Elastic Graph Neural Networks

TL;DR

This paper introduces Elastic GNNs, a new family of graph neural networks that use both $ ext{L}_1$ and $ ext{L}_2$ graph smoothing to improve local adaptivity and robustness against adversarial attacks.

Contribution

The paper proposes a novel message passing scheme for GNNs that incorporates $ ext{L}_1$ and $ ext{L}_2$ smoothing with theoretical convergence guarantees.

Findings

Elastic GNNs outperform existing models on benchmark datasets.

They demonstrate enhanced local adaptivity in semi-supervised learning.

Elastic GNNs show increased robustness to graph adversarial attacks.

Abstract

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}.