  The success of deep neural networks in image classification and learning can
be partly attributed to the features they extract from images. It is often
speculated about the properties of a low-dimensional manifold that models
extract and learn from images. However, there is not sufficient understanding
about this low-dimensional space based on theory or empirical evidence. For
image classification models, their last hidden layer is the one where images of
each class is separated from other classes and it also has the least number of
features. Here, we develop methods and formulations to study that feature space
for any model. We study the partitioning of the domain in feature space,
identify regions guaranteed to have certain classifications, and investigate
its implications for the pixel space. We observe that geometric arrangements of
decision boundaries in feature space is significantly different compared to
pixel space, providing insights about adversarial vulnerabilities, image
morphing, extrapolation, ambiguity in classification, and the mathematical
understanding of image classification models.
