Complex-Valued Associative Memories with Projection and Iterative Learning Rules

In this paper, we investigate the stability of patterns embedded as the associative memory distributed on the complex-valued Hopfield neural network, in which the neuron states are encoded by the phase values on a unit circle of complex plane. As learning schemes for embedding patterns onto the network, projection rule and iterative learning rule are formally expanded to the complex-valued case. The retrieval of patterns embedded by iterative learning rule is demonstrated and the stability for embedded patterns is quantitatively investigated.