MGNNI: Multiscale Graph Neural Networks with Implicit Layers
This work addresses a domain-specific problem for graph learning researchers by improving implicit GNNs, though it is incremental as it builds on existing implicit GNN frameworks.
The paper tackles the limited effective range and inability to capture multiscale information in implicit graph neural networks (GNNs), proposing MGNNI, which outperforms baselines in node and graph classification tasks.
Recently, implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. In this paper, we introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their limited effective range for capturing long-range dependencies, and their lack of ability to capture multiscale information on graphs at multiple resolutions. To show the limited effective range of previous implicit GNNs, We first provide a theoretical analysis and point out the intrinsic relationship between the effective range and the convergence of iterative equations used in these models. To mitigate the mentioned weaknesses, we propose a multiscale graph neural network with implicit layers (MGNNI) which is able to model multiscale structures on graphs and has an expanded effective range for capturing long-range dependencies. We conduct comprehensive experiments for both node classification and graph classification to show that MGNNI outperforms representative baselines and has a better ability for multiscale modeling and capturing of long-range dependencies.