Coarformer: Transformer for large graph via graph coarsening

Although Transformer has been generalized to graph data, its advantages are mostly observed on small graphs, such as molecular graphs. In this paper, we identify the obstacles of applying Transformer to large graphs: (1) The vast number of distant nodes distract the necessary attention of each target node from its local neighborhood; (2) The quadratic computational complexity regarding the number of nodes makes the learning procedure costly. We get rid of these obstacles by exploiting the complementary natures of GNN and Transformer, and trade the fine-grained long-range information for the efficiency of Transformer. In particular, we present Coarformer, a two-view architecture that captures fine-grained local information using a GNN-based module on the original graph and coarse yet long-range information using a Transformer-based module on the coarse graph (with far fewer nodes). Meanwhile, we design a scheme to enable message passing across these two views to enhance each other. Finally, we conduct extensive experiments on real-world datasets, where Coarformer outperforms any single-view method that solely applies a GNN or Transformer. Besides, the coarse global view and the cross-view propagation scheme enable Coarformer to perform better than the combinations of different GNN-based and Transformer-based modules while consuming the least running time and GPU memory.