RETHINKING THE EXPRESSIVE POWER OF GNNS VIA GRAPH BICONNECTIVITY.pptx
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This document discusses graph convolutional networks (GCNs) and their ability to represent graph biconnectivity properties. It introduces the generalized distance Weisfeiler-Lehman test (GD-WL) framework for analyzing the expressive power of GNNs with respect to biconnectivity. The document presents experimental results demonstrating the effectiveness of the Graphormer-GD architecture based on the GD-WL framework.
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- 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.
- 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.
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