Parametric Information Bottleneck to Optimize Stochastic Neural Networks

In this paper, we present a layer-wise learning of stochastic neural networks (SNNs) in an information-theoretic perspective. In each layer of an SNN, the compression and the relevance are defined to quantify the amount of information that the layer contains about the input space and the target space, respectively. We jointly optimize the compression and the relevance of all parameters in an SNN to better exploit the neural network's representation. Previously, the Information Bottleneck (IB) framework (\cite{Tishby99}) extracts relevant information for a target variable. Here, we propose Parametric Information Bottleneck (PIB) for a neural network by utilizing (only) its model parameters explicitly to approximate the compression and the relevance. We show that, as compared to the maximum likelihood estimate (MLE) principle, PIBs : (i) improve the generalization of neural networks in classification tasks, (ii) push the representation of neural networks closer to the optimal information-theoretical representation in a faster manner.