Constructing associative memories using high-order neural networks

A class of neural network for constructing associative memories that learn the memory patterns as well as their neighbouring patterns is presented. The network is basically a layer of perceptrons with high-order polynomials as their discriminant functions. A learning algorithm is proposed for the network to learn arbitrary bipolar patterns. The simulation results show that the associative memories implemented in this way achieve a set of desirable characteristics, namely high storage capacity, nearest convergence, and existence of a ´no decision´ state which attracts indistinguishable inputs. Furthermore, it is also possible to shape the attraction basin of a memory pattern under any metrics definition of distance.