  The information bottleneck principle (Shwartz-Ziv & Tishby, 2017) suggests
that SGD-based training of deep neural networks results in optimally compressed
hidden layers, from an information theoretic perspective. However, this claim
was established on toy data. The goal of the work we present here is to test
whether the information bottleneck principle is applicable to a realistic
setting using a larger and deeper convolutional architecture, a ResNet model.
We trained PixelCNN++ models as inverse representation decoders to measure the
mutual information between hidden layers of a ResNet and input image data, when
trained for (1) classification and (2) autoencoding. We find that two stages of
learning happen for both training regimes, and that compression does occur,
even for an autoencoder. Sampling images by conditioning on hidden layers'
activations offers an intuitive visualisation to understand what a ResNets
learns to forget.
