Lorentz Group Equivariant Neural Network for Particle Physics

Alexander Bogatskiy, Brandon Anderson, Jan Offermann, Marwah Roussi, David Miller, Risi Kondor
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:992-1002, 2020.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Lorentz Group Equivariant Neural Network for Particle Physics %A Alexander Bogatskiy %A Brandon Anderson %A Jan Offermann %A Marwah Roussi %A David Miller %A Risi Kondor %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-bogatskiy20a %I PMLR %P 992--1002 %U https://proceedings.mlr.press/v119/bogatskiy20a.html %V 119 %X 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.
APA
Bogatskiy, A., Anderson, B., Offermann, J., Roussi, M., Miller, D. & Kondor, R.. (2020). Lorentz Group Equivariant Neural Network for Particle Physics. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:992-1002 Available from https://proceedings.mlr.press/v119/bogatskiy20a.html.

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