Related papers: Stability of Graph Scattering Transforms
Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…
Graph convolution is a fundamental building block for many deep neural networks on graph-structured data. In this paper, we introduce a simple, yet very effective graph convolutional network with skip connections for semi-supervised anomaly…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
Graph Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed…
Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed…
Graph Convolutional Networks (GCNs) are one of the most popular architectures that are used to solve classification problems accompanied by graphical information. We present a rigorous theoretical understanding of the effects of graph…
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
The transformer architecture has shown remarkable success in various domains, such as natural language processing and computer vision. When it comes to graph learning, transformers are required not only to capture the interactions between…
Graph neural networks are becoming increasingly popular in the field of machine learning due to their unique ability to process data structured in graphs. They have also been applied in safety-critical environments where perturbations…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…
Networks are fundamental building blocks for representing data, and computations. Remarkable progress in learning in structurally defined (shallow or deep) networks has recently been achieved. Here we introduce evolutionary exploratory…
Graph transformers are the state-of-the-art for learning from graph-structured data and are empirically known to avoid several pitfalls of message-passing architectures. However, there is limited theoretical analysis on why these models…
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others.…
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such…
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…