# Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distance

arXiv: https://arxiv.org/abs/2111.12849 · HTML: https://mlsanity.com/paper/2111.12849/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 18 of 18)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [ParticleNet: Jet Tagging via Particle Clouds](https://mlsanity.com/paper/1902.08570/) (2019)
- [FSPool: Learning Set Representations with Featurewise Sort Pooling](https://mlsanity.com/paper/1906.02795/) (2019)
- [Learning representations of irregular particle-detector geometry with distance-weighted graph networks](https://mlsanity.com/paper/1902.07987/) (2019)
- [Variational Autoencoders for New Physics Mining at the Large Hadron Collider](https://mlsanity.com/paper/1811.10276/) (2018)
- [Distance-Weighted Graph Neural Networks on FPGAs for Real-Time Particle Reconstruction in High Energy Physics](https://mlsanity.com/paper/2008.03601/) (2020)
- [Variational Autoencoders for Anomalous Jet Tagging](https://mlsanity.com/paper/2007.01850/) (2020)
- [Bump Hunting in Latent Space](https://mlsanity.com/paper/2103.06595/) (2021)
- [Charged particle tracking via edge-classifying interaction networks](https://mlsanity.com/paper/2103.16701/) (2021)
- [Linearized Optimal Transport for Collider Events](https://mlsanity.com/paper/2008.08604/) (2020)

## Built on by (most cited first, 10 of 10)

- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Anomalies, Representations, and Self-Supervision](https://mlsanity.com/paper/2301.04660/) (2023)
- [Neural Embedding: Learning the Embedding of the Manifold of Physics Data](https://mlsanity.com/paper/2208.05484/) (2022)
- [Machine-Learning Compression for Particle Physics Discoveries](https://mlsanity.com/paper/2210.11489/) (2022)
- [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)

Autoencoders have useful applications in high energy physics in anomaly detection, particularly for jets - collimated showers of particles produced in collisions such as those at the CERN Large Hadron Collider. We explore the use of graph-based autoencoders, which operate on jets in their "particle cloud" representations and can leverage the interdependencies among the particles within a jet, for such tasks. Additionally, we develop a differentiable approximation to the energy mover's distance via a graph neural network, which may subsequently be used as a reconstruction loss function for autoencoders.