Chaotic Wandering and Search in a Cycle-Memory Neural Network

S. Nara, P. Davis
1992 Progress of theoretical physics  
845 Numerical investigation of a single layer recurrent neural network model in which the synaptic connection matrix is formed by summing direct products of succesive patterns in cyclic sequences shows that chaotic wandering dynamics can occur with the reduction of a connectivity parameter. The structure in these dynamics is discussed from the viewpoint of search among stored memory patterns. § 1. Introduction In this paper we consider chaotic dynamics in a neural network in the context of a
more » ... ory search task. Our motivation for this is two-fold; (1) as a way of characterizing dynamics, and (2) to get insights into the usefulness of a chaotic network for processing tasks. Neural network models have been extensively investigated from the viewpoint of understanding mechanisms for parallel distributed information processing (see, for example, the collection of pioneering papers in 1) and 2». Although some neural networks are known to show complex dynamics such as chaos,3),4) only a small proportion of the works so far has been devoted to functional aspects of complex dynamics. In order to advance the argument that chaos could play significant functional roles in adaptive, self-organizing and evolving systems,5H) it is important to consider chaos dynamics in neural networks in a functional context. ParisP O ) proposed that temporal instability due to strong asymmetry could be useful in the learning process, with the metastability of memory states serving to distinguish them from other, "chaotic" states. It is known from information processing tasks such as optimization and learning, that stochastic dynamics can be useful in the right context. llH5 ) Using chaos for search has been mentioned elsewhere (for example, Tsuda et aF». It is natural to speculate that the onset of deterministic chaotic dynamics may make it possible for a processing network system to intrinsically generate all the stochasticity needed, easily and efficiently. We might expect that (a) use of intrinsic complex dynamics means we do not need a separate complex sequence generation mechanism, and (b) non-uniform randomness of the complex dynamics,i.e., the balance between structure and randomness, may allow the possibility of more efficient search. Inoue et aP6) have shown that chaos in a network of chaotic oscillators with neural-type coupling can help the network reach low energy states. This type of "self-annealing" is useful in neural networks when the information determining the Downloaded from by guest on 30 July 2018
doi:10.1143/ptp/88.5.845 fatcat:m622jjaw3bf5tako3e2ytsglfm