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Abstract:
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Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from inability to accurately account for local graph information and associated over-smoothing issues and are found to be vulnerable to adversarial attacks. To address these challenges, we propose a novel topological neural framework which allows for integrating higher-order graph information to GNNs and for systematic learning a local graph structure. The key idea is to extract persistent homology induced by node attributes within a small radius neighborhood of each node and then to incorporate the extracted topological summaries as the side information in the local algorithm. As a result, our framework allows for harnessing both the conventional information on the graph structure and information on higher order topological properties of the graph. To evaluate robustness against attacks, we conduct experiments on adversarially manipulated graphs and show that the proposed methodology delivers substantially higher resistance to all types of graph attacks than the state-of-the-art baselines on all 6 datasets.
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