Fragmented Basins of Attraction of Recursive Processing Elements in Associative Neural Networks and its Impact on Pattern Recovery Performance

This paper addresses recurrent neural architectures based on coupled bifurcating nodes that exhibit chaotic dynamics. The nodes are composed of logistic recursive maps, which interact through parametric coupling, i.e., through dynamic modulation of the bifurcation parameters. These networks are used to implement associative memories in which the coding of binary strings is done through spatio-temporal attractors with period-2 cycles. The associative performance of such arrangements is measured under several levels of analog noise in the prompting pattern (initial conditions of the coupled recursions). The phenomena of unbalanced power of attractors is detected. The paper also identifies and analyzes the issue of fragmented (non-convex) regions associated to the attractors representing binary zeros and binary ones of the stored strings. This subject is approached in the context of associative networks operating under analog noise and the related degradation of performance. A simple pre-processing technique aiming to overcome the mentioned fragmentation of basins of attraction resulted in marked improvement of network performance, particularly in highly noisy situations.