Graph neural networks (GNNs) are widely used in the applications based on graph structured data, such as node classification and link prediction. However, GNNs are often used as a black-box tool and rarely get in-depth investigated regarding whether they fit certain applications that may have various properties. A recently proposed technique distance encoding (DE) (Li et al. 2020) magically makes GNNs work well in many applications, including node classification and link prediction. The theory provided in (Li et al. 2020) supports DE by proving that DE improves the representation power of GNNs. However, it is not obvious how the theory assists the applications accordingly. Here, we revisit GNNs and DE from a more practical point of view. We want to explain how DE makes GNNs fit for node classification and link prediction. Specifically, for link prediction, DE can be viewed as a way to establish correlations between a pair of node representations. For node classification, the problem becomes more complicated as different classification tasks may hold node labels that indicate different physical meanings. We focus on the most widely-considered node classification scenarios and categorize the node labels into two types, community type and structure type, and then analyze different mechanisms that GNNs adopt to predict these two types of labels. We also run extensive experiments to compare eight different configurations of GNNs paired with DE to predict node labels over eight real-world graphs. The results demonstrate the uniform effectiveness of DE to predict structure-type labels. Lastly, we reach three pieces of conclusions on how to use GNNs and DE properly in tasks of node classification.
Graph neural networks (GNNs) have received massive attention in the field of machine learning on graphs. Inspired by the success of neural networks, a line of research has been conducted to train GNNs to deal with various tasks, such as node classification, graph classification, and link prediction. In this work, our task of interest is graph classification. Several GNN models have been proposed and shown great accuracy in this task. However, the question is whether usual training methods fully realize the capacity of the GNN models. In this work, we propose a two-stage training framework based on triplet loss. In the first stage, GNN is trained to map each graph to a Euclidean-space vector so that graphs of the same class are close while those of different classes are mapped far apart. Once graphs are well-separated based on labels, a classifier is trained to distinguish between different classes. This method is generic in the sense that it is compatible with any GNN model. By adapting five GNN models to our method, we demonstrate the consistent improvement in accuracy and utilization of each GNN's allocated capacity over the original training method of each model up to 5.4\% points in 12 datasets.
Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical variational Bayes to implicitly capture posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and highly correlated latent structures. We show that the existing semi-implicit variational inference objective provably reduces information in the observed graph. Based on this observation, we estimate and add an additional mutual information term to the semi-implicit variational inference learning objective to capture rich correlations arising between the input and latent spaces. We show that the inclusion of this regularization term in conjunction with the Poincare embedding boosts the quality of learned high-level representations and enables more flexible and faithful graphical modeling. We experimentally demonstrate that our approach outperforms existing graph variational auto-encoders both in Euclidean and in hyperbolic spaces for edge link prediction and node classification.
Graph Neural Networks (GNNs) are effective in many applications. Still, there is a limited understanding of the effect of common graph structures on the learning process of GNNs. In this work, we systematically study the impact of community structure on the performance of GNNs in semi-supervised node classification on graphs. Following an ablation study on six datasets, we measure the performance of GNNs on the original graphs, and the change in performance in the presence and the absence of community structure. Our results suggest that communities typically have a major impact on the learning process and classification performance. For example, in cases where the majority of nodes from one community share a single classification label, breaking up community structure results in a significant performance drop. On the other hand, for cases where labels show low correlation with communities, we find that the graph structure is rather irrelevant to the learning process, and a feature-only baseline becomes hard to beat. With our work, we provide deeper insights in the abilities and limitations of GNNs, including a set of general guidelines for model selection based on the graph structure.
Heterogeneous graph representation learning aims to learn low-dimensional vector representations of different types of entities and relations to empower downstream tasks. Existing methods either capture semantic relationships but indirectly leverage node/edge attributes in a complex way, or leverage node/edge attributes directly without taking semantic relationships into account. When involving multiple convolution operations, they also have poor scalability. To overcome these limitations, this paper proposes a flexible and efficient Graph information propagation Network (GripNet) framework. Specifically, we introduce a new supergraph data structure consisting of supervertices and superedges. A supervertex is a semantically-coherent subgraph. A superedge defines an information propagation path between two supervertices. GripNet learns new representations for the supervertex of interest by propagating information along the defined path using multiple layers. We construct multiple large-scale graphs and evaluate GripNet against competing methods to show its superiority in link prediction, node classification, and data integration.
In this paper, we provide a theory of using graph neural networks (GNNs) for multi-node representation learning (where we are interested in learning a representation for a set of more than one node, such as link). We know that GNN is designed to learn single-node representations. When we want to learn a node set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN into a joint node set representation. In this paper, we show a fundamental constraint of such an approach, namely the inability to capture the dependence between nodes in the node set, and argue that directly aggregating individual node representations does not lead to an effective joint representation for multiple nodes. Then, we notice that a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, and ID-GNN, all used node labeling. These methods first label nodes in the graph according to their relationships with the target node set before applying a GNN. Then, the node representations obtained in the labeled graph are aggregated into a node set representation. By investigating their inner mechanisms, we unify these node labeling techniques into a single and most general form -- labeling trick. We prove that with labeling trick a sufficiently expressive GNN learns the most expressive node set representations, thus in principle solves any joint learning tasks over node sets. Experiments on one important two-node representation learning task, link prediction, verified our theory. Our work explains the superior performance of previous node-labeling-based methods, and establishes a theoretical foundation of using GNNs for multi-node representation learning.
Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.
In this work we propose Pathfinder Discovery Networks (PDNs), a method for jointly learning a message passing graph over a multiplex network with a downstream semi-supervised model. PDNs inductively learn an aggregated weight for each edge, optimized to produce the best outcome for the downstream learning task. PDNs are a generalization of attention mechanisms on graphs which allow flexible construction of similarity functions between nodes, edge convolutions, and cheap multiscale mixing layers. We show that PDNs overcome weaknesses of existing methods for graph attention (e.g. Graph Attention Networks), such as the diminishing weight problem. Our experimental results demonstrate competitive predictive performance on academic node classification tasks. Additional results from a challenging suite of node classification experiments show how PDNs can learn a wider class of functions than existing baselines. We analyze the relative computational complexity of PDNs, and show that PDN runtime is not considerably higher than static-graph models. Finally, we discuss how PDNs can be used to construct an easily interpretable attention mechanism that allows users to understand information propagation in the graph.
Thanks to graph neural networks (GNNs), semi-supervised node classification has shown the state-of-the-art performance in graph data. However, GNNs have not considered different types of uncertainties associated with class probabilities to minimize risk of increasing misclassification under uncertainty in real life. In this work, we propose a multi-source uncertainty framework using a GNN that reflects various types of predictive uncertainties in both deep learning and belief/evidence theory domains for node classification predictions. By collecting evidence from the given labels of training nodes, the Graph-based Kernel Dirichlet distribution Estimation (GKDE) method is designed for accurately predicting node-level Dirichlet distributions and detecting out-of-distribution (OOD) nodes. We validated the outperformance of our proposed model compared to the state-of-the-art counterparts in terms of misclassification detection and OOD detection based on six real network datasets. We found that dissonance-based detection yielded the best results on misclassification detection while vacuity-based detection was the best for OOD detection. To clarify the reasons behind the results, we provided the theoretical proof that explains the relationships between different types of uncertainties considered in this work.
Graph Neural Networks (GNNs) are the predominant technique for learning over graphs. However, there is relatively little understanding of why GNNs are successful in practice and whether they are necessary for good performance. Here, we show that for many standard transductive node classification benchmarks, we can exceed or match the performance of state-of-the-art GNNs by combining shallow models that ignore the graph structure with two simple post-processing steps that exploit correlation in the label structure: (i) an "error correlation" that spreads residual errors in training data to correct errors in test data and (ii) a "prediction correlation" that smooths the predictions on the test data. We call this overall procedure Correct and Smooth (C&S), and the post-processing steps are implemented via simple modifications to standard label propagation techniques from early graph-based semi-supervised learning methods. Our approach exceeds or nearly matches the performance of state-of-the-art GNNs on a wide variety of benchmarks, with just a small fraction of the parameters and orders of magnitude faster runtime. For instance, we exceed the best known GNN performance on the OGB-Products dataset with 137 times fewer parameters and greater than 100 times less training time. The performance of our methods highlights how directly incorporating label information into the learning algorithm (as was done in traditional techniques) yields easy and substantial performance gains. We can also incorporate our techniques into big GNN models, providing modest gains. Our code for the OGB results is at https://github.com/Chillee/CorrectAndSmooth.
Recently, increasing attention has been paid to heterogeneous graph representation learning (HGRL), which aims to embed rich structural and semantic information in heterogeneous information networks (HINs) into low-dimensional node representations. To date, most HGRL models rely on hand-crafted meta-paths. However, the dependency on manually-defined meta-paths requires domain knowledge, which is difficult to obtain for complex HINs. More importantly, the pre-defined or generated meta-paths of all existing HGRL methods attached to each node type or node pair cannot be personalised to each individual node. To fully unleash the power of HGRL, we present a novel framework, Personalised Meta-path based Heterogeneous Graph Neural Networks (PM-HGNN), to jointly generate meta-paths that are personalised for each individual node in a HIN and learn node representations for the target downstream task like node classification. Precisely, PM-HGNN treats the meta-path generation as a Markov Decision Process and utilises a policy network to adaptively generate a meta-path for each individual node and simultaneously learn effective node representations. The policy network is trained with deep reinforcement learning by exploiting the performance improvement on a downstream task. We further propose an extension, PM-HGNN++, to better encode relational structure and accelerate the training during the meta-path generation. Experimental results reveal that both PM-HGNN and PM-HGNN++ can significantly and consistently outperform 16 competing baselines and state-of-the-art methods in various settings of node classification. Qualitative analysis also shows that PM-HGNN++ can identify meaningful meta-paths overlooked by human knowledge.
