AI Seminar: A Topology Layer for Machine Learning
We present an approach to incorporating topological information into machine learning models using persistent homology, as well as several novel applications. First, we show how to directly penalize or promote certain topological features directly in a machine learning model. Second, we show how a topological loss can be used to improve a deep generative network by incorporating topological priors. Finally, we investigate the use of adversarial attacks on networks trained using topolgical features. The tools we present have been implemented as a publicly available PyTorch layer which we hope will facilitate the incorporation of these methods into a variety of applications.