MGNNI: Multiscale Graph Neural Networks with Implicit Layers

TL;DR

This paper introduces MGNNI, a multiscale graph neural network with implicit layers, designed to overcome limitations of previous implicit GNNs in capturing long-range dependencies and multiscale information.

Contribution

We propose MGNNI, a novel multiscale GNN with implicit layers that enhances effective range and models multiscale structures on graphs.

Findings

MGNNI outperforms baseline models in node and graph classification.

MGNNI effectively captures long-range dependencies.

Theoretical analysis links effective range to convergence in implicit GNNs.

Abstract

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.