Graph Structure from Point Clouds: Geometric Attention is All You Need

The use of graph neural networks has produced significant advances in pointcloud problems, such as those found in high energy physics. The question ofhow to produce a graph structure in these problems is usually treated as a matterof heuristics, employing fully connected graphs or K-nearest neighbors. In thiswork, we elevate this question to utmost importance as the "Topology Problem". Wepropose an attention mechanism that allows a graph to be constructed in a learnedspace that captures all the relevant pairwise flow of information, potentially solvingthe Topology Problem. We test this architecture, called the Massless GravNet, onthe task of top jet tagging, and show that it is competitive in tagging accuracy, anduses far less computational resources than all other comparable models