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

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 a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

In this paper, we study the problem of node representation learning with graph neural networks. We present a graph neural network class named recurrent graph neural network (RGNN), that address the shortcomings of prior methods. By using…

Graph autoencoders are efficient at embedding graph-based data sets. Most graph autoencoder architectures have shallow depths which limits their ability to capture meaningful relations between nodes separated by multi-hops. In this paper,…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…

Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph…

Graph Convolutional Networks (GCNs) and subsequent variants have been proposed to solve tasks on graphs, especially node classification tasks. In the literature, however, most tricks or techniques are either briefly mentioned as…

Graph Neural Networks (GNNs), a type of neural network that can learn from graph-structured data through neighborhood information aggregation, have shown superior performance in various downstream tasks. However, as the number of layers…

Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

In this paper, we propose Graph Retention Networks (GRNs) as a unified architecture for deep learning on dynamic graphs. The GRN extends the concept of retention into dynamic graph data as graph retention, equipping the model with three key…

Graph-structured data such as social networks, functional brain networks, gene regulatory networks, communications networks have brought the interest in generalizing deep learning techniques to graph domains. In this paper, we are…

Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete…

A Multigrid Full Approximation Storage algorithm for solving Deep Residual Networks is developed to enable neural network parallelized layer-wise training and concurrent computational kernel execution on GPUs. This work demonstrates a 10.2x…

Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

We define a novel type of ensemble Graph Convolutional Network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its…