mlsanityData to 14 Oct 2026

Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks

arXiv 2305.18965 ↗First posted 30 May 2023cs.LG math.DS physics.class-phcited by 12

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Abstract (arXiv)

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at urlhttps://github.com/zknus/Hamiltonian-GNN.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 46 of its 72 references that are in the map. First posted on arXiv 30 May 2023.

Builds on

46 of 72 references.

References · 46

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34 more
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Cited by year

Citing papers per year: 2023: 4; 2024: 6; 2025: 2.

12 papers.

  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  3. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 17
  4. 2024Matrix Manifold Neural Networks++cited by 13
  5. 2024PANDA: Expanded Width-Aware Message Passing Beyond Rewiringcited by 10
  6. 2024FedSheafHN: Personalized Federated Learning on Graph-structured Datacited by 3
  7. 2023Graph Neural Networks with a Distribution of Parametrized Graphscited by 1
  8. 2023Symplectic Structure-Aware Hamiltonian (Graph) Embeddingscited by 0
  9. 2024Information propagation dynamics in Deep Graph Networkscited by 0
  10. 2024Graph Spring Neural ODEs for Link Sign Predictioncited by 0
  11. 2025Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  12. 2025Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0