Graph neural networks at the Large Hadron Collider

From raw detector activations to reconstructed particles, data at the Large Hadron Collider (LHC) are sparse, irregular, heterogeneous and highly relational in nature. Graph neural networks (GNNs), a class of algorithms belonging to the rapidly growing field of geometric deep learning (GDL), are well suited to tackling such data because GNNs are equipped with relational inductive biases that explicitly make use of localized information encoded in graphs. Furthermore, graphs offer a flexible and efficient alternative to rectilinear structures when representing sparse or irregular data, and can naturally encode heterogeneous information. For these reasons, GNNs have been applied to a number of LHC physics tasks including reconstructing particles from detector readouts and discriminating physics signals against background processes. We introduce and categorize these applications in a manner accessible to both physicists and non-physicists. Our explicit goal is to bridge the gap between the particle physics and GDL communities. After an accessible description of LHC physics, including theory, measurement, simulation and analysis, we overview applications of GNNs at the LHC. We conclude by highlighting technical challenges and future directions that may inspire further collaboration between the physics and GDL communities.