Elastic Graph Neural Networks
This work addresses the need for more adaptive and robust GNNs for semi-supervised learning tasks, representing an incremental improvement over existing methods.
The paper tackles the problem of enhancing local smoothness adaptivity in graph neural networks (GNNs) by introducing Elastic GNNs based on ℓ₁ and ℓ₂-based graph smoothing, resulting in better adaptivity on benchmark datasets and significant robustness to graph adversarial attacks.
While many existing graph neural networks (GNNs) have been proven to perform $\ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via $\ell_1$-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on $\ell_1$ and $\ell_2$-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 \url{https://github.com/lxiaorui/ElasticGNN}.