  Cross-entropy loss with softmax output is a standard choice to train neural
network classifiers. We give a new view of neural network classifiers with
softmax and cross-entropy as mutual information evaluators. We show that when
the dataset is balanced, training a neural network with cross-entropy maximises
the mutual information between inputs and labels through a variational form of
mutual information. Thereby, we develop a new form of softmax that also
converts a classifier to a mutual information evaluator when the dataset is
imbalanced. Experimental results show that the new form leads to better
classification accuracy, in particular for imbalanced datasets.
