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

TL;DR

This paper introduces a method for embedding complex physics data manifolds into simpler metric spaces, enhancing analysis and anomaly detection in collider physics, with broad practical applications.

Contribution

It presents a novel approach for embedding physics data manifolds into lower-dimensional spaces, enabling better analysis and anomaly detection in high-dimensional datasets.

Findings

Successfully embedded physics data manifolds into Euclidean and Hyperbolic spaces.

Provided a method to quantify search capabilities in collider physics.

Demonstrated effectiveness with simulated collider collision data.

Abstract

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.