  Deep learning models develop successive representations of their input in
sequential layers, the last of which maps the final representation to the
output. Here we investigate the informational content of these representations
by observing the ability of convolutional image classification models to
autoencode the model's input using embeddings existing in various layers. We
find that the deeper the layer, the less accurate that layer's representation
of the input is before training. Inaccurate representation results from
non-uniqueness in which various distinct inputs give approximately the same
embedding. Non-unique representation is a consequence of both exact and
approximate non-invertibility of transformations present in the forward pass.
Learning to classify natural images leads to an increase in representation
clarity for early but not late layers, which instead form abstract images.
Rather than simply selecting for features present in the input necessary for
classification, deep layer representations are found to transform the input so
that it matches representations of the training data such that arbitrary inputs
are mapped to manifolds learned during training. This work provides support for
the theory that the tasks of image recognition and input generation are
inseparable even for models trained exclusively to classify.
