Attention-enabled adaptive Markov graph convolution

GNNs (Graph Neural Networks) have attracted increasing attention for their strong power on dealing with the graph structures. However, it remains a challenge to design an ideal GNN suitable for various downstream tasks. By revisiting the framework of MPNN (Message Passing Neural Network), we argue that an ideal GNN should satisfy following two conditions. First, the node embedding can absorb the knowledge from a wide range of neighbors while maintaining locality. Second, the first-order information aggregation can adapt to unknown graphs. In this paper, we first extend $$\rm{S}^{2} \rm{GC}$$ to GMGC (Generalized Markov Graph Convolution), which can maintain the node locality regardless the type of the embedded diffusion kernel. Next, we embed the improved self-gating mechanism into the GMGC framework and propose a novel model named AMGC (Attention-enabled Adaptive Markov Graph Convolution), which well satisfies the above conditions. Moreover, the advantages of AMGC can be explained in the frequency domain. First, the frequency of the first-order diffusion kernel is adaptive and no longer limited to low-pass as $$\rm{S}^{2} \rm{GC}$$ . Second, the multi-order diffusion kernel can retain more components around the core frequency compared with FAGCN. To verify the ability of AMGC, extensive experiments are conducted, including graph regression, graph classification and semi-supervised node classification. The results show that AMGC can achieve comparable performance in all graph tasks.