  PELICAN is a novel permutation equivariant and Lorentz invariant or covariant
aggregator network designed to overcome common limitations found in
architectures applied to particle physics problems. Compared to many approaches
that use non-specialized architectures that neglect underlying physics
principles and require very large numbers of parameters, PELICAN employs a
fundamentally symmetry group-based architecture that demonstrates benefits in
terms of reduced complexity, increased interpretability, and raw performance.
We present a comprehensive study of the PELICAN algorithm architecture in the
context of both tagging (classification) and reconstructing (regression)
Lorentz-boosted top quarks, including the difficult task of specifically
identifying and measuring the $W$-boson inside the dense environment of the
Lorentz-boosted top-quark hadronic final state. We also extend the application
of PELICAN to the tasks of identifying quark-initiated vs.~gluon-initiated
jets, and a multi-class identification across five separate target categories
of jets. When tested on the standard task of Lorentz-boosted top-quark tagging,
PELICAN outperforms existing competitors with much lower model complexity and
high sample efficiency. On the less common and more complex task of 4-momentum
regression, PELICAN also outperforms hand-crafted, non-machine learning
algorithms. We discuss the implications of symmetry-restricted architectures
for the wider field of machine learning for physics.
