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Minimizing cross-entropy is a widely used method for training artificialneural networks. Many training procedures based on backpropagation usecross-entropy directly as their loss function. Instead, this theoretical essayinvestigates a dual process model with two processes, in which one processminimizes the Kullback-Leibler divergence while its dual counterpart minimizesthe Shannon entropy. Postulating that learning consists of two dual processescomplementing each other, the model defines an equilibrium state for bothprocesses in which the loss function assumes its minimum. An advantage of theproposed model is that it allows deriving the optimal learning rate andmomentum weight to update network weights for backpropagation. Furthermore, themodel introduces the golden ratio and complex numbers as important new conceptsin machine learning.

A Dual Process Model for Optimizing Cross Entropy in Neural Networks