Lorentz Group Equivariant Neural Network for Particle Physics
Alexander Bogatskiy, Brandon Anderson, Jan Offermann, Marwah Roussi, David Miller, Risi Kondor
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 show 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 performance of the network is tested on a public classification dataset [https://zenodo.org/record/2603256] for tagging top quark decays given energy-momenta of jet constituents produced in proton-proton collisions.
BibTeX
@InProceedings{pmlr-v119-bogatskiy20a,
title = {{L}orentz Group Equivariant Neural Network for Particle Physics},
author = {Bogatskiy, Alexander and Anderson, Brandon and Offermann, Jan and Roussi, Marwah and Miller, David and Kondor, Risi},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {992--1002},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/bogatskiy20a/bogatskiy20a.pdf},
url = {https://proceedings.mlr.press/v119/bogatskiy20a.html},
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 show 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 performance of the network is tested on a public classification dataset [https://zenodo.org/record/2603256] for tagging top quark decays given energy-momenta of jet constituents produced in proton-proton collisions.}
}