On the Need for Topology-Aware Generative Models for Manifold-Based Defenses

[comath]

This paper has interesting concepts that I think people would like.

Good:
Density Levels sets, a good idea to solidify a continuous open set to study from the data. Essentially a reinvention of the ideas behind some of the TDA complexes, but is easier to reason around for data scientists who don't have a topology background.
Good literature review generative models.
Good review of the math behind the ideas.

Bad:
They assume there are no outliers.
They make no minimum dataset requirements.
Their "topology" is restricted to just connectedness.