# Neural Embedding: Learning the Embedding of the Manifold of Physics Data

arXiv: https://arxiv.org/abs/2208.05484 · HTML: https://mlsanity.com/paper/2208.05484/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Classification without labels: Learning from mixed samples in high energy physics](https://mlsanity.com/paper/1708.02949/) (2017)
- [Variational Autoencoders for New Physics Mining at the Large Hadron Collider](https://mlsanity.com/paper/1811.10276/) (2018)
- [Divide and Conquer the Embedding Space for Metric Learning](https://mlsanity.com/paper/1906.05990/) (2019)
- [Autoencoders for unsupervised anomaly detection in high energy physics](https://mlsanity.com/paper/2104.09051/) (2021)
- [Learning Wasserstein Embeddings](https://mlsanity.com/paper/1710.07457/) (2017)
- [Novelty Detection Meets Collider Physics](https://mlsanity.com/paper/1807.10261/) (2018)
- [Neural Distance Embeddings for Biological Sequences](https://mlsanity.com/paper/2109.09740/) (2021)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [Learning Embeddings into Entropic Wasserstein Spaces](https://mlsanity.com/paper/1905.03329/) (2019)
- [Online-compatible Unsupervised Non-resonant Anomaly Detection](https://mlsanity.com/paper/2111.06417/) (2021)
- [Learning Role-based Graph Embeddings](https://mlsanity.com/paper/1802.02896/) (2018)
- [Fast Sequence-Based Embedding with Diffusion Graphs](https://mlsanity.com/paper/2001.07463/) (2020)
- [Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distance](https://mlsanity.com/paper/2111.12849/) (2021)
- [An Exploration of Learnt Representations of W Jets](https://mlsanity.com/paper/2109.10919/) (2021)
- ["Flux+Mutability": A Conditional Generative Approach to One-Class Classification and Anomaly Detection](https://mlsanity.com/paper/2204.08609/) (2022)
- [New Methods and Datasets for Group Anomaly Detection From Fundamental Physics](https://mlsanity.com/paper/2107.02821/) (2021)
- [WordNet2Vec: Corpora Agnostic Word Vectorization Method](https://mlsanity.com/paper/1606.03335/) (2016)
- [A Visual Embedding for the Unsupervised Extraction of Abstract Semantics](https://mlsanity.com/paper/1507.08818/) (2015)

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

- [OmniJet-α: The first cross-task foundation model for particle physics](https://mlsanity.com/paper/2403.05618/) (2024)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [Universal New Physics Latent Space](https://mlsanity.com/paper/2407.20315/) (2024)
- [Robust Anomaly Detection for Particle Physics Using Multi-Background Representation Learning](https://mlsanity.com/paper/2401.08777/) (2024)
- [TRANSIT your events into a new mass: Fast background interpolation for weakly-supervised anomaly searches](https://mlsanity.com/paper/2503.04342/) (2025)
- [Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification](https://mlsanity.com/paper/2604.13992/) (2026)
- [Learning the Geometry of Collider Events with Metric-Aware Deep Sets](https://mlsanity.com/paper/2609.12024/) (2026)
- [Local Diagnostics of Learned Event Representations for Anomaly Detection at the HL-LHC](https://mlsanity.com/paper/2610.13437/) (2026)

## Abstract (arXiv)

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in the data analysis pipeline for many applications. Using progressively more realistic simulated collisions at the Large Hadron Collider, we show that this embedding approach learns the underlying latent structure. With the notion of volume in Euclidean spaces, we provide for the first time a viable solution to quantifying the true search capability of model agnostic search algorithms in collider physics (i.e. anomaly detection). Finally, we discuss how the ideas presented in this paper can be employed to solve many practical challenges that require the extraction of physically meaningful representations from information in complex high dimensional datasets.