mlsanityData to 14 Oct 2026

MGNNI: Multiscale Graph Neural Networks with Implicit Layers

arXiv 2210.08353 ↗First posted 15 Oct 2022cs.LG cs.AIcited by 19

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Abstract (arXiv)

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.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 28 of its 40 references that are in the map. First posted on arXiv 15 Oct 2022.

Builds on

28 of 40 references.

References · 28

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16 more
  1. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
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  9. 2020Implicit Graph Neural Networkscited by 100
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  13. 2021On the Theory of Implicit Deep Learning: Global Convergence with Implicit Layerscited by 35
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 7; 2024: 5; 2025: 4; 2026: 1.

19 papers.

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  1. 2023Parallelizing non-linear sequential models over the sequence lengthcited by 45
  2. 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
  3. 2022Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graphcited by 14
  4. 2024Minimum Topology Attacks for Graph Neural Networkscited by 6
  5. 2025DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomoleculescited by 5
  6. 2025Reversible Deep Equilibrium Modelscited by 5
  7. 2023G-Signatures: Global Graph Propagation With Randomized Signaturescited by 4
  8. 2023Bridging Trustworthiness and Open-World Learning: An Exploratory Neural Approach for Enhancing Interpretability, Generalization, and Robustnesscited by 4
  9. 2024OpenViewer: Openness-Aware Multi-View Learningcited by 4
  10. 2024IGNN-Solver: A Graph Neural Solver for Implicit Graph Neural Networkscited by 3
  11. 2025Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guaranteescited by 3
  12. 2023Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothingcited by 2
7 more
  1. 2022Unifying Label-inputted Graph Neural Networks with Deep Equilibrium Modelscited by 1
  2. 2023A Model-Agnostic Graph Neural Network for Integrating Local and Global Informationcited by 1
  3. 2023Dynamic Spiking Framework for Graph Neural Networkscited by 1
  4. 2024Thermodynamics-informed graph neural networks for real-time simulation of digital human twinscited by 1
  5. 2024SCNode: Spatial and Contextual Coordinates for Graph Representation Learningcited by 0
  6. 2025Virtual Nodes based Heterogeneous Graph Convolutional Neural Network for Efficient Long-Range Information Aggregationcited by 0
  7. 2026Reachability is not enough: Diagnosing long-range behavior in GNNscited by 0