Learning the Space of Collider Events

The Energy Mover's Distance (EMD) imposes a metric on the space of collider events. This metric is desirable because it packages many essential physics properties, such as standard observables and infrared and collinear (IRC) safety, under a single geometric framework. However, an exact EMD solver scales as N^3log(N) and even approximation methods scale worse than N^2, which becomes increasingly unsustainable on large/complicated datasets. We propose predicting the EMD using a Particle Flow Network (PFN), which is a Deep Sets architecture for particle physics. We demonstrate that not only can the PFN predict the EMD to a high degree of accuracy much faster than traditional approaches, but it also learns key properties of the underlying metric space.