Graph Diffusion Neural Network Controlled by State Space Model for Semi-Supervised Node Classification

Graph Neural Networks (GNNs) have demonstrated their effectiveness in various real-world applications on complex non-Euclidean data, such as semi-supervised classification of social networks, molecules, and recommender systems. Substantial paradigms have been proposed to exploit the potentialities contained in graph topologies. However, the essential, high-level abstracted, but universal pattern of graphs, especially how information flows among nodes and edges, is still unrecognized. To remedy the deficiencies of existing architectures, we first provide a possible interpretation of graph diffusion patterns from the perspective of control. Similar to the physical process of thermal diffusion, the information contained in nodes can also be passed under the control of graph topology. To promote the flexibility of the model and alleviate over-smoothing phenomenon, we further propose a graph diffusion neural network controlled by the State Space Model (namely GraphDiCtate). In particular, we devise a jointly learnable diffusion and controlling strategy that simultaneously controls natural diffusion tendencies and message passing patterns recognized from training data. Within a single controller, the update of latent states of nodes follows both structure-driven and data-driven principles. Experimental results show that the proposed model outperforms the baselines on various semi-supervised node classification benchmarks, and effectively alleviates the over-smoothing problem over different depths of layers compared with regular MPNNs, which enables future work to train very deep GNNs even Large Graph Models.