Data from the LHC detectors are not easily represented using regular data structures. These detectors are comprised of several species of subdetectors and therefore produce heterogeneous data. LHC detectors are granular by design so that nearby particles may be distinguished. As a consequence, LHC data are sparse, in that many detector channels are not active during a given collision event. Graphs offer a flexible and efficient alternative to rectilinear data structures for representing LHC data. Accordingly, graph-based machine learning algorithms are becoming increasingly popular for a large number of LHC physics tasks . This popularity, and the corresponding potential for substantial increase in physics output, are illustrated on the cover of a recent issue  of the CERN Courier magazine.
The graphs used in almost all practical applications at the LHC so far are homogeneous, i.e. each node is assigned the same features, and each edge is assigned the same features . In other words, the power of graphs to represent sparse data has been exploited in applications for the LHC, but the potential of graphs to represent heterogeneous data has not. The pink graph on the cover of the CERN Courier  can be seen as an illustration of this limitation: all nodes are pink, regardless of their position in the detector.
We present novel fully-heterogeneous GNN designs and apply them to simulated data from a tracking detector that resembles the trackers that will be used at the HL-LHC. It contains a pixel subsystem that provides 3D hits and a strip subsystem that provides 2D hits. Our designs aim at solving the degraded performance that is observed in the strip detector in the first GNN-based tracking studies presented by the ATLAS Collaboration .
 Shlomi, Battaglia and Vlimant, “Graph neural networks in particle physics”, Mach. Learn.: Sci. Technol. 2 021001 (2021), https://doi.org/10.1088/2632-2153/abbf9a
 Sometimes quasi-heterogeneous node representations are used: the same data structure is assigned to each node, but different parts of it are zeroed out in subsets of nodes.
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