Elastic Graph Neural Networks
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While many existing graph neural networks (GNNs) have been proven to perform ℓ_2-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via ℓ_1-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on ℓ_1 and ℓ_2-based graph smoothing. In particular, we propose a novel and general message passing scheme into GNNs. This message passing algorithm is not only friendly to back-propagation training but also achieves the desired smoothing properties with a theoretical convergence guarantee. Experiments on semi-supervised learning tasks demonstrate that the proposed Elastic GNNs obtain better adaptivity on benchmark datasets and are significantly robust to graph adversarial attacks. The implementation of Elastic GNNs is available at <https://github.com/lxiaorui/ElasticGNN>.
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