https://doi.org/10.1140/epjb/s10051-026-01163-w
Research – Statistical and Nonlinear Physics
Retrieval properties of attractor neural networks with regulated levels of activity
Faculty of Physics, Kim Il Sung University, Taesong District, Pyongyang, Democratic People’s Republic of Korea
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
8
September
2025
Accepted:
1
April
2026
Published online:
7
May
2026
Abstract
As a special case of the Potts model of cortical dynamics, we study a network of McCulloch–Pitts neurons which can be considered as Potts units with only one active state (S = 1). We add anti-symmetric Gaussian noise to the Hebbian component of the interaction matrix, and introduce an extra term in the dynamics of the network in order to constrain its mean activity around a prescribed level. We have investigated maximal storage capacity, basin of attraction and distribution of metastable states in terms of mean-field theory as well as computer simulations. When we constrain the mean activity of the network, maximal storage capacity improves but by tiny amount, while the basin of attraction shrinks a lot. The retrieval band and bandgap of metastable states become wider upon constraining the mean activity. When we introduce asymmetry into the interaction matrix, basin of attraction shrinks a little while the total number of metastable states decreases. Given that constraining mean activity increases storage capacity by several orders of magnitude for the Potts model with S > 1, our results show that the network with S = 1 behaves quite differently in terms of retrieval dynamics.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
