CurvDrop: a Ricci Curvature based approach to prevent graph neural networks from over-smoothing and over-squashing

Graph neural networks (GNNs) are powerful models to handle graph data and can achieve state-of-the-art in many critical tasks including node classification and link prediction. However, existing graph neural networks still face both challenges of over-smoothing and over-squashing based on previous literature. To this end, we propose a new Curvature-based topology-aware Dropout sampling technique named CurvDrop, in which we integrate the Discrete Ricci Curvature into graph neural networks to enable more expressive graph models. Also, this work can improve graph neural networks by quantifying connections in graphs and using structural information such as community structures in graphs. As a result, our method can tackle the both challenges of over-smoothing and over-squashing with theoretical justification. Also, numerous experiments on public datasets show the effectiveness and robustness of our proposed method. The code and data are released in https://github.com/liu-yang-maker/Curvature-based-Dropout.