Related papers: A PAC-Bayesian Approach to Generalization Bounds f…

We study the approximation power of Graph Neural Networks (GNNs) on latent position random graphs. In the large graph limit, GNNs are known to converge to certain "continuous" models known as c-GNNs, which directly enables a study of their…

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler--Leman algorithm ($1\text{-}\mathsf{WL}$). Here, the $1\text{-}\mathsf{WL}$ is a well-studied heuristic for…

Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions…

Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions…

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,…

Graph Convolutional Networks (GCNs) have been shown to be a powerful concept that has been successfully applied to a large variety of tasks across many domains over the past years. In this work we study the theory that paved the way to the…

The crux of graph classification lies in the effective representation learning for the entire graph. Typical graph neural networks focus on modeling the local dependencies when aggregating features of neighboring nodes, and obtain the…

Graph neural networks (GNNs) use graph convolutions to exploit network invariances and learn meaningful feature representations from network data. However, on large-scale graphs convolutions incur in high computational cost, leading to…

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of…

In recent years, Graph Convolutional Networks (GCNs) have achieved great success in learning from graph-structured data. With the growing tendency of graph nodes and edges, GCN training by single processor cannot meet the demand for time…

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better…

Considering a probability distribution over parameters is known as an efficient strategy to learn a neural network with non-differentiable activation functions. We study the expectation of a probabilistic neural network as a predictor by…

Graph neural networks (GNNs) are composed of layers consisting of graph convolutions and pointwise nonlinearities. Due to their invariance and stability properties, GNNs are provably successful at learning representations from data…

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…

In this paper, we establish generalization bounds for transductive learning algorithms in the context of information theory and PAC-Bayes, covering both the random sampling and the random splitting setting. First, we show that the…

In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not…

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…

Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…

Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…

We extend PAC-Bayesian theory to generative models and develop generalization bounds for models based on the Wasserstein distance and the total variation distance. Our first result on the Wasserstein distance assumes the instance space is…