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In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Graph-based Semi-Supervised Learning (SSL) aims to transfer the labels of a handful of labeled data to the remaining massive unlabeled data via a graph. As one of the most popular graph-based SSL approaches, the recently proposed Graph Convolutional Networks (GCNs) have gained remarkable progress by combining the sound expressiveness of neural networks with graph structure. Nevertheless, the existing graph-based methods do not directly address the core problem of SSL, i.e., the shortage of supervision, and thus their performances are still very limited. To accommodate this issue, a novel GCN-based SSL algorithm is presented in this paper to enrich the supervision signals by utilizing both data similarities and graph structure. Firstly, by designing a semi-supervised contrastive loss, improved node representations can be generated via maximizing the agreement between different views of the same data or the data from the same class. Therefore, the rich unlabeled data and the scarce yet valuable labeled data can jointly provide abundant supervision information for learning discriminative node representations, which helps improve the subsequent classification result. Secondly, the underlying determinative relationship between the data features and input graph topology is extracted as supplementary supervision signals for SSL via using a graph generative loss related to the input features. Intensive experimental results on a variety of real-world datasets firmly verify the effectiveness of our algorithm compared with other state-of-the-art methods.

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the actual task the GNN is solving. In absence of reliable domain expertise, one might resort to inferring the latent graph structure, which is often difficult due to the vast search space of possible graphs. Here we introduce Pointer Graph Networks (PGNs) which augment sets or graphs with additional inferred edges for improved model expressivity. PGNs allow each node to dynamically point to another node, followed by message passing over these pointers. The sparsity of this adaptable graph structure makes learning tractable while still being sufficiently expressive to simulate complex algorithms. Critically, the pointing mechanism is directly supervised to model long-term sequences of operations on classical data structures, incorporating useful structural inductive biases from theoretical computer science. Qualitatively, we demonstrate that PGNs can learn parallelisable variants of pointer-based data structures, namely disjoint set unions and link/cut trees. PGNs generalise out-of-distribution to 5x larger test inputs on dynamic graph connectivity tasks, outperforming unrestricted GNNs and Deep Sets.

Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph convolution to directed graphs by using first- and second-order proximity, which can not only retain the connection properties of the directed graph, but also expand the receptive field of the convolution operation. A new GCN model, called DGCN, is then designed to learn representations on the directed graph, leveraging both the first- and second-order proximity information. We empirically show the fact that GCNs working only with DGCNs can encode more useful information from graph and help achieve better performance when generalized to other models. Moreover, extensive experiments on citation networks and co-purchase datasets demonstrate the superiority of our model against the state-of-the-art methods.

Meta-learning has received a tremendous recent attention as a possible approach for mimicking human intelligence, i.e., acquiring new knowledge and skills with little or even no demonstration. Most of the existing meta-learning methods are proposed to tackle few-shot learning problems such as image and text, in rather Euclidean domain. However, there are very few works applying meta-learning to non-Euclidean domains, and the recently proposed graph neural networks (GNNs) models do not perform effectively on graph few-shot learning problems. Towards this, we propose a novel graph meta-learning framework -- Meta-GNN -- to tackle the few-shot node classification problem in graph meta-learning settings. It obtains the prior knowledge of classifiers by training on many similar few-shot learning tasks and then classifies the nodes from new classes with only few labeled samples. Additionally, Meta-GNN is a general model that can be straightforwardly incorporated into any existing state-of-the-art GNN. Our experiments conducted on three benchmark datasets demonstrate that our proposed approach not only improves the node classification performance by a large margin on few-shot learning problems in meta-learning paradigm, but also learns a more general and flexible model for task adaption.

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representation and graph generation, most of them can not handle isolated new nodes without nontrivial modifications. The challenge arises due to the fact that learning to generate representations for nodes in observed graph relies heavily on topological features, whereas for new nodes only node attributes are available. Here we propose a unified generative graph convolutional network that learns node representations for all nodes adaptively in a generative model framework, by sampling graph generation sequences constructed from observed graph data. We optimize over a variational lower bound that consists of a graph reconstruction term and an adaptive Kullback-Leibler divergence regularization term. We demonstrate the superior performance of our approach on several benchmark citation network datasets.

Knowledge graph embedding has been an active research topic for knowledge base completion, with progressive improvement from the initial TransE, TransH, DistMult et al to the current state-of-the-art ConvE. ConvE uses 2D convolution over embeddings and multiple layers of nonlinear features to model knowledge graphs. The model can be efficiently trained and scalable to large knowledge graphs. However, there is no structure enforcement in the embedding space of ConvE. The recent graph convolutional network (GCN) provides another way of learning graph node embedding by successfully utilizing graph connectivity structure. In this work, we propose a novel end-to-end Structure-Aware Convolutional Network (SACN) that takes the benefit of GCN and ConvE together. SACN consists of an encoder of a weighted graph convolutional network (WGCN), and a decoder of a convolutional network called Conv-TransE. WGCN utilizes knowledge graph node structure, node attributes and edge relation types. It has learnable weights that adapt the amount of information from neighbors used in local aggregation, leading to more accurate embeddings of graph nodes. Node attributes in the graph are represented as additional nodes in the WGCN. The decoder Conv-TransE enables the state-of-the-art ConvE to be translational between entities and relations while keeps the same link prediction performance as ConvE. We demonstrate the effectiveness of the proposed SACN on standard FB15k-237 and WN18RR datasets, and it gives about 10% relative improvement over the state-of-the-art ConvE in terms of HITS@1, HITS@3 and HITS@10.

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

Random walks are at the heart of many existing network embedding methods. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new nodes and graphs as they are tied to vertex identity. In this work, we introduce the Role2Vec framework which uses the flexible notion of attributed random walks, and serves as a basis for generalizing existing methods such as DeepWalk, node2vec, and many others that leverage random walks. Our proposed framework enables these methods to be more widely applicable for both transductive and inductive learning as well as for use on graphs with attributes (if available). This is achieved by learning functions that generalize to new nodes and graphs. We show that our proposed framework is effective with an average AUC improvement of 16:55% while requiring on average 853x less space than existing methods on a variety of graphs.