Cluster Synchronization as a Mechanism of Free Recall in Working Memory Networks

This article studies free recall, i.e., the reactivation of stored memory items, namely patterns , in any order, of a model of working memory. Our free recall model is based on a biologically plausible modular neural network composed of $H$ modules, namely hypercolumns , each of which is a bundle of $M$ minicolumns . The coupling weights and constant bias values of the network are determined by a Hebbian plasticity rule. Using techniques from nonlinear stability theory, we show that cluster synchronization is the central mechanism governing free recall of orthogonally encoded patterns. Particularly, we show that free recall's cluster synchronization is the combination of two main mechanisms: simultaneous activities of minicolumns representing an encoded pattern, i.e., within-pattern synchronization, together with time-divided activities of minicolumns representing different patterns. We characterize the coupling and bias value conditions under which cluster synchronization emerges. We also discuss the role of heterogeneous coupling weights and bias values of minicolumns' dynamics in free recall. Specifically, we compare the behaviour of two $H \times 2$ networks with identical and non-identical coupling weights and bias values. For these two networks, we obtain bounds on couplings and bias values under which both encoded patterns are recalled. Our analysis shows that having non-identical couplings and bias values for different patterns increases the possibility of their free recall. Numerical simulations are given to validate the theoretical analysis.