  This paper studies probability distributions of penultimate activations of
classification networks. We show that, when a classification network is trained
with the cross-entropy loss, its final classification layer forms a
Generative-Discriminative pair with a generative classifier based on a specific
distribution of penultimate activations. More importantly, the distribution is
parameterized by the weights of the final fully-connected layer, and can be
considered as a generative model that synthesizes the penultimate activations
without feeding input data. We empirically demonstrate that this generative
model enables stable knowledge distillation in the presence of domain shift,
and can transfer knowledge from a classifier to variational autoencoders and
generative adversarial networks for class-conditional image generation.
