  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.
