  The outstanding performance of deep learning in various fields has been a
fundamental query, which can be potentially examined using information theory
that interprets the learning process as the transmission and compression of
information. Information plane analyses of the mutual information between the
input-hidden-output layers demonstrated two distinct learning phases of fitting
and compression. It is debatable if the compression phase is necessary to
generalize the input-output relations extracted from training data. In this
study, we investigated this through experiments with various species of
autoencoders and evaluated their information processing phase with an accurate
kernel-based estimator of mutual information. Given sufficient training data,
vanilla autoencoders demonstrated the compression phase, which was amplified
after imposing sparsity regularization for hidden activities. However, we found
that the compression phase is not universally observed in different species of
autoencoders, including variational autoencoders, that have special constraints
on network weights or manifold of hidden space. These types of autoencoders
exhibited perfect generalization ability for test data without requiring the
compression phase. Thus, we conclude that the compression phase is not
necessary for generalization in representation learning.
