# Graph Dilated Network with Rejection Mechanism
## 2 Related Work  
Recently, a vast amount of literature has focused on analyzing graph-based problems by leveraging the graph neural networks [6; 10; 17; 22; 23; 24]. GCN [17] is a pilot work, which simplifies the localized spectral filters used in [18], and extracts the 1-localized information for each node in each convolution layer. Then, the deeper relational features can be captured by stacking multiple convolution layers. GraphSAGE [6] takes the representation learning into a formal pattern, i.e., aggregation and combination, and proposes several kinds of aggregation strategies. Actually, GCN can be taken as a special case of GraphSAGE. GAT [10] considers the diversity in neighborhoods, and leverages the self-attention mechanism [19] to effectively select important information in neighborhoods. GG-NN [25] designs a gate mechanism-based aggregation function, which provides a weighted average of the messages from neighbors and the center node. Besides, there are some works [26; 27] considering the imbalanced nodes in representation. Although these GNNs can characterize the node structure and learn the representations of nodes, most of them suffer from the over-smoothing problem.  
Meanwhile, there are several works analyzing the mechanism of the graph neural networks, which are related to the over-smoothing problem. [PERSON] et al. (2018) [20] took graph neural networks as a special form of Laplacian smoothing, which is the main reason why GNNs work. At the same time, it shows the limitation of current GNNs, i.e., GNNs cannot capture the global graph structure due to the over-smoothing problem. Although [PERSON] et al. (2018) [20] proposed to leverage co- and self-training to improve the GNN performance, both co- and self-training are designed to deal with the limited validation issue. Therefore, the over-smoothing problem mentioned by [PERSON] et al. (2018) [20] still needs to be solved. [PERSON] et al. (2018) [21] provide another viewpoint of GNNs. The message propagation of GNNs can be considered as a modified random walk. The distribution of influence scores between two nodes converges to a stationary distribution, which also reflects the over-smoothing problem. [PERSON] et al. (2018) [21] proposed a densenet-like [28] module to aggregate neighbors from different hops adaptively as well as to address the over-smoothing problem. The PN [29] model proposes a novel normalization layer, which is applied on the output of the graph convolution layer to address the over-smoothingproblem. Normalizing the representations of nodes can prevent these representations from being too similar. MADReg [30] provides a topological view of the over-smoothing problem and brings a MADReg loss to avoid the representations of the distant nodes to be similar to the representations of the neighbor nodes. Experimental results (see Section 6.5) show MADReg can only relieve rather than prevent this problem. Although some of these works can solve the over-smoothing problem, none of them considers how to capture a suitable larger neighborhood well to learn better node representations in a situation where GNNs are free of the over-smoothing problem. In this paper, GraphDRej can not only overcome the over-smoothing problem by a rejection mechanism, but also better characterize node structures by multiple graph dilated convolution kernels. Related experimental results are shown in Sections 6.4 and 6.5.