Activation Function


Activation Function

In a complex domain ANN, each neuron receives several complex input values and produces an output complex value. Thus, the activation of a complex domain neuron is different to the activation of a real domain neuron. The figure below shows how the activation of a complex domain neuron works. The module of y is computed and used produced a scaling factor using the tanh function. Second, the real and imaginary output components are computed as shown.

ActivationFunction

Problem 1
Proof that in a complex domain neuron the output can be expressed as shown.

Proof

mse

In a complex domain ANN, the mse must be calculated using the real and imaginary parts of the output and the target as shown below.

Mse

Derivatives of the Activation Function

In order to train a complex domain ANN, it is necessary to compute the partial derivatives of the output of the network as shown.

AFDerivatives

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