Complex-Valued Neural Networks

By Akira Hirose. Studies in Computational Intelligence, 2006

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An optical neural chip for implementing complex-valued neural network (2021, background): “…signi ﬁ cant slowdown when executing algorithms using complex-valued operations because complex numbers have to be represented by two real numbers 7,13 , which increases the number of MAC operations — the most frequently used and computationally expensive component of the neural network…”
Generalization Characteristics of Complex-Valued Feedforward Neural Networks in Relation to Signal Coherence (2012, methodology): “In a CVNN, we first employ a phase– amplitude-type sigmoid activation function and the teacher– signal–backpropagation learning process, [19] , [22] with the following notations: Comparison in evaluation of generalization CVNN RVNN z I S ˆ z I s ˆ z I 1 ˆ z O 1 ˆ z O s ˆ z O S ˆ Fig.”
An Introduction to Deep Learning for the Physical Layer (2017, background): “For this reason, it would be desirable to have NNs operate on complex rather than real numbers [61].”
Metaheuristic design of feedforward neural networks: A review of two decades of research (2017, methodology): “Similarly, the nodes of a GMDH neural network is designed as an Ivakhnenko polynomial [245]; the nodes of a complex value neural network or multivalued neural network is designed with a complex value activation functions [234]; the node of spiking neural networks has specific behavior, in which a no”