  The information-theoretic framework promises to explain the predictive power
of neural networks. In particular, the information plane analysis, which
measures mutual information (MI) between input and representation as well as
representation and output, should give rich insights into the training process.
This approach, however, was shown to strongly depend on the choice of estimator
of the MI. The problem is amplified for deterministic networks if the MI
between input and representation is infinite. Thus, the estimated values are
defined by the different approaches for estimation, but do not adequately
represent the training process from an information-theoretic perspective. In
this work, we show that dropout with continuously distributed noise ensures
that MI is finite. We demonstrate in a range of experiments that this enables a
meaningful information plane analysis for a class of dropout neural networks
that is widely used in practice.
