Graph Attention Retrospective

Graph-based learning is a rapidly growing sub-field of machine learning with applications in social networks, citation networks, and bioinformatics. One of the most popular models is graph attention networks. They were introduced to allow a node to aggregate information from features of neighbor nodes in a non-uniform way, in contrast to simple graph convolution which does not distinguish the neighbors of a node. In this paper, we study theoretically this expected behaviour of graph attention networks. We prove multiple results on the performance of graph attention mechanism for the problem of node classification for a contextual stochastic block model. Here the node features are obtained from a mixture of Gaussians and the edges from a stochastic block model. We show that in an "easy" regime, where the distance between the means of the Gaussians is large enough, graph attention is able to distinguish inter-class from intra-class edges, and thus it maintains the weights of important edges and significantly reduces the weights of unimportant edges. Consequently, we show that this implies perfect node classification. In the "hard" regime, we show that every attention mechanism fails to distinguish intra-class from inter-class edges. We evaluate our theoretical results on synthetic and real-world data.