Complex-valued neural associative memory on the complex hypercube

A model of a complex multivalued neural associative memory is presented. This memory uses a newer form of a complex signum function that allows the state space to be a complex hypercube. Using a quadratic energy function, a new convergence theorem is proved. Thus the convergence properties and the network stability for asynchronous dynamics can be observed. The convergence properties of such a network prove that the network serves to be a generalization of the real-valued neural network. The analogies to the behavior of the latter render the network to be applied to a variety of applications like grayscale image processing and pattern recognition.