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.

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.

Machine learning (ML) is revolutionizing protein structural analysis, including an important subproblem of predicting protein residue contact maps, i.e., which amino-acid residues are in close spatial proximity given the amino-acid sequence of a protein. Despite recent progresses in ML-based protein contact prediction, predicting contacts with a wide range of distances (commonly classified into short-, medium- and long-range contacts) remains a challenge. Here, we propose a multiscale graph neural network (GNN) based approach taking a cue from multiscale physics simulations, in which a standard pipeline involving a recurrent neural network (RNN) is augmented with three GNNs to refine predictive capability for short-, medium- and long-range residue contacts, respectively. Test results on the ProteinNet dataset show improved accuracy for contacts of all ranges using the proposed multiscale RNN+GNN approach over the conventional approach, including the most challenging case of long-range contact prediction.