{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T06:11:07Z","timestamp":1781590267210,"version":"3.54.5"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,3]],"date-time":"2017-09-03T00:00:00Z","timestamp":1504396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study latching dynamics in the adaptive Potts model network, through numerical simulations with randomly and also weakly correlated patterns, and we focus on comparing its slowly and fast adapting regimes. A measure, Q, is used to quantify the quality of latching in the phase space spanned by the number of Potts states S, the number of connections per Potts unit C and the number of stored memory patterns p. We find narrow regions, or bands in phase space, where distinct pattern retrieval and duration of latching combine to yield the highest values of Q. The bands are confined by the storage capacity curve, for large p, and by the onset of finite latching, for low p. Inside the band, in the slowly adapting regime, we observe complex structured dynamics, with transitions at high crossover between correlated memory patterns; while away from the band latching, transitions lose complexity in different ways: below, they are clear-cut but last such few steps as to span a transition matrix between states with few asymmetrical entries and limited entropy; while above, they tend to become random, with large entropy and bi-directional transition frequencies, but indistinguishable from noise. Extrapolating from the simulations, the band appears to scale almost quadratically in the p\u2013S plane, and sublinearly in p\u2013C. In the fast adapting regime, the band scales similarly, and it can be made even wider and more robust, but transitions between anti-correlated patterns dominate latching dynamics. This suggest that slow and fast adaptation have to be integrated in a scenario for viable latching in a cortical system. The results for the slowly adapting regime, obtained with randomly correlated patterns, remain valid also for the case with correlated patterns, with just a simple shift in phase space.<\/jats:p>","DOI":"10.3390\/e19090468","type":"journal-article","created":{"date-parts":[[2017,9,4]],"date-time":"2017-09-04T11:11:52Z","timestamp":1504523512000},"page":"468","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Life on the Edge: Latching Dynamics in a Potts Neural Network"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7602-2845","authenticated-orcid":false,"given":"Chol","family":"Kang","sequence":"first","affiliation":[{"name":"Cognitive Neuroscience, SISSA\u2014International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy"},{"name":"The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4419-9301","authenticated-orcid":false,"given":"Michelangelo","family":"Naim","sequence":"additional","affiliation":[{"name":"Cognitive Neuroscience, SISSA\u2014International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy"},{"name":"Department of Physics, La Sapienza Universit\u00e0 di Roma, Piazzale Aldo Moro, 5, 00185 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2476-8714","authenticated-orcid":false,"given":"Vezha","family":"Boboeva","sequence":"additional","affiliation":[{"name":"Cognitive Neuroscience, SISSA\u2014International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":"Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hauser, M.D., Chomsky, N., and Fitch, W.T. (2002). The Faculty of language: What is it, who has it, and how did it evolve?. Science, 298.","DOI":"10.1126\/science.298.5598.1569"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Amit, D.J. (1995). The Hebbian paradigm reintegrated: Local reverberations as internal representations. Behav. Brain. Sci., 18.","DOI":"10.1017\/S0140525X00040164"},{"key":"ref_3","unstructured":"Kaneko, K., and Tsuda, I. (2003). Dynamic link of memory\u2014Chaotic memory map in nonequilibrium neural networks. Chaos, 13."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","unstructured":"Amit, D.J., Gutfreund, H., and Sompolinsky, H. (1987). Statistical mechanics of neural networks near saturation. Ann. Phys., 173.","DOI":"10.1016\/0003-4916(87)90092-3"},{"key":"ref_6","unstructured":"Amit, D.J. (1992). Modeling Brain Function, Cambridge University Press."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Rolls, E.T., and Treves, A. (1998). Neural Networks and Brain Function, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198524328.001.0001"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1038\/nature12112","article-title":"Hippocampal place cell sequences depict future paths to remembered goals","volume":"497","author":"Pfeiffer","year":"2013","journal-title":"Nature"},{"key":"ref_9","unstructured":"Abeles, M. (2012). Local Cortical Circuits: An Electrophysiological Study, Springer Science & Business Media."},{"key":"ref_10","unstructured":"Chossat, P., Krupa, M., and Lavigne, F. (2016). Latching dynamics in neural networks with synaptic depression. arXiv."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1080\/096582196388906","article-title":"Confabulation and the control of recollection","volume":"4","author":"Burgess","year":"1996","journal-title":"Memory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1006\/ccog.2000.0486","article-title":"The neural-cognitive basis of the Jamesian stream of thought","volume":"9","author":"Epstein","year":"2000","journal-title":"Conscious. Cognit."