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Entropy 2017, 19(9), 468; https://doi.org/10.3390/e19090468

Life on the Edge: Latching Dynamics in a Potts Neural Network

1
Cognitive Neuroscience, SISSA—International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
2
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
3
Department of Physics, La Sapienza Università di Roma, Piazzale Aldo Moro, 5, 00185 Roma, Italy
4
Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Received: 2 August 2017 / Revised: 25 August 2017 / Accepted: 29 August 2017 / Published: 3 September 2017
(This article belongs to the Special Issue Information Theory in Neuroscience)
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Abstract

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 pS plane, and sublinearly in pC. 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. View Full-Text
Keywords: neural network; Potts model; latching; recursion neural network; Potts model; latching; recursion
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kang, C.J.; Naim, M.; Boboeva, V.; Treves, A. Life on the Edge: Latching Dynamics in a Potts Neural Network. Entropy 2017, 19, 468.

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