  Minimizing cross-entropy is a widely used method for training artificial
neural networks. Many training procedures based on backpropagation use
cross-entropy directly as their loss function. Instead, this theoretical essay
investigates a dual process model with two processes, in which one process
minimizes the Kullback-Leibler divergence while its dual counterpart minimizes
the Shannon entropy. Postulating that learning consists of two dual processes
complementing each other, the model defines an equilibrium state for both
processes in which the loss function assumes its minimum. An advantage of the
proposed model is that it allows deriving the optimal learning rate and
momentum weight to update network weights for backpropagation. Furthermore, the
model introduces the golden ratio and complex numbers as important new concepts
in machine learning.
