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Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space, with all nodes' representations embedded in a single space. However, a graph can have hyperbolic and Euclidean geometries…

Recent years have witnessed the significant success of applying graph neural networks (GNNs) in learning effective node representations for classification. However, current GNNs are mostly built under the balanced data-splitting, which is…

Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…

In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

Graph convolutional networks (GCNs) are powerful deep neural networks for graph-structured data. However, GCN computes the representation of a node recursively from its neighbors, making the receptive field size grow exponentially with the…

Graph convolutional network (GCN) emerges as a promising direction to learn the inductive representation in graph data commonly used in widespread applications, such as E-commerce, social networks, and knowledge graphs. However, learning…

Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

Graph neural networks (GNNs) are powerful deep learning models for graph-structured data, demonstrating remarkable success across diverse domains. Recently, the database (DB) community has increasingly recognized the potentiality of GNNs,…

Graphs are essential for modeling complex relationships and capturing structured interactions in data. Graph Neural Networks (GNNs) are particularly effective when such relational structure is explicitly available, but many real-world…

Over the past few years, graph neural networks (GNN) and label propagation-based methods have made significant progress in addressing node classification tasks on graphs. However, in addition to their reliance on elaborate architectures and…

Many interesting datasets ubiquitous in machine learning and deep learning can be described via graphs. As the scale and complexity of graph-structured datasets increase, such as in expansive social networks, protein folding, chemical…

Graph neural networks (GNNs) have been widely applied to numerous fields. A recent work which combines layered structure and residual connection proposes an improved deep architecture to extend CAmouflage-REsistant GNN (CARE-GNN) to deep…

Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…

In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…

Graph neural networks (GNNs) achieve remarkable success in graph-based semi-supervised node classification, leveraging the information from neighboring nodes to improve the representation learning of target node. The success of GNNs at node…

Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with…