Revisiting the Information Plane

Martin Schiemer, Juan Ye

Keywords: Deep Learning, Information Theory, Information Bottleneck, Neural Network Design

TL;DR: We give a detailed explanation of the trajectories in the information plane and investigate its usage for neural network design (pruning)

Abstract: There has recently been a heated debate (e.g. Schwartz-Ziv & Tishby (2017), Saxe et al. (2018), Noshad et al. (2018), Goldfeld et al. (2018)) about measuring the information flow in Deep Neural Networks using techniques from information theory. It is claimed that Deep Neural Networks in general have good generalization capabilities since they not only learn how to map from an input to an output but also how to compress information about the training data input (Schwartz-Ziv & Tishby, 2017). That is, they abstract the input information and strip down any unnecessary or over-specific information. If so, the message compression method, Information Bottleneck (IB), could be used as a natural comparator for network performance, since this method gives an optimal information compression boundary. This claim was then later denounced as well as reaffirmed (e.g. Saxe et al. (2018), Achille et al. (2017), Noshad et al. (2018)), as the employed method of mutual information measuring is not actually measuring information but clustering of the internal layer representations (Goldfeld et al. (2018)). In this paper, we will present a detailed explanation of the development in the Information Plain (IP), which is a plot-type that compares mutual information to judge compression (Schwartz-Ziv & Tishby (2017)), when noise is retroactively added (using binning estimation). We also explain why different activation functions show different trajectories on the IP. Further, we have looked into the effect of clustering on the network loss through early and perfect stopping using the Information Plane and how clustering can be used to help network pruning.

Code: https://drive.google.com/open?id=1CwBthST4bwtvMtw39Fy1bWMQ6hrz0Hzo