Task: Summarization
Input (English): 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.
Output (English): 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.