Neural Network Classifier as Mutual Information Evaluator

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.