Exact Information Bottleneck with Invertible Neural Networks: Getting the Best of Discriminative and Generative Modeling

The Information Bottleneck (IB) principle offers a unified approach to many learning and prediction problems. Although optimal in an information-theoretic sense, practical applications of IB are hampered by a lack of accurate high-dimensional estimators of mutual information, its main constituent. We propose to combine IB with invertible neural networks (INNs), which for the first time allows exact calculation of the required mutual information. Applied to classification, our proposed method results in a generative classifier we call IB-INN. It accurately models the class conditional likelihoods, generalizes well to unseen data and reliably recognizes out-of-distribution examples. In contrast to existing generative classifiers, these advantages incur only minor reductions in classification accuracy in comparison to corresponding discriminative methods such as feed-forward networks. Furthermore, we provide insight into why IB-INNs are superior to other generative architectures and training procedures and show experimentally that our method outperforms alternative models of comparable complexity.