Lorentz Group Equivariant Neural Network for Particle Physics

TL;DR

This paper introduces a Lorentz group equivariant neural network architecture tailored for particle physics, leveraging symmetry principles to improve interpretability and efficiency in classifying particle collision data.

Contribution

The paper develops a novel neural network architecture that is fully equivariant under the Lorentz group, enhancing interpretability and reducing model complexity in physics applications.

Findings

Achieves competitive classification accuracy on particle physics datasets.

Uses fewer parameters than traditional CNN and point cloud models.

Provides more physically interpretable results.

Abstract

We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the finite-dimensional representations of the Lorentz group and the equivariant nonlinearity involves the tensor product. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters and are much more physically interpretable than leading approaches that use CNNs and point cloud approaches. The competitive performance of the network is demonstrated on a public classification dataset [27] for tagging top quark decays given energy-momenta of jet constituents produced in proton-proton collisions.