A Topology Layer for Machine Learning

We often use machine learning to try to uncover patterns in data. In order for those patterns to be useful they should be meaningful and express some underlying structure. This can be seen in the Euclidean-inspired loss functions we use for generative models as well as for regularization. However, global geometry, which is the focus of Topology, also deals with meaningful structure, the only difference being that the structure is global instead of local. Topology is at present less exploited in machine learning, which is also why it is important to make it more available to the machine learning community at large. Still, topology applied to real world data using persistent homology has started to find applications within machine learning (including deep learning), but again, compared to its sibling local geometry, it is heavily underrepresented in these domains. In this post, we provide a high-level description of how our TopologyLayer allows (in just a few lines of PyTorch) for backpropagation through Persistent Homology computations and provides instructive, novel, and useful applications within machine learning and deep learning.