Graph neural networks (GNNs) are widely used for analyzing graph-structural data and solving graph-related tasks due to their powerful expressiveness. However, existing off-the-shelf GNN-based models usually consist of no more than three layers. Deeper GNNs usually suffer from severe performance degradation due to several issues including the infamous "over-smoothing" issue, which restricts the further development of GNNs. In this article, we investigate the over-smoothing issue in deep GNNs. We discover that over-smoothing not only results in indistinguishable embeddings of graph nodes, but also alters and even corrupts their semantic structures, dubbed semantic over-smoothing. Existing techniques, e.g., graph normalization, aim at handling the former concern, but neglect the importance of preserving the semantic structures in the spatial domain, which hinders the further improvement of model performance. To alleviate the concern, we propose a cluster-keeping sparse aggregation strategy to preserve the semantic structure of embeddings in deep GNNs (especially for spatial GNNs). Particularly, our strategy heuristically redistributes the extent of aggregations for all the nodes from layers, instead of aggregating them equally, so that it enables aggregate concise yet meaningful information for deep layers. Without any bells and whistles, it can be easily implemented as a plug-and-play structure of GNNs via weighted residual connections. Last, we analyze the over-smoothing issue on the GNNs with weighted residual structures and conduct experiments to demonstrate the performance comparable to the state-of-the-arts.

Despite Graph neural networks' significant performance gain over many classic techniques in various graph-related downstream tasks, their successes are restricted in shallow models due to over-smoothness and the difficulties of optimizations among many other issues. In this paper, to alleviate the over-smoothing issue, we propose a soft graph normalization method to preserve the diversities of node embeddings and prevent indiscrimination due to possible over-closeness. Combined with residual connections, we analyze the reason why the method can effectively capture the knowledge in both input graph structures and node features even with deep networks. Additionally, inspired by Curriculum Learning that learns easy examples before the hard ones, we propose a novel label-smoothing-based learning framework to enhance the optimization of deep GNNs, which iteratively smooths labels in an auxiliary graph and constructs many gradual non-smooth tasks for extracting increasingly complex knowledge and gradually discriminating nodes from coarse to fine. The method arguably reduces the risk of overfitting and generalizes better results. Finally, extensive experiments are carried out to demonstrate the effectiveness and potential of the proposed model and learning framework through comparison with twelve existing baselines including the state-of-the-art methods on twelve real-world node classification benchmarks.

Recent studies have shown that Graph Transformers (GTs) can be effective for specific graph-level tasks. However, when it comes to node classification, training GTs remains challenging, especially in semi-supervised settings with a severe scarcity of labeled data. Our paper aims to address this research gap by focusing on semi-supervised node classification. To accomplish this, we develop a curriculum-enhanced attention distillation method that involves utilizing a Local GT teacher and a Global GT student. Additionally, we introduce the concepts of in-class and out-of-class and then propose two improvements, out-of-class entropy and top-k pruning, to facilitate the student's out-of-class exploration under the teacher's in-class guidance. Taking inspiration from human learning, our method involves a curriculum mechanism for distillation that initially provides strict guidance to the student and gradually allows for more out-of-class exploration by a dynamic balance. Extensive experiments show that our method outperforms many state-of-the-art approaches on seven public graph benchmarks, proving its effectiveness.