# An Exploration of Learnt Representations of W Jets

arXiv: https://arxiv.org/abs/2109.10919 · HTML: https://mlsanity.com/paper/2109.10919/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance](https://mlsanity.com/paper/1805.11897/) (2018)
- [Variational Autoencoders for Anomalous Jet Tagging](https://mlsanity.com/paper/2007.01850/) (2020)
- [Better Latent Spaces for Better Autoencoders](https://mlsanity.com/paper/2104.08291/) (2021)
- [Linearized Optimal Transport for Collider Events](https://mlsanity.com/paper/2008.08604/) (2020)
- [Variational Autoencoders for Jet Simulation](https://mlsanity.com/paper/2009.04842/) (2020)
- [TherML: Thermodynamics of Machine Learning](https://mlsanity.com/paper/1807.04162/) (2018)

## Built on by (most cited first, 8 of 8)

- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [Online-compatible Unsupervised Non-resonant Anomaly Detection](https://mlsanity.com/paper/2111.06417/) (2021)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [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)
- [Universal New Physics Latent Space](https://mlsanity.com/paper/2407.20315/) (2024)

## Abstract (arXiv)

I present a Variational Autoencoder (VAE) trained on collider physics data (specifically boosted W jets), with reconstruction error given by an approximation to the Earth Movers Distance (EMD) between input and output jets. This VAE learns a concrete representation of the data manifold, with semantically meaningful and interpretable latent space directions which are hierarchically organized in terms of their relation to physical EMD scales in the underlying physical generative process. The variation of the latent space structure with a resolution hyperparameter provides insight into scale dependent structure of the dataset and its information complexity. I introduce two measures of the dimensionality of the learnt representation that are calculated from this scaling.