mlsanityData to 14 Oct 2026

EIGNN: Efficient Infinite-Depth Graph Neural Networks

arXiv 2202.10720 ↗First posted 22 Feb 2022cs.LGcited by 32

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Abstract (arXiv)

Graph neural networks (GNNs) are widely used for modelling graph-structured data in numerous applications. However, with their inherently finite aggregation layers, existing GNN models may not be able to effectively capture long-range dependencies in the underlying graphs. Motivated by this limitation, we propose a GNN model with infinite depth, which we call Efficient Infinite-Depth Graph Neural Networks (EIGNN), to efficiently capture very long-range dependencies. We theoretically derive a closed-form solution of EIGNN which makes training an infinite-depth GNN model tractable. We then further show that we can achieve more efficient computation for training EIGNN by using eigendecomposition. The empirical results of comprehensive experiments on synthetic and real-world datasets show that EIGNN has a better ability to capture long-range dependencies than recent baselines, and consistently achieves state-of-the-art performance. Furthermore, we show that our model is also more robust against both noise and adversarial perturbations on node features.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). Builds on 27 of its 40 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

27 of 40 references.

References · 27

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Graph Attention Networkscited by 8,923
  4. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  5. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  6. 2017Inductive Representation Learning on Large Graphscited by 6,320
  7. 2018Neural Ordinary Differential Equationscited by 3,779
  8. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
  9. 2019Simplifying Graph Convolutional Networkscited by 1,477
  10. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  11. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 993
  12. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 877
15 more
  1. 2020Simple and Deep Graph Convolutional Networkscited by 860
  2. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  3. 2015Gated Graph Sequence Neural Networkscited by 796
  4. 2019Deep Equilibrium Modelscited by 615
  5. 2019Multi-scale Attributed Node Embeddingcited by 548
  6. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 397
  7. 2018Deep Learning on Graphs: A Surveycited by 393
  8. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  9. 2020Graph Information Bottleneckcited by 168
  10. 2020Multiscale Deep Equilibrium Modelscited by 151
  11. 2019Implicit Deep Learningcited by 124
  12. 2020Implicit Graph Neural Networkscited by 100
  13. 2021Scaling Up Graph Neural Networks Via Graph Coarseningcited by 80
  14. 2021Graph Coarsening with Neural Networkscited by 55
  15. 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: 12; 2023: 7; 2024: 6; 2025: 4; 2026: 3.

32 papers.

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  1. 2022Long Range Graph Benchmarkcited by 263
  2. 2022A Survey on Graph Representation Learning Methodscited by 66
  3. 2022Deep Equilibrium Optical Flow Estimationcited by 64
  4. 2022Rank Diminishing in Deep Neural Networkscited by 47
  5. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 47
  6. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 43
  7. 2022Deep Equilibrium Approaches to Diffusion Modelscited by 42
  8. 2022Path Independent Equilibrium Models Can Better Exploit Test-Time Computationcited by 38
  9. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
  10. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 24
  11. 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
  12. 2022MGNNI: Multiscale Graph Neural Networks with Implicit Layerscited by 19
20 more
  1. 2022Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graphcited by 14
  2. 2024From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networkscited by 6
  3. 2023Bridging Trustworthiness and Open-World Learning: An Exploratory Neural Approach for Enhancing Interpretability, Generalization, and Robustnesscited by 4
  4. 2024OpenViewer: Openness-Aware Multi-View Learningcited by 4
  5. 2024Efficient and Effective Implicit Dynamic Graph Neural Networkcited by 3
  6. 2024IGNN-Solver: A Graph Neural Solver for Implicit Graph Neural Networkscited by 3
  7. 2025ADMP-GNN: Adaptive Depth Message Passing GNNcited by 3
  8. 2023Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothingcited by 2
  9. 2024Graph Neural Networks Gone Hogwildcited by 2
  10. 2026Consistency Deep Equilibrium Modelscited by 2
  11. 2022Unifying Label-inputted Graph Neural Networks with Deep Equilibrium Modelscited by 1
  12. 2023Towards a GML-Enabled Knowledge Graph Platformcited by 1
  13. 2023Revisiting Generalized p-Laplacian Regularized Framelet GCNs: Convergence, Energy Dynamic and Training with Non-Linear Diffusioncited by 1
  14. 2024Hybrid Quantum Graph Neural Network for Molecular Property Predictioncited by 1
  15. 2026Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approachcited by 1
  16. 2022Generalized Laplacian Regularized Framelet Graph Neural Networkscited by 0
  17. 2023Provably Convergent Subgraph-wise Sampling for Fast GNN Trainingcited by 0
  18. 2025Implicit Hypergraph Neural Networkcited by 0
  19. 2025Virtual Nodes based Heterogeneous Graph Convolutional Neural Network for Efficient Long-Range Information Aggregationcited by 0
  20. 2026Reachability is not enough: Diagnosing long-range behavior in GNNscited by 0