  A key question for machine learning approaches in particle physics is how to
best represent and learn from collider events. As an event is intrinsically a
variable-length unordered set of particles, we build upon recent machine
learning efforts to learn directly from sets of features or "point clouds".
Adapting and specializing the "Deep Sets" framework to particle physics, we
introduce Energy Flow Networks, which respect infrared and collinear safety by
construction. We also develop Particle Flow Networks, which allow for general
energy dependence and the inclusion of additional particle-level information
such as charge and flavor. These networks feature a per-particle internal
(latent) representation, and summing over all particles yields an overall
event-level latent representation. We show how this latent space decomposition
unifies existing event representations based on detector images and radiation
moments. To demonstrate the power and simplicity of this set-based approach, we
apply these networks to the collider task of discriminating quark jets from
gluon jets, finding similar or improved performance compared to existing
methods. We also show how the learned event representation can be directly
visualized, providing insight into the inner workings of the model. These
architectures lend themselves to efficiently processing and analyzing events
for a wide variety of tasks at the Large Hadron Collider. Implementations and
examples of our architectures are available online in our EnergyFlow package.
