On Information Plane Analyses of Neural Network Classifiers -- A Review
This review clarifies theoretical and empirical issues in information bottleneck theory for researchers in machine learning, highlighting incremental insights into estimation challenges.
The paper reviews literature on information plane analyses of neural network classifiers, finding that empirical evidence on the link between information-theoretic compression and generalization is mixed, and suggests that observed compression is often geometric rather than information-theoretic.
We review the current literature concerned with information plane analyses of neural network 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 information planes is not necessarily information-theoretic, but is rather often compatible with geometric compression of the latent representations. This insight gives the information plane a renewed justification. Aside from this, we shed light on the problem of estimating mutual information in deterministic neural networks and its consequences. Specifically, we argue that even in feed-forward neural networks the data processing inequality need not hold for estimates of mutual information. Similarly, while a fitting phase, in which the mutual information 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 need not be visible in the information plane.