  Persistent homology is a method for computing the topological features
present in a given data. Recently, there has been much interest in the
integration of persistent homology as a computational step in neural networks
or deep learning. In order for a given computation to be integrated in such a
way, the computation in question must be differentiable. Computing the
gradients of persistent homology is an ill-posed inverse problem with
infinitely many solutions. Consequently, it is important to perform
regularization so that the solution obtained agrees with known priors. In this
work we propose a novel method for regularizing persistent homology gradient
computation through the addition of a grouping term. This has the effect of
helping to ensure gradients are defined with respect to larger entities and not
individual points.
