  Topology applied to real world data using persistent homology has started to
find applications within machine learning, including deep learning. We present
a differentiable topology layer that computes persistent homology based on
level set filtrations and edge-based filtrations. We present three novel
applications: the topological layer can (i) regularize data reconstruction or
the weights of machine learning models, (ii) construct a loss on the output of
a deep generative network to incorporate topological priors, and (iii) perform
topological adversarial attacks on deep networks trained with persistence
features. The code (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly
available and we hope its availability will facilitate the use of persistent
homology in deep learning and other gradient based applications.
