Finding NEEMo: Geometric Fitting using Neural Estimation of the Energy Mover's Distance
This work addresses the need for a differentiable metric in particle-collider event analysis, representing a major step towards revolutionizing data-driven collider phenomenology, though it builds on existing neural architectures.
The paper tackled the problem of estimating the Wasserstein metric for geometric fitting in high-energy particle physics by introducing a differentiable method to calculate the Energy Mover's Distance, enabling novel clustering algorithms.
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.