mlsanityData to 7 Oct 2026

Directional Graph Networks

arXiv 2010.02863 ↗First posted 6 Oct 2020cs.LG cs.CG cs.SIcited by 132

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Abstract (arXiv)

The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then, we propose the use of the Laplacian eigenvectors as such vector field. We show that the method generalizes CNNs on an n-dimensional grid and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. We evaluate our method on different standard benchmarks and see a relative error reduction of 8% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset, and a relative increase in precision of 1.6% on the MolPCBA dataset. An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.

Key facts. Cited by 132 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 27; 2022: 29; 2023: 30; 2024: 29; 2025: 13; 2026: 4.

132 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2022Recipe for a General, Powerful, Scalable Graph Transformercited by 702
  3. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
  4. 2021Rethinking Graph Transformers with Spectral Attentioncited by 468
  5. 2021Graph Neural Networks with Learnable Structural and Positional Representationscited by 326
  6. 2021Do Transformers Really Perform Bad for Graph Representation?cited by 318
  7. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  8. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  9. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  10. 2023Exphormer: Sparse Transformers for Graphscited by 166
  11. 2021Equivariant Subgraph Aggregation Networkscited by 154
  12. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 154
38 more
  1. 2023Graph Inductive Biases in Transformers without Message Passingcited by 150
  2. 2021Nested Graph Neural Networkscited by 136
  3. 2022Graph-Coupled Oscillator Networkscited by 123
  4. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  5. 2021Global Self-Attention as a Replacement for Graph Convolutioncited by 113
  6. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  7. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  8. 2023Attending to Graph Transformerscited by 81
  9. 2022GRPE: Relative Positional Encoding for Graph Transformercited by 67
  10. 2022A Survey on Graph Representation Learning Methodscited by 66
  11. 2021Reconstruction for Powerful Graph Representationscited by 65
  12. 2022Ordered Subgraph Aggregation Networkscited by 57
  13. 2022Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNscited by 55
  14. 2022Multimodal learning with graphscited by 54
  15. 2022Message passing all the way upcited by 47
  16. 2021Walking Out of the Weisfeiler Leman Hierarchy: Graph Learning Beyond Message Passingcited by 46
  17. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
  18. 2021Autobahn: Automorphism-based Graph Neural Netscited by 39
  19. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
  20. 2023Towards Foundational Models for Molecular Learning on Large-Scale Multi-Task Datasetscited by 37
  21. 2024On the Scalability of GNNs for Molecular Graphscited by 36
  22. 2023Path Neural Networks: Expressive and Accurate Graph Neural Networkscited by 32
  23. 2022KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Predictioncited by 31
  24. 2023WL meet VCcited by 30
  25. 2023Graph Positional Encoding via Random Feature Propagationcited by 30
  26. 2022Interpretable Geometric Deep Learning via Learnable Randomness Injectioncited by 27
  27. 2021Directional Message Passing on Molecular Graphs via Synthetic Coordinatescited by 24
  28. 2021A New Perspective on the Effects of Spectrum in Graph Neural Networkscited by 24
  29. 2022High-Order Pooling for Graph Neural Networks with Tensor Decompositioncited by 24
  30. 2022Molecular Representation Learning via Heterogeneous Motif Graph Neural Networkscited by 23
  31. 2023Over-Squashing in Graph Neural Networks: A Comprehensive surveycited by 23
  32. 2023Uncovering Neural Scaling Laws in Molecular Representation Learningcited by 23
  33. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  34. 2023Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embeddingcited by 21
  35. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  36. 2021Evaluating Deep Graph Neural Networkscited by 19
  37. 2022Geodesic Graph Neural Network for Efficient Graph Representation Learningcited by 19
  38. 2021Do We Need Anisotropic Graph Neural Networks?cited by 18

50 most cited of 132 All 132 (JSON)