Information Plane Analysis Visualization in Deep Learning via Transfer Entropy

In a feedforward network, Transfer Entropy (TE) can be used to measure the influence that one layer has on another by quantifying the information transfer between them during training. According to the Information Bottleneck principle, a neural model's internal representation should compress the input data as much as possible while still retaining sufficient information about the output. Information Plane analysis is a visualization technique used to understand the trade-off between compression and information preservation in the context of the Information Bottleneck method by plotting the amount of information in the input data against the compressed representation. The claim that there is a causal link between information-theoretic compression and generalization, measured by mutual information, is plausible, but results from different studies are conflicting. In contrast to mutual information, TE can capture temporal relationships between variables. To explore such links, in our novel approach we use TE to quantify information transfer between neural layers and perform Information Plane analysis. We obtained encouraging experimental results, opening the possibility for further investigations.

I. Introduction

Transfer Entropy (TE) is a statistical measure that is commonly used to quantify the degree of coherence between events, usually those represented as time series. This measure was introduced by Schreiber [1] and has been linked by some authors [2], [3] to Granger's causality. Using the term “causality” alone is a misnomer. To avoid further confusion, Granger himself used in 1977 the term “temporally related” [4]. Causality is concerned with whether interventions on a source can have an impact on the target, while information transfer relates to whether observations of the source can aid in predicting state transitions on the target [5]. While TE may indicate temporal relationships between two variables, it is not a definitive test for causality, and care should be taken when interpreting the results of TE analysis in this context.