  We introduce the Particle Convolution Network (PCN), a new type of
equivariant neural network layer suitable for many tasks in jet physics. The
particle convolution layer can be viewed as an extension of Deep Sets and
Energy Flow network architectures, in which the permutation-invariant operator
is promoted to a group convolution. While the PCN can be implemented for
various kinds of symmetries, we consider the specific case of rotation about
the jet axis the $\eta - \phi$ plane. In two standard benchmark tasks, q/g
tagging and top tagging, we show that the rotational PCN (rPCN) achieves
performance comparable to graph networks such as ParticleNet. Moreover, we show
that it is possible to implement an IRC-safe rPCN, which significantly
outperforms existing IRC-safe tagging methods on both tasks. We speculate that
by generalizing the PCN to include additional convolutional symmetries relevant
to jet physics, it may outperform the current state-of-the-art set by graph
networks, while offering a new degree of control over physically-motivated
inductive biases.
