The complex-signum function has been widely used as an activation function in complex-valued recurrent neural networks for multistate associative memory. This paper presents two alternative activation functions with circularity. One is the complex-sigmoid function based on a multilevel sigmoid function defined on a circle. The other is a characteristic of a bifurcating neuron represented by a circle map. The performance of the complex-valued neural networks with the two kinds of activation functions is investigated in multistate associative memory tests. In both networks, the connection weights to store the memory patterns are determined by the generalized projection rule. We also demonstrate gray-level image reconstruction as a possible application of the proposed methods.
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