Graph convolutional network with tree-guided anisotropic message passing.

Graph Convolutional Networks (GCNs) with naive message passing mechanisms have limited performance due to the isotropic aggregation strategy. To remedy this drawback, some recent works focus on how to design anisotropic aggregation strategies with tricks on feature mapping or structure mining. However, these models still suffer from the low ability of expressiveness and long-range modeling for the needs of high performance in practice. To this end, this paper proposes a tree-guided anisotropic GCN, which applies an anisotropic aggregation strategy with competitive expressiveness and a large receptive field. Specifically, the anisotropic aggregation is decoupled into two stages. The first stage is to establish the path of the message passing on a tree-like hypergraph consisting of substructures. The second one is to aggregate the messages with constrained intensities by employing an effective gating mechanism. In addition, a novel anisotropic readout mechanism is constructed to generate representative and discriminative graph-level features for downstream tasks. Our model outperforms baseline methods and recent works on several synthetic benchmarks and datasets from different real-world tasks. In addition, extensive ablation studies and theoretical analyses indicate the effectiveness of our proposed method.