Unifying gradient regularization for Heterogeneous Graph Neural Networks

Heterogeneous Graph Neural Networks (HGNNs) are a class of powerful deep learning methods widely used to learn representations of heterogeneous graphs. Despite the fast development of HGNNs, they still face some challenges such as over-smoothing, and non-robustness. Previous studies have shown that these problems can be reduced by using gradient regularization methods. However, the existing gradient regularization methods focus on either graph topology or node features. There is no universal approach to integrate these features, which severely affects the efficiency of regularization. In addition, the inclusion of gradient regularization into HGNNs sometimes leads to some problems, such as an unstable training process, increased complexity and insufficient coverage regularized information. Furthermore, there is still short of a complete theoretical analysis of the effects of gradient regularization on HGNNs. In this paper, we propose a novel gradient regularization method called Grug, which iteratively applies regularization to the gradients generated by both propagated messages and the node features during the message-passing process. Grug provides a unified framework integrating graph topology and node features, based on which we conduct a detailed theoretical analysis of their effectiveness. Specifically, the theoretical analyses elaborate the advantages of Grug: 1) Decreasing sample variance during the training process (Stability); 2) Enhancing the generalization of the model (Universality); 3) Reducing the complexity of the model (Simplicity); 4) Improving the integrity and diversity of graph information utilization (Diversity). As a result, Grug has the potential to surpass the theoretical upper bounds set by DropMessage (AAAI-23 Distinguished Papers). In addition, we evaluate Grug on five public real-world datasets with two downstream tasks.