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A novel neural architecture was recently developed that enforces an exactupper bound on the Lipschitz constant of the model by constraining the norm ofits weights in a minimal way, resulting in higher expressiveness compared toother techniques. We present a new and interesting direction for thisarchitecture: estimation of the Wasserstein metric (Earth Mover's Distance) inoptimal transport by employing the Kantorovich-Rubinstein duality to enable itsuse in geometric fitting applications. Specifically, we focus on the field ofhigh-energy particle physics, where it has been shown that a metric for thespace of particle-collider events can be defined based on the Wassersteinmetric, referred to as the Energy Mover's Distance (EMD). This metrization hasthe potential to revolutionize data-driven collider phenomenology. The workpresented here represents a major step towards realizing this goal by providinga differentiable way of directly calculating the EMD. We show how theflexibility that our approach enables can be used to develop novel clusteringalgorithms.

Finding NEEMo: Geometric Fitting using Neural Estimation of the Energy Mover's Distance