We introduce an analytic distance function for moderately sized point sets of known cardinality that is shown to have very desirable properties, both as a loss function as well as a regularizer for machine learning applications. We compare our novel construction to other point set distance functions and show proof of concept experiments for training neural networks end-to-end on point set prediction tasks such as object detection.
Permutation-invariant loss function for point set prediction. Proposes a new loss for points registration (aligning two point sets) with preferable permutation invariant property.  This paper introduces a novel distance function between point sets, applies two other permutation distances in an end-to-end object detection task, and shows that in two dimensions all local minima of the holographic loss are global minima. Proposes permutation invariant loss functions which depend on the distance of sets.