Opening the Black Box of Deep Neural Networks via Information

Despite their great success, there is still no com- prehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their in- ner organization. Previous work [Tishby & Zaslavsky (2015)] proposed to analyze DNNs in the Information Plane; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the In- formation Bottleneck (IB) tradeoff between com- pression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information- Plane visualization of DNNs. We first show that the stochastic gradient descent (SGD) epochs have two distinct phases: fast empirical error minimization followed by slow representation compression, for each layer. We then argue that the DNN layers end up very close to the IB theo- retical bound, and present a new theoretical argu- ment for the computational benefit of the hidden layers.