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

arXiv: https://arxiv.org/abs/2209.15624 · HTML: https://mlsanity.com/paper/2209.15624/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 4 of 4)

- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Robust and Provably Monotonic Networks](https://mlsanity.com/paper/2112.00038/) (2021)

## Built on by (most cited first, 4 of 4)

- [Differentiable Earth Mover's Distance for Data Compression at the High-Luminosity LHC](https://mlsanity.com/paper/2306.04712/) (2023)
- [A Step Toward Interpretability: Smearing the Likelihood](https://mlsanity.com/paper/2501.07643/) (2025)
- [Non-Gaussianities in Collider Metric Binning](https://mlsanity.com/paper/2503.03809/) (2025)
- [Learning the Geometry of Collider Events with Metric-Aware Deep Sets](https://mlsanity.com/paper/2609.12024/) (2026)

## Abstract (arXiv)

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.