Complex-Valued Associative Memories with Projection and Iterative Learning Rules

Teijiro Isokawa 1 , Hiroki Yamamoto 1 , Haruhiko Nishimura 2 , Takayuki Yumoto 1 , Naotake Kamiura 1 ,  and Nobuyuki Matsui 1
  • 1 Graduate School of Engineering, University of Hyogo, 671-2280, Himeji, Japan
  • 2 Graduate School of Applied Informatics, University of Hyogo, 650-0047, Kobe, Japan


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.

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