Understanding the groundbreaking performance of Deep Neural Networks is one
 of the greatest challenges to the scientific community today. In this work, we
 introduce an information theoretic viewpoint on the behavior of deep networks
 optimization processes and their generalization abilities. By studying the Information
 Plane, the plane of the mutual information between the input variable and
 the desired label, for each hidden layer. Specifically, we show that the training of
 the network is characterized by a rapid increase in the mutual information (MI)
 between the layers and the target label, followed by a longer decrease in the MI
 between the layers and the input variable. Further, we explicitly show that these
 two fundamental information-theoretic quantities correspond to the generalization
 error of the network, as a result of introducing a new generalization bound that is
 exponential in the representation compression. The analysis focuses on typical
 patterns of large-scale problems. For this purpose, we introduce a novel analytic
 bound on the mutual information between consecutive layers in the network.
 An important consequence of our analysis is a super-linear boost in training time
 with the number of non-degenerate hidden layers, demonstrating the computational
 benefit of the hidden layers.
Introduce an information theoretic viewpoint on the behavior of deep networks optimization processes and their generalization abilities