MGNNI: Multiscale Graph Neural Networks with Implicit Layers

Juncheng Liu · Bryan Hooi · Kenji Kawaguchi · Xiaokui Xiao

Hall J #341

Keywords: [ implicit graph neural networks ] [ Graph Representation Learning ] [ graph neural networks ] [ equilibrium models ] [ implicit models ]

[ Abstract ]
[ OpenReview
Tue 29 Nov 2 p.m. PST — 4 p.m. PST


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.

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