  This paper is focused on studying the view-manifold structure in the feature
spaces implied by the different layers of Convolutional Neural Networks (CNN).
There are several questions that this paper aims to answer: Does the learned
CNN representation achieve viewpoint invariance? How does it achieve viewpoint
invariance? Is it achieved by collapsing the view manifolds, or separating them
while preserving them? At which layer is view invariance achieved? How can the
structure of the view manifold at each layer of a deep convolutional neural
network be quantified experimentally? How does fine-tuning of a pre-trained CNN
on a multi-view dataset affect the representation at each layer of the network?
In order to answer these questions we propose a methodology to quantify the
deformation and degeneracy of view manifolds in CNN layers. We apply this
methodology and report interesting results in this paper that answer the
aforementioned questions.
