1973","journal-title":"J. Verbal Learn. Verbal Behav."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/0010-0285(75)90024-9","article-title":"Family resemblances: Studies in the internal structure of categories","volume":"7","author":"Rosch","year":"1975","journal-title":"Cognit. Psychol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"93","DOI":"10.3758\/BF03212211","article-title":"Human adults and human infants show a \u201cperceptual magnet effect\u201d for the prototypes of speech categories, monkeys do not","volume":"50","author":"Kuhl","year":"1991","journal-title":"Percept. Psychophys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1037\/a0017196","article-title":"The influence of categories on perception: Explaining the perceptual magnet effect as optimal statistical inference","volume":"116","author":"Feldman","year":"2009","journal-title":"Psychol. Rev."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2425","DOI":"10.1126\/science.1063736","article-title":"Distributed and overlapping representations of faces and objects in ventral temporal cortex","volume":"293","author":"Haxby","year":"2001","journal-title":"Science"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.tics.2006.07.005","article-title":"Beyond mind-reading: Multi-voxel pattern analysis of fMRI data","volume":"10","author":"Norman","year":"2006","journal-title":"Trends Cognit. Sci."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"R764","DOI":"10.1016\/j.cub.2013.05.041","article-title":"Interplay of hippocampus and prefrontal cortex in memory","volume":"23","author":"Preston","year":"2013","journal-title":"Curr. Biol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.jphysparis.2006.09.008","article-title":"Dissociating episodic from semantic access mode by mutual information measures: Evidence from aging and Alzheimer\u2019s disease","volume":"100","author":"Ciaramelli","year":"2006","journal-title":"J. Physiol. Paris"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1146\/annurev.psych.53.100901.135114","article-title":"Episodic memory: From mind to brain","volume":"53","author":"Tulving","year":"2002","journal-title":"Annu. Rev. Psychol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1136\/jnnp.62.5.431","article-title":"Disorders of semantic memory","volume":"62","author":"Garrard","year":"1997","journal-title":"J. Neurol. Neurosurg. Psychiatry"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Conrad, C. (1972). Cognitive Economy in Semantic Memory, American Psychological Association.","DOI":"10.1037\/h0032072"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Spivey, M., Joanisse, M., and McRae, K. (2012). The Cambridge Handbook of Psycholinguistics, Cambridge University Press.","DOI":"10.1017\/CBO9781139029377"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1126\/science.aam6808","article-title":"Engrams and circuits crucial for systems consolidation of a memory","volume":"356","author":"Kitamura","year":"2017","journal-title":"Science"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1037\/0033-295X.102.3.419","article-title":"Why there are complementary learning systems in the hippocampus and neocortex: Insights from the successes and failures of connectionist models of learning and memory","volume":"102","author":"McClelland","year":"1995","journal-title":"Psychol. Rev."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/824\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:26Z","timestamp":1760196386000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/824"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,26]]},"references-count":59,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["e20110824"],"URL":"https:\/\/doi.org\/10.3390\/e20110824","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201808.0251.v1","asserted-by":"object"},{"id-type":"doi","id":"10.1101\/321703","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,26]]}}}