Associative memory in fractal neural networks

Neural networks consisting of small subnetworks interconnected in a layered hierarchy are described, and their performance as associative memories is analyzed. The networks are fractal when the subnetworks corresponding to different layers have the same geometric forms but different sizes and may be related to different spatial frequencies in the pattern field. Information is stored naturally in the form of subpatterns and retrieved in the form of their permutations. Storage of two subpatterns or of mutually orthogonal subpatterns in each of the subnetworks, which is shown to guarantee local stability at the stored subpatterns, can be readily accomplished by simple saturation and threshold mechanisms. The error-correction capability of the subnetworks in a fractal network is shown to be higher than that of disconnected subnetworks of the same sizes due to the interlayer connections