Lorentz Group Equivariant Neural Network for Particle Physics
This work addresses the need for physically interpretable models in particle physics by introducing a novel equivariant architecture, though it is incremental in applying group theory to a specific domain.
The authors tackled the problem of designing neural networks that respect Lorentz symmetry in particle physics, resulting in a simpler, more interpretable model with competitive performance on a top quark decay classification dataset.
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.