RETHINKING THE EXPRESSIVE POWER OF GNNS VIA GRAPH BICONNECTIVITY

1. Van Thuy Hoang
Network Science Lab
Dept. of Artificial Intelligence
The Catholic University of Korea
E-mail: hoangvanthuy90@gmail.com
2023-11-13
Bohang Zhang et. al.; ICLR 23

2. 2
Graph Convolutional Networks (GCNs)
 Generate node embeddings based on local network neighborhoods
 Nodes have embeddings at each layer, repeating combine messages
from their neighbor using neural networks

3. 3
Message Computation
 Intuition: Each node will create a message, which will be sent to other nodes later
 Example: A Linear layer
 Multiply node features with weight matrix
Message function:

4. 4
edge-biconnectivity and vertex-biconnectivity
 An illustration of edge-biconnectivity and vertex-biconnectivity.
 Cut vertices/edges are outlined in bold red.
 Gray nodes in (b)/(c) are edge/vertex-biconnected components, respectively.

5. 5
Expressive power of different GNN
 expressive power of different GNN models for various biconnectivity problems.

6. 6
PRELIMINARY
 Connectivity
 Biconnectivity

7. 7
INVESTIGATING KNOWN GNN ARCHITECTURES VIA BICONNECTIVITY
 Graphs in the first row have cut vertices (outlined in bold red) and some also
have cut edges (denoted as red lines), while graphs in the second row do not
have any cut vertex or cut edge.

8. 8
GENERALIZED DISTANCE WEISFEILER-LEHMAN TEST
 The update rule of GD-WL is very simple and can be written as:
 SPD-WL for edge-biconnectivity

9. 9
GENERALIZED DISTANCE WEISFEILER-LEHMAN
TEST
 Corollary 4.3.
 Practical implementation:
 GD-WL can be easily implemented using a Transformer-like architecture by
injecting distance information into Multi-head Attention

10. 10
Experimental results
 Accuracy on Mean Absolute Error (MAE) on ZINC test set

11. 11
Experimental results
 X

12. 12
CONCLUSION
 investigate the expressive power of GNNs via the perspective of graph
biconnectivity.
 strong theoretical insights into the power and limits of existing popular GNNs.
We then introduce the principled GD-WL framework that is fully expressive for
all biconnectivity metrics.
 design the Graphormer-GD architecture that is provably powerful while
enjoying practical efficiency and parallelizability.
 Experiments on both synthetic and real-world datasets demonstrate the
effectiveness of Graphormer-GD.