  We investigate the effects of the unsupervised pre-training method under the
perspective of information theory. If the input distribution displays multiple
views of the supervision, then unsupervised pre-training allows to learn
hierarchical representation which communicates these views across layers, while
disentangling the supervision. Disentanglement of supervision leads learned
features to be independent conditionally to the label. In case of binary
features, we show that conditional independence allows to extract label's
information with a linear model and therefore helps to solve under-fitting. We
suppose that representations displaying multiple views help to solve
over-fitting because each view provides information that helps to reduce
model's variance. We propose a practical method to measure both disentanglement
of supervision and quantity of views within a binary representation. We show
that unsupervised pre-training helps to conserve views from input distribution,
whereas representations learned using supervised models disregard most of them.
