mlsanityData to 7 Oct 2026

Implicit Graph Neural Networks

arXiv 2009.06211 ↗First posted 14 Sep 2020cs.LG stat.MLcited by 98

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Abstract (arXiv)

Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture long-range dependencies in underlying graphs. To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving implicitly defined "state" vectors. We use the Perron-Frobenius theory to derive sufficient conditions that ensure well-posedness of the framework. Leveraging implicit differentiation, we derive a tractable projected gradient descent method to train the framework. Experiments on a comprehensive range of tasks show that IGNNs consistently capture long-range dependencies and outperform the state-of-the-art GNN models.

Key facts. Cited by 98 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Sep 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 24; 2023: 23; 2024: 18; 2025: 9; 2026: 12.

98 papers.

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  1. 2021GRAND: Graph Neural Diffusioncited by 258
  2. 2022Long Range Graph Benchmarkcited by 258
  3. 2023NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classificationcited by 207
  4. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  5. 2021On Training Implicit Modelscited by 73
  6. 2022A Survey on Graph Representation Learning Methodscited by 66
  7. 2022Deep Equilibrium Optical Flow Estimationcited by 63
  8. 2021Graph Neural Networks Inspired by Classical Iterative Algorithmscited by 60
  9. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  10. 2021Nonsmooth Implicit Differentiation for Machine Learning and Optimizationcited by 43
  11. 2022Deep Equilibrium Approaches to Diffusion Modelscited by 42
  12. 2021Transformers Generalize DeepSets and Can be Extended to Graphs and Hypergraphscited by 35
38 more
  1. 2022Path Independent Equilibrium Models Can Better Exploit Test-Time Computationcited by 33
  2. 2022EIGNN: Efficient Infinite-Depth Graph Neural Networkscited by 32
  3. 2024Linear-Time Graph Neural Networks for Scalable Recommendationscited by 31
  4. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
  5. 2023One-step differentiation of iterative algorithmscited by 28
  6. 2023LMC: Fast Training of GNNs via Subgraph Sampling with Provable Convergencecited by 26
  7. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  8. 2025G-Refer: Graph Retrieval-Augmented Large Language Model for Explainable Recommendationcited by 26
  9. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  10. 2022Alternating Differentiation for Optimization Layerscited by 22
  11. 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
  12. 2022MGNNI: Multiscale Graph Neural Networks with Implicit Layerscited by 19
  13. 2021VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queriescited by 18
  14. 2021Multiset-Equivariant Set Prediction with Approximate Implicit Differentiationcited by 17
  15. 2023Deep Equilibrium Diffusion Restoration with Parallel Samplingcited by 17
  16. 2021Simultaneous Missing Value Imputation and Structure Learning with Groupscited by 16
  17. 2023LazyGNN: Large-Scale Graph Neural Networks via Lazy Propagationcited by 16
  18. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  19. 2022Equivariant Hypergraph Neural Networkscited by 14
  20. 2023Knowledge Graph Completion with Counterfactual Augmentationcited by 13
  21. 2023Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Designcited by 13
  22. 2021Implicit vs Unfolded Graph Neural Networkscited by 12
  23. 2026Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoningcited by 12
  24. 2021Convergent Graph Solverscited by 11
  25. 2022Transforming PageRank into an Infinite-Depth Graph Neural Networkcited by 11
  26. 2024Path-based Explanation for Knowledge Graph Completioncited by 11
  27. 2021Adversarial Attack Framework on Graph Embedding Models with Limited Knowledgecited by 10
  28. 2022Revisiting Adversarial Attacks on Graph Neural Networks for Graph Classificationcited by 8
  29. 2022Neuro-Symbolic Learning: Principles and Applications in Ophthalmologycited by 7
  30. 2024Graph Neural Reaction Diffusion Modelscited by 6
  31. 2024LPGD: A General Framework for Backpropagation through Embedded Optimization Layerscited by 6
  32. 2022Equilibrium Aggregation: Encoding Sets via Optimizationcited by 5
  33. 2023Efficient End-to-end Language Model Fine-tuning on Graphscited by 5
  34. 2025DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomoleculescited by 5
  35. 2025Reversible Deep Equilibrium Modelscited by 5
  36. 2023G-Signatures: Global Graph Propagation With Randomized Signaturescited by 4
  37. 2023Rumor Detection with Diverse Counterfactual Evidencecited by 4
  38. 2024Simplifying the Theory on Over-Smoothingcited by 4

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