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The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings…

Graph Convolutional Networks (GCNs) are known to suffer from performance degradation as the number of layers increases, which is usually attributed to over-smoothing. Despite the apparent consensus, we observe that there exists a…

\emph{Over-fitting} and \emph{over-smoothing} are two main obstacles of developing deep Graph Convolutional Networks (GCNs) for node classification. In particular, over-fitting weakens the generalization ability on small dataset, while…

Graph neural networks (GNNs) have shown state-of-the-art performances in various applications. However, GNNs often struggle to capture long-range dependencies in graphs due to oversmoothing. In this paper, we generalize the concept of…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer…

Recent years have witnessed remarkable success achieved by graph neural networks (GNNs) in many real-world applications such as recommendation and drug discovery. Despite the success, oversmoothing has been identified as one of the key…

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from…

Deep Graph Neural Networks struggle with oversmoothing. This paper introduces a novel, physics-inspired GNN model designed to mitigate this issue. Our approach integrates with existing GNN architectures, introducing an entropy-aware message…

Graph Convolutional Networks (GCNs) have become pivotal in recommendation systems for learning user and item embeddings by leveraging the user-item interaction graph's node information and topology. However, these models often face the…

Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the…

Graph Convolutional Network (GCN) with the powerful capacity to explore graph-structural data has gained noticeable success in recent years. Nonetheless, most of the existing GCN-based models suffer from the notorious over-smoothing issue,…

Graph Convolutional Networks (GCNs) are powerful for processing graph-structured data and have achieved state-of-the-art performance in several tasks such as node classification, link prediction, and graph classification. However, it is…

Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their…

Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience…

Graph neural networks (GNNs) are a powerful solution for various structure learning applications due to their strong representation capabilities for graph data. However, traditional GNNs, relying on message-passing mechanisms that gather…

Graph Convolutional Networks (GCNs) suffer from performance degradation when models go deeper. However, earlier works only attributed the performance degeneration to over-smoothing. In this paper, we conduct theoretical and experimental…

Message Passing Graph Neural Networks are known to suffer from two problems that are sometimes believed to be diametrically opposed: over-squashing and over-smoothing. The former results from topological bottlenecks that hamper the…

Training high-quality deep models necessitates vast amounts of data, resulting in overwhelming computational and memory demands. Recently, data pruning, distillation, and coreset selection have been developed to streamline data volume by…

Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as…