# Moments of Clarity: Streamlining Latent Spaces in Machine Learning using Moment Pooling

arXiv: https://arxiv.org/abs/2403.08854 · HTML: https://mlsanity.com/paper/2403.08854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 89 references that are in the map.
- First posted on arXiv 13 Mar 2024.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Long Short-Term Memory-Networks for Machine Reading](https://mlsanity.com/paper/1601.06733/) (2016)
- [Interpretable Machine Learning -- A Brief History, State-of-the-Art and Challenges](https://mlsanity.com/paper/2010.09337/) (2020)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [ParticleNet: Jet Tagging via Particle Clouds](https://mlsanity.com/paper/1902.08570/) (2019)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Machine Learning in High Energy Physics Community White Paper](https://mlsanity.com/paper/1807.02876/) (2018)
- [PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics](https://mlsanity.com/paper/2211.00454/) (2022)
- [Explainable Equivariant Neural Networks for Particle Physics: PELICAN](https://mlsanity.com/paper/2307.16506/) (2023)
- [Jet tagging in the Lund plane with graph networks](https://mlsanity.com/paper/2012.08526/) (2020)
- [Deep learning in color: towards automated quark/gluon jet discrimination](https://mlsanity.com/paper/1612.01551/) (2016)
- [Interpretability of Machine Learning: Recent Advances and Future Prospects](https://mlsanity.com/paper/2305.00537/) (2023)
- [Recursive Neural Networks in Quark/Gluon Tagging](https://mlsanity.com/paper/1711.02633/) (2017)
- [IRC-safe Graph Autoencoder for unsupervised anomaly detection](https://mlsanity.com/paper/2204.12231/) (2022)
- [On the Topic of Jets: Disentangling Quarks and Gluons at Colliders](https://mlsanity.com/paper/1802.00008/) (2018)
- [Mapping the Multiverse of Latent Representations](https://mlsanity.com/paper/2402.01514/) (2024)
- [Image-Based Jet Analysis](https://mlsanity.com/paper/2012.09719/) (2020)

## Abstract (arXiv)

Many machine learning applications involve learning a latent representation of data, which is often high-dimensional and difficult to directly interpret. In this work, we propose "Moment Pooling", a natural extension of Deep Sets networks which drastically decrease latent space dimensionality of these networks while maintaining or even improving performance. Moment Pooling generalizes the summation in Deep Sets to arbitrary multivariate moments, which enables the model to achieve a much higher effective latent dimensionality for a fixed latent dimension. We demonstrate Moment Pooling on the collider physics task of quark/gluon jet classification by extending Energy Flow Networks (EFNs) to Moment EFNs. We find that Moment EFNs with latent dimensions as small as 1 perform similarly to ordinary EFNs with higher latent dimension. This small latent dimension allows for the internal representation to be directly visualized and interpreted, which in turn enables the learned internal jet representation to be extracted in closed form.