The Latent Information Geometry of Jet Classification

TL;DR

This paper introduces a differential geometric framework to analyze the latent representations in neural networks, focusing on curvature and nonmetricities, and applies it to particle physics classification tasks.

Contribution

It develops new methods for analyzing learned latent geometries using information geometry, providing insights into physics-based classification problems.

Findings

Latent geometries can be characterized by curvature and nonmetricities.

The methods reveal geometric structures underlying particle physics classification.

Insights gained can improve understanding of neural network representations in physics.

Abstract

Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information geometry. We introduce the main concepts needed to analyze learned latent geometries, specifically curvature and nonmetricities, and show how they can be used for decoder and classifier geometries. We then apply our new methods to understand the physics behind binary quark-gluon classification and three-fold fat jet tagging.