Graph Neural Networks

Description

We focus on advancing the theoretical understanding of Graph Neural Networks (GNNs), which are powerful tools for learning on graph-structured data. Despite their success, GNNs face several fundamental challenges that limit their full potential.
Our research addresses key problems, including:

Expressivity: Exploring the ability of GNNs to distinguish and represent complex graph structures.
Generalization: Understanding why GNNs with many parameters can generalize effectively to unseen data.
Oversmoothing: Addressing the loss of information that occurs as the number of layers increases.
Transferability: Ensuring that GNN outputs remain stable under small perturbations of input graphs.

By mathematically formulating these challenges and developing rigorous solutions, we aim to enable more robust, efficient, and reliable GNNs.

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 Sohir Maskey, one of our PhD students in the field of GNNs.

Inquiries from students are very welcome!