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1126\/science.1097725","article-title":"Time is precious","volume":"304","author":"Abeles","year":"2004","journal-title":"Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1038\/nrn1706","article-title":"Brain mechanisms linking language and action","volume":"6","year":"2005","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2645","DOI":"10.1152\/jn.00798.2005","article-title":"Temporally precise cortical firing patterns are associated with distinct action segments","volume":"96","author":"Shmiel","year":"2006","journal-title":"J. Neurophysiol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s11571-007-9025-x","article-title":"The point of no return in planar hand movements: An indication of the existence of high level motion primitives","volume":"1","author":"Sosnik","year":"2007","journal-title":"Cognit. Neurodyn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2739","DOI":"10.1103\/PhysRevA.37.2739","article-title":"Potts-glass models of neural networks","volume":"37","author":"Kanter","year":"1988","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Boll\u00e9, D., Dupont, P., and Mourik, J.V. (1991). Stability properties of potts neural networks with biased patterns and low loading. J. Phys. A Math. Gen., 24.","DOI":"10.1088\/0305-4470\/24\/5\/021"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Boll\u00e9, D., Dupont, P., and Huyghebaert, J. (1992). Thermodynamic properties of the Q-state potts-glass neural network. Phys. Rev. A, 45.","DOI":"10.1103\/PhysRevA.45.4194"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1007\/BF01049424","article-title":"On the parallel dynamics of the Q-state potts and Q-ising neural networks","volume":"70","author":"Inck","year":"1993","journal-title":"J. Stat. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Boll\u00e9, D., Cools, R., Dupont, P., and Huyghebaert, J. (1993). Mean-field theory for the Q-state potts-glass neural network with biased patterns. J. Phys. A Math. Gen., 26.","DOI":"10.1088\/0305-4470\/26\/3\/017"},{"key":"ref_22","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":"Cogn. Neuropsychol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kropff, E., and Treves, A. (2005). The storage capacity of potts models for semantic memory retrieval. J. Stat. Mech. Theor. Exp.","DOI":"10.1088\/1742-5468\/2005\/08\/P08010"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Russo, E., Namboodiri, V.M.K., Treves, A., and Kropff, E. (2008). Free association transitions in models of cortical latching dynamics. New J. Phys., 10.","DOI":"10.1088\/1367-2630\/10\/1\/015008"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Russo, E., and Treves, A. (2012). Cortical free-association dynamics: Distinct phases of a latching network. Phys. Rev. E, 85.","DOI":"10.1103\/PhysRevE.85.051920"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Abdollah-nia, M.F., Saeedghalati, M., and Abbassian, A. (2012). Optimal region of latching activity in an adaptive Potts model for networks of neurons. J. Stat. Mech. Theory Exp.","DOI":"10.1088\/1742-5468\/2012\/02\/P02018"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1111\/cogs.12007","article-title":"Spreading activation in an attractor network with latching dynamics: Automatic semantic priming revisited","volume":"36","author":"Lerner","year":"2012","journal-title":"Cogn. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lerner, I., Bentin, S., and Shriki, O. (2012). Excessive attractor instability accounts for semantic priming in schizophrenia. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0040663"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"O\u2019Kane, D., and Treves, A. (1992). Short-and long-range connections in autoassociative memory. J. Phys. A Math. Gen., 25.","DOI":"10.1088\/0305-4470\/25\/19\/018"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2523","DOI":"10.1162\/NECO_a_00499","article-title":"Scaling laws of associative memory retrieval","volume":"25","author":"Romani","year":"2013","journal-title":"Neural Comput."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Recanatesi, S., Katkov, M., Romani, S., and Tsodyks, M. (2015). Neural network model of memory retrieval. Front. Comput. Neurosci., 9.","DOI":"10.3389\/fncom.2015.00149"},{"key":"ref_32","unstructured":"Naim, M., Boboeva, V., Kang, C.J., and Treves, A. (2017). From multi-modular Hopfield networks to the Potts network and its storage capacity, Unpublished work."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11047-006-9019-3","article-title":"The complexity of latching transitions in large scale cortical networks","volume":"6","author":"Kropff","year":"2007","journal-title":"Nat. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hebb, D.O. (2005). The Organization of Behavior: A Neuropsychological Theory, John Wiley & Sons.","DOI":"10.4324\/9781410612403"},{"key":"ref_35","unstructured":"Boboeva, V., and Treves, A. (2017). The storage capacity of the Potts network with correlated patterns, Unpublished work."},{"key":"ref_36","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, John Wiley & Sons. [2nd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, R., and Gu, F. (2011). Associative latching dynamics vs. syntax. Advances in Cognitive Neurodynamics (II), Springer.","DOI":"10.1007\/978-90-481-9695-1"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s11571-013-9261-1","article-title":"A modular latching chain","volume":"8","author":"Song","year":"2014","journal-title":"Cogn. Neurodyn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.cognition.2006.04.002","article-title":"On the emergence of modern humans","volume":"103","author":"Amati","year":"2007","journal-title":"Cognition"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.neuron.2016.02.009","article-title":"Recurrent network models of sequence generation and memory","volume":"9","author":"Rajan","year":"2016","journal-title":"Neuron"},{"key":"ref_41","first-page":"548","article-title":"Multitask TSK fuzzy system modeling by mining intertask common hidden structure","volume":"45","author":"Jiang","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1016\/j.eswa.2011.08.100","article-title":"Recurrent type-2 fuzzy neural network using Haar wavelet energy and entropy features for speech detection in noisy environments","volume":"39","author":"Tu","year":"2012","journal-title":"Expert Syst. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/9\/468\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:44:01Z","timestamp":1760208241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/9\/468"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,3]]},"references-count":42,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["e19090468"],"URL":"https:\/\/doi.org\/10.3390\/e19090468","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,3]]}}}