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Graph neural networks (GNNs) are effective machine learning models for various graph learning problems. Despite their empirical successes, the theoretical limitations of GNNs have been revealed recently. Consequently, many GNN models have…
In recent years, Graph Neural Networks (GNNs) have been popular in the graph classification task. Currently, shallow GNNs are more common due to the well-known over-smoothing problem facing deeper GNNs. However, they are sub-optimal without…
Oversmoothing has been claimed as a primary bottleneck for multi-layered graph neural networks (GNNs). Multiple analyses have examined how and why oversmoothing occurs. However, none of the prior work addressed how optimization is performed…
Message-passing graph neural networks (MPNNs) have emerged as a powerful paradigm for graph-based machine learning. Despite their effectiveness, MPNNs face challenges such as under-reaching and over-squashing, where limited receptive fields…
While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently. Those include the inability to accurately leverage…
Graph Convolutional Networks (GCN) is a pioneering model for graph-based semi-supervised learning. However, GCN does not perform well on sparsely-labeled graphs. Its two-layer version cannot effectively propagate the label information to…
Mesh-based simulation using Graph Neural Networks (GNNs) has been recognized as a promising approach for modeling fluid dynamics. However, the mesh refinement techniques which allocate finer resolution to regions with steep gradients can…
Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only…
Linearized Graph Neural Networks (GNNs) have attracted great attention in recent years for graph representation learning. Compared with nonlinear Graph Neural Network (GNN) models, linearized GNNs are much more time-efficient and can…
Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…
Graph neural networks (GNNs) are widely used for learning node embeddings in graphs, typically adopting a message-passing scheme. This approach, however, leads to the neighbor explosion problem, with exponentially growing computational and…
Changing the transmission system topology is an efficient and costless lever to reduce congestion or increase exchange capacities. The problem of finding the optimal switch states within substations is called Optimal Substation…
Most graph neural networks follow the message passing mechanism. However, it faces the over-smoothing problem when multiple times of message passing is applied to a graph, causing indistinguishable node representations and prevents the…
Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified…
Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for…
Graph convolutional networks (GCNs) have achieved remarkable learning ability for dealing with various graph structural data recently. In general, deep GCNs do not work well since graph convolution in conventional GCNs is a special form of…
The expressive power of message-passing graph neural networks (MPNNs) is reasonably well understood, primarily through combinatorial techniques from graph isomorphism testing. However, MPNNs' generalization abilities -- making meaningful…
While Graph Neural Networks (GNNs) are powerful models for learning representations on graphs, most state-of-the-art models do not have significant accuracy gain beyond two to three layers. Deep GNNs fundamentally need to address: 1).…
Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks. It is an important problem that is known to significantly impact the training of graph neural networks (GNNs), as the…
Existing Graph Neural Networks (GNNs) follow the message-passing mechanism that conducts information interaction among nodes iteratively. While considerable progress has been made, such node interaction paradigms still have the following…