  The point of this paper is to question typical assumptions in deep learning
and suggest alternatives. A particular contribution is to prove that even if a
Stacked Convolutional Auto-Encoder is good at reconstructing pictures, it is
not necessarily good at discriminating their classes. When using Auto-Encoders,
intuitively one assumes that features which are good for reconstruction will
also lead to high classification accuracy. Indeed, it became research practice
and is a suggested strategy by introductory books. However, we prove that this
is not always the case. We thoroughly investigate the quality of features
produced by Stacked Convolutional Auto-Encoders when trained to reconstruct
their input. In particular, we analyze the relation between the reconstruction
and classification capabilities of the network, if we were to use the same
features for both tasks. Experimental results suggest that in fact, there is no
correlation between the reconstruction score and the quality of features for a
classification task. This means, more formally, that the sub-dimension
representation space learned from the Stacked Convolutional Auto-Encoder (while
being trained for input reconstruction) is not necessarily better separable
than the initial input space. Furthermore, we show that the reconstruction
error is not a good metric to assess the quality of features, because it is
biased by the decoder quality. We do not question the usefulness of
pre-training, but we conclude that aiming for the lowest reconstruction error
is not necessarily a good idea if afterwards one performs a classification
task.
