Graph Structure from Point Clouds: Geometric Attention is All You Need
Daniel Murnane
The use of graph neural networks has produced significant advances in point
cloud problems, such as those found in high energy physics. The question of how
to produce a graph structure in these problems is usually treated as a matter
of heuristics, employing fully connected graphs or K-nearest neighbors. In this
work, we elevate this question to utmost importance as the Topology Problem. We
propose an attention mechanism that allows a graph to be constructed in a
learned space that handles geometrically the flow of relevance, providing one
solution to the Topology Problem. We test this architecture, called
GravNetNorm, on the task of top jet tagging, and show that it is competitive in
tagging accuracy, and uses far fewer computational resources than all other
comparable models.