Towards Dynamic Message Passing on Graphs

Message passing plays a vital role in graph neural networks (GNNs) for effective feature learning. However, the over-reliance on input topology diminishes the efficacy of message passing and restricts the ability of GNNs. Despite efforts to mitigate the reliance, existing study encounters message-passing bottlenecks or high computational expense problems, which invokes the demands for flexible message passing with low complexity. In this paper, we propose a novel dynamic message-passing mechanism for GNNs. It projects graph nodes and learnable pseudo nodes into a common space with measurable spatial relations between them. With nodes moving in the space, their evolving relations facilitate flexible pathway construction for a dynamic message-passing process. Associating pseudo nodes to input graphs with their measured relations, graph nodes can communicate with each other intermediately through pseudo nodes under linear complexity. We further develop a GNN model named $N^2$ based on our dynamic message-passing mechanism. $N^2$ employs a single recurrent layer to recursively generate the displacements of nodes and construct optimal dynamic pathways. Evaluation on eighteen benchmarks demonstrates the superior performance of $N^2$ over popular GNNs. $N^2$ successfully scales to large-scale benchmarks and requires significantly fewer parameters for graph classification with the shared recurrent layer.