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Graph neural networks (GNNs) have achieved strong performance across various real-world domains. Nevertheless, they suffer from oversquashing, where long-range information is distorted as it is compressed through limited message-passing…

Training deep graph neural networks (GNNs) poses a challenging task, as the performance of GNNs may suffer from the number of hidden message-passing layers. The literature has focused on the proposals of {over-smoothing} and…

Graph neural networks (GNNs) are known to be vulnerable to oversmoothing due to their implicit homophily assumption. We mitigate this problem with a novel scheme that regulates the aggregation of messages, modulating the type and extent of…

The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited.…

The analogy to heat diffusion has enhanced our understanding of information flow in graphs and inspired the development of Graph Neural Networks (GNNs). However, most diffusion-based GNNs emulate passive heat diffusion, which still suffers…

Graph neural networks (GNNs) have received tremendous attention due to their superiority in learning node representations. These models rely on message passing and feature transformation functions to encode the structural and feature…

We present Gradient Gating (G$^2$), a novel framework for improving the performance of Graph Neural Networks (GNNs). Our framework is based on gating the output of GNN layers with a mechanism for multi-rate flow of message passing…

The smoothing issue in graph learning leads to indistinguishable node representations, posing significant challenges for graph-related tasks. However, our experiments reveal that this problem can uncover underlying properties of node…

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…

We study the problem of semi-supervised learning on graphs, for which graph neural networks (GNNs) have been extensively explored. However, most existing GNNs inherently suffer from the limitations of over-smoothing, non-robustness, and…

Graph Convolution Networks (GCN) are widely used in learning graph representations due to their effectiveness and efficiency. However, they suffer from the notorious over-smoothing problem, in which the learned representations of densely…

Training deep neural networks (DNNs) in the presence of noisy labels is an important and challenging task. Probabilistic modeling, which consists of a classifier and a transition matrix, depicts the transformation from true labels to noisy…

Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of…

This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…

Recent works reveal that feature or label smoothing lies at the core of Graph Neural Networks (GNNs). Concretely, they show feature smoothing combined with simple linear regression achieves comparable performance with the carefully designed…

Message Passing Neural Networks (MPNNs) are a class of Graph Neural Networks (GNNs) that propagate information across the graph via local neighborhoods. The scheme gives rise to two key challenges: over-smoothing and over-squashing. While…

Deep graph neural networks (GNNs) often suffer from oversmoothing, where node representations become overly homogeneous with increasing depth. While techniques like normalization, residual connections, and edge dropout have been proposed to…

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to…

Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer…