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We review the current literature concerned with information plane (IP) analyses of neural network (NN) classifiers. While the underlying information bottleneck theory and the claim that information-theoretic compression is causally linked to generalization are plausible, empirical evidence was found to be both supporting and conflicting. We review this evidence together with a detailed analysis of how the respective information quantities were estimated. Our survey suggests that compression visualized in IPs is not necessarily information-theoretic but is rather often compatible with geometric compression of the latent representations. This insight gives the IP a renewed justification. Aside from this, we shed light on the problem of estimating mutual information in deterministic NNs and its consequences. Specifically, we argue that, even in feedforward NNs, the data processing inequality needs not to hold for estimates of mutual information. Similarly, while a fitting phase, in which the mutual information is between the latent representation and the target increases, is necessary (but not sufficient) for good classification performance, depending on the specifics of mutual information estimation, such a fitting phase needs to not be visible in the IP. [ABSTRACT FROM AUTHOR]

In this work, we investigate the use of three information-theoretic quantities—entropy, mutual information with the class variable, and a class selectivity measure based on Kullback–Leibler (KL) divergence—to understand and study the behavior of already trained fully connected feedforward neural networks (NNs). We analyze the connection between these information-theoretic quantities and classification performance on the test set by cumulatively ablating neurons in networks trained on MNIST, FashionMNIST, and CIFAR-10. Our results parallel those recently published by Morcos et al., indicating that class selectivity is not a good indicator for classification performance. However, looking at individual layers separately, both mutual information and class selectivity are positively correlated with classification performance, at least for networks with ReLU activation functions. We provide explanations for this phenomenon and conclude that it is ill-advised to compare the proposed information-theoretic quantities across layers. Furthermore, we show that cumulative ablation of neurons with ascending or descending information-theoretic quantities can be used to formulate hypotheses regarding the joint behavior of multiple neurons, such as redundancy and synergy, with comparably low computational cost. We also draw connections to the information bottleneck theory for NNs. [ABSTRACT FROM AUTHOR]

We propose a semi-supervised generative model, SeGMA, which learns a joint probability distribution of data and their classes and is implemented in a typical Wasserstein autoencoder framework. We choose a mixture of Gaussians as a target distribution in latent space, which provides a natural splitting of data into clusters. To connect Gaussian components with correct classes, we use a small amount of labeled data and a Gaussian classifier induced by the target distribution. SeGMA is optimized efficiently due to the use of the Cramer–Wold distance as a maximum mean discrepancy penalty, which yields a closed-form expression for a mixture of spherical Gaussian components and, thus, obviates the need of sampling. While SeGMA preserves all properties of its semi-supervised predecessors and achieves at least as good generative performance on standard benchmark data sets, it presents additional features: 1) interpolation between any pair of points in the latent space produces realistically looking samples; 2) combining the interpolation property with disentangling of class and style information, SeGMA is able to perform continuous style transfer from one class to another; and 3) it is possible to change the intensity of class characteristics in a data point by moving the latent representation of the data point away from specific Gaussian components. [ABSTRACT FROM AUTHOR]