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Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…

In deep learning, Residual Networks (ResNets) have proven effective in addressing the vanishing gradient problem, allowing for the successful training of very deep networks. However, skip connections in ResNets can lead to gradient overlap,…

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic…

Recommendation models utilizing Graph Convolutional Networks (GCNs) have achieved state-of-the-art performance, as they can integrate both the node information and the topological structure of the user-item interaction graph. However, these…

Implicit neural networks have become increasingly attractive in the machine learning community since they can achieve competitive performance but use much less computational resources. Recently, a line of theoretical works established the…

Jumping connections enable Graph Convolutional Networks (GCNs) to overcome over-smoothing, while graph sparsification reduces computational demands by selecting a sub-matrix of the graph adjacency matrix during neighborhood aggregation.…

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…

Graph Neural Networks (GNNs) revolutionize machine learning for graph-structured data, effectively capturing complex relationships. They disseminate information through interconnected nodes, but long-range interactions face challenges known…

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…

A common issue in graph learning under the semi-supervised setting is referred to as gradient scarcity. That is, learning graphs by minimizing a loss on a subset of nodes causes edges between unlabelled nodes that are far from labelled ones…

Graph neural networks (GNNs) hold the promise of learning efficient representations of graph-structured data, and one of its most important applications is semi-supervised node classification. However, in this application, GNN frameworks…

Graph Neural Networks (GNNs) are powerful tools for learning from graph-structured data, but their scalability is increasingly strained by the size of real-world graphs in domains like recommender systems, fraud detection, and molecular…

Graph Convolutional Networks (GCNs) have been drawing significant attention with the power of representation learning on graphs. Unlike Convolutional Neural Networks (CNNs), which are able to take advantage of stacking very deep layers,…

Many modern neural network architectures are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Sufficiently overparameterized neural network architectures in principle have the…

Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when…

Gradient Descent (GD) is a powerful workhorse of modern machine learning thanks to its scalability and efficiency in high-dimensional spaces. Its ability to find local minimisers is only guaranteed for losses with Lipschitz gradients, where…

Graph Neural Networks (GNNs) have been studied through the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the…

In this paper, we propose a novel normalization method called gradient normalization (GN) to tackle the training instability of Generative Adversarial Networks (GANs) caused by the sharp gradient space. Unlike existing work such as gradient…

Uncovering rationales behind predictions of graph neural networks (GNNs) has received increasing attention over the years. Existing literature mainly focus on selecting a subgraph, through combinatorial optimization, to provide faithful…

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…