  The attention that deep learning has garnered from the academic community and
industry continues to grow year over year, and it has been said that we are in
a new golden age of artificial intelligence research. However, neural networks
are still often seen as a "black box" where learning occurs but cannot be
understood in a human-interpretable way. Since these machine learning systems
are increasingly being adopted in security contexts, it is important to explore
these interpretations. We consider an Android malware traffic dataset for
approaching this problem. Then, using the information plane, we explore how
homeomorphism affects learned representation of the data and the invariance of
the mutual information captured by the parameters on that data. We empirically
validate these results, using accuracy as a second measure of similarity of
learned representations.
  Our results suggest that although the details of learned representations and
the specific coordinate system defined over the manifold of all parameters
differ slightly, the functional approximations are the same. Furthermore, our
results show that since mutual information remains invariant under
homeomorphism, only feature engineering methods that alter the entropy of the
dataset will change the outcome of the neural network. This means that for some
datasets and tasks, neural networks require meaningful, human-driven feature
engineering or changes in architecture to provide enough information for the
neural network to generate a sufficient statistic. Applying our results can
serve to guide analysis methods for machine learning engineers and suggests
that neural networks that can exploit the convolution theorem are equally
accurate as standard convolutional neural networks, and can be more
computationally efficient.
