  A novel neural architecture was recently developed that enforces an exact
upper bound on the Lipschitz constant of the model by constraining the norm of
its weights in a minimal way, resulting in higher expressiveness compared to
other techniques. We present a new and interesting direction for this
architecture: estimation of the Wasserstein metric (Earth Mover's Distance) in
optimal transport by employing the Kantorovich-Rubinstein duality to enable its
use in geometric fitting applications. Specifically, we focus on the field of
high-energy particle physics, where it has been shown that a metric for the
space of particle-collider events can be defined based on the Wasserstein
metric, referred to as the Energy Mover's Distance (EMD). This metrization has
the potential to revolutionize data-driven collider phenomenology. The work
presented here represents a major step towards realizing this goal by providing
a differentiable way of directly calculating the EMD. We show how the
flexibility that our approach enables can be used to develop novel clustering
algorithms.
