mlsanityData to 7 Oct 2026

Capturing Graphs with Hypo-Elliptic Diffusions

arXiv 2205.14092 ↗First posted 27 May 2022cs.LG math.PRcited by 12

Not on the map. Why?

Abstract (arXiv)

Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves according to a diffusion equation defined using the graph Laplacian. We extend this approach by leveraging classic mathematical results about hypo-elliptic diffusions. This results in a novel tensor-valued graph operator, which we call the hypo-elliptic graph Laplacian. We provide theoretical guarantees and efficient low-rank approximation algorithms. In particular, this gives a structured approach to capture long-range dependencies on graphs that is robust to pooling. Besides the attractive theoretical properties, our experiments show that this method competes with graph transformers on datasets requiring long-range reasoning but scales only linearly in the number of edges as opposed to quadratically in nodes.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 46 of its 75 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

46 of 75 references.

References · 46

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34 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 2; 2025: 2; 2026: 2.

12 papers.

  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  3. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 23
  4. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  5. 2023Random Fourier Signature Featurescited by 9
  6. 2023The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNscited by 7
  7. 2025Improving the Effective Receptive Field of Message-Passing Neural Networkscited by 6
  8. 2023G-Signatures: Global Graph Propagation With Randomized Signaturescited by 4
  9. 2024Foundations and Frontiers of Graph Learning Theorycited by 3
  10. 2025TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flowscited by 0
  11. 2026S3GNN: Efficient Global Mixing and Local Message Passing for Long-Range Graph Learningcited by 0
  12. 2026Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentationcited by 0