Graph Neural Networks

Research at our chair

• Generalization Bounds for GNNs based on graphons
  Generalization Analysis of Message Passing Neural Networks on Large Random Graphs (https://arxiv.org/abs/2202.00645)
  Generalization Bounds for Message Passing Networks on Mixture of Graphons (https://arxiv.org/abs/2404.03473)
• A Neural ODE framework to analyse and solve oversmoothing in directed graphs
  A Fractional Graph Laplacian Approach to Oversmooth (https://arxiv.org/abs/2305.13084)
• Improve the Expressivity of GNNs beyond 1-WL
  Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning (https://arxiv.org/abs/2403.13749)
  Generalized Laplacian Positional Encodings for Graph Representational Learning (https://arxiv.org/abs/2210.15956)
• Transferability of GNNs
  Unveiling the Sampling Density in Non-Uniform Geometric Graphs (https://arxiv.org/abs/2210.08219)
  Transferability of Graph Neural Networks: an Extended Graphon Appraoch (https://arxiv.org/abs/2109.10096)
  Transferability of Spectral Graph Convolutional Neural Networks (https://arxiv.org/abs/1907.12972)

General References

• General Overview of the Theory of GNNs:
  Theory of Graph Neural Networks: Representation and Learning (https://arxiv.org/abs/2204.07697)
  Future Directions in the Theory of Graph Machine Learning (https://arxiv.org/abs/2402.02287)
• Expressivity of GNNs
  How Powerful are Graph Neural Networks? (https://arxiv.org/abs/1810.00826)
  Beyond Weisfeiler-Leham: A Quantitative Framework for GNN Expressiveness (https://arxiv.org/abs/2401.08514)
  Sign and basis invariant networks for spectral graph representational learning (https://arxiv.org/abs/2202.13013)
  Equivariant Subgraph Attention Networks (https://arxiv.org/abs/2110.02910)
  Homomorphism Counts for Graph Neural Networks: All About That Basis (https://arxiv.org/abs/2402.08595)
• Oversmoothing of GNNs
  A Survey On Oversmoothing in Graph Neural Networks (https://arxiv.org/abs/2303.10993)
  Understanding convolution on graphs via energies (https://arxiv.org/abs/2206.10991)
  Graph Neural Networks Exponentially Lose Expressive Power for Node Classification (https://arxiv.org/abs/1905.10947)
• Generalization in GNNs
  Generalization and Representational Limits of Graph Neural Networks (https://arxiv.org/abs/2002.06157)
• Applications of GNNs
  FAENet: Frame Averaging Equivariant GNN for Material Modeling (https://arxiv.org/abs/2305.05577)
  Message Passing Neural PDE Solvers (https://arxiv.org/abs/2202.03376)
  Geometric and Physical Quantities Improve E(3) Equivariant Message Passing (https://arxiv.org/abs/2110.02905)

Contact

Do you have questions about our research in this area?

Please do not hesitate to contact us directly. Feel free to write an e-mail to Massimiliano Datres, one of our PostDocs in the field of GNNs.

Inquiries from students are very welcome!