DOMAINS OF ATTRACTION IN AUTOASSOCIATIVE MEMORY NETWORKS

An autoassociative memory network is constructed by storing reference pattern vectors whose components consist of a small positive number ep silon and 1 - epsilon. Although its connection weights can not be dete rmined only by this storing condition, it is proved that the output fu nction of the network becomes a contraction mapping in a region around each stored pattern if epsilon is sufficiently small. This implies th at the region is a domain of attraction in the network. The shape of t he region is clarified in our analysis. Domains of attraction larger t han this region are also found. Any noisy pattern vector in such domai ns, which may have real valued components, can be recognized as one of the stored patterns. We propose a method for determining connection w eights of the network, which uses the shape of the domains of attracti on. The model obtained by this method has symmetric connection weights and is successfully applied to character pattern recognition.