Chaotic Memory Dynamics in a Recurrent Neural Network With Cycle Memories Embedded by Pseudo-Inverse Method

Abstract

It is shown that hierarchical bifurcation of chaotic intermittency among memories can be induced by reducing neural connectivity when sequences of similar patterns are stored in a recurrent neural network using the pseudo-inverse method. This chaos is potentially useful for memory search and synthesis.

Numerically evaluated functional equivalence between chaotic dynamics in neural networks and cellular automata under totalistic rules

“…In several pioneering works (Tsuda 2001;Kaneko and Tsuda 2001;Tokuda et al 1997;Fujii et al 1996), coupled map systems are models proposed to describe these systems related to the functional roles of chaos. Examples include systems composed of binary map elements, cellular automata (Aizawa and Nishikawa 1986;Kim and Aizawa 2000), or binary neuron networks (Davis and Nara 1990;Nara and Davis 1992;Nara et al 1995). Also, a globally coupled map lattice (GCM) was proposed by Kaneko (1990), and a chaotic neural network (CNN) was put forward by Aihara et al (1990).…”

“…For instance, Nara and Davis have been studying the functional role of chaotic dynamics in a recurrent neural network of binary neurons (abbreviated as NN hereafter) (Davis and Nara 1990;Nara and Davis 1992;Nara et al 1995;Mikami and Nara 2003;Nara 2003;Suemitsu and Nara 2004). They have also shown, in their series of papers, that complex dynamics generated by Cellular Automata (abbreviated as CA hereafter) could be useful in the sense that CA can describe or reproduce arbitrarily given or observed complex dynamics with use of the rule dynamics of CA.…”

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

“…This method was confirmed to be effective to avoid spurious attractors that affect L attractors with K-step maps embedded in the network when connectivity r = N (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Nara 2003;Suemitsu and Nara 2003).…”

“…In order to investigate the dynamical structure, we calculated basin visiting measures and it suggests that the trajectory can pass the whole N-dimensional state space, that is, cyclic memory attractors ruin due to a quite small connectivity (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Nara 2003;Suemitsu and Nara 2003).…”

“…Artificial neural networks for chaotic itinerancy were studied with great interests (Aihara et al 1990;Tsuda 1991Tsuda , 2001Kaneko and Tsuda 2003;Fuji et al 1996). As one of those works, by Nara and Davis, chaotic dynamics was introduced in a recurrent neural network model (RNNM) consisting of binary neurons, and for investigating the functional aspects of chaos, they have applied chaotic dynamics by means of numerical methods to solving, for instance, a memory search task which is set in an ill-posed context (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Kuroiwa et al 1999;Suemitsu and Nara 2003). In their papers, they proposed that chaotic itinerancy could be potentially useful dynamics to solve complex problem, such as ill-posed problems.…”