Online social networks (OSNs) classify users into different categories based on their online activities and interests, a task which is referred as a node classification task. Such a task can be solved effectively using Graph Convolutional Networks (GCNs). However, a small number of users, so-called perturbators, may perform random activities on an OSN, which significantly deteriorate the performance of a GCN-based node classification task. Existing works in this direction defend GCNs either by adversarial training or by identifying the attacker nodes followed by their removal. However, both of these approaches require that the attack patterns or attacker nodes be identified first, which is difficult in the scenario when the number of perturbator nodes is very small. In this work, we develop a GCN defense model, namely GraphLT, which uses the concept of label transition. GraphLT assumes that perturbators' random activities deteriorate GCN's performance. To overcome this issue, GraphLT subsequently uses a novel Bayesian label transition model, which takes GCN's predicted labels and applies label transitions by Gibbs-sampling-based inference and thus repairs GCN's prediction to achieve better node classification. Extensive experiments on seven benchmark datasets show that GraphLT considerably enhances the performance of the node classifier in an unperturbed environment; furthermore, it validates that GraphLT can successfully repair a GCN-based node classifier with superior performance than several competing methods.
While numerous approaches have been developed to embed graphs into either Euclidean or hyperbolic spaces, they do not fully utilize the information available in graphs, or lack the flexibility to model intrinsic complex graph geometry. To utilize the strength of both Euclidean and hyperbolic geometries, we develop a novel Geometry Interaction Learning (GIL) method for graphs, a well-suited and efficient alternative for learning abundant geometric properties in graph. GIL captures a more informative internal structural features with low dimensions while maintaining conformal invariance of each space. Furthermore, our method endows each node the freedom to determine the importance of each geometry space via a flexible dual feature interaction learning and probability assembling mechanism. Promising experimental results are presented for five benchmark datasets on node classification and link prediction tasks.
The original design of Graph Convolution Network (GCN) couples feature transformation and neighborhood aggregation for node representation learning. Recently, some work shows that coupling is inferior to decoupling, which supports deep graph propagation better and has become the latest paradigm of GCN (e.g., APPNP and SGCN). Despite effectiveness, the working mechanisms of the decoupled GCN are not well understood. In this paper, we explore the decoupled GCN for semi-supervised node classification from a novel and fundamental perspective -- label propagation. We conduct thorough theoretical analyses, proving that the decoupled GCN is essentially the same as the two-step label propagation: first, propagating the known labels along the graph to generate pseudo-labels for the unlabeled nodes, and second, training normal neural network classifiers on the augmented pseudo-labeled data. More interestingly, we reveal the effectiveness of decoupled GCN: going beyond the conventional label propagation, it could automatically assign structure- and model- aware weights to the pseudo-label data. This explains why the decoupled GCN is relatively robust to the structure noise and over-smoothing, but sensitive to the label noise and model initialization. Based on this insight, we propose a new label propagation method named Propagation then Training Adaptively (PTA), which overcomes the flaws of the decoupled GCN with a dynamic and adaptive weighting strategy. Our PTA is simple yet more effective and robust than decoupled GCN. We empirically validate our findings on four benchmark datasets, demonstrating the advantages of our method. The code is available at https://github.com/DongHande/PT_propagation_then_training.
Graph Convolutional Network (GCN) is an emerging technique for information retrieval (IR) applications. While GCN assumes the homophily property of a graph, real-world graphs are never perfect: the local structure of a node may contain discrepancy, e.g., the labels of a node's neighbors could vary. This pushes us to consider the discrepancy of local structure in GCN modeling. Existing work approaches this issue by introducing an additional module such as graph attention, which is expected to learn the contribution of each neighbor. However, such module may not work reliably as expected, especially when there lacks supervision signal, e.g., when the labeled data is small. Moreover, existing methods focus on modeling the nodes in the training data, and never consider the local structure discrepancy of testing nodes. This work focuses on the local structure discrepancy issue for testing nodes, which has received little scrutiny. From a novel perspective of causality, we investigate whether a GCN should trust the local structure of a testing node when predicting its label. To this end, we analyze the working mechanism of GCN with causal graph, estimating the causal effect of a node's local structure for the prediction. The idea is simple yet effective: given a trained GCN model, we first intervene the prediction by blocking the graph structure; we then compare the original prediction with the intervened prediction to assess the causal effect of the local structure on the prediction. Through this way, we can eliminate the impact of local structure discrepancy and make more accurate prediction. Extensive experiments on seven node classification datasets show that our method effectively enhances the inference stage of GCN.
Attention modules, as simple and effective tools, have not only enabled deep neural networks to achieve state-of-the-art results in many domains, but also enhanced their interpretability. Most current models use deterministic attention modules due to their simplicity and ease of optimization. Stochastic counterparts, on the other hand, are less popular despite their potential benefits. The main reason is that stochastic attention often introduces optimization issues or requires significant model changes. In this paper, we propose a scalable stochastic version of attention that is easy to implement and optimize. We construct simplex-constrained attention distributions by normalizing reparameterizable distributions, making the training process differentiable. We learn their parameters in a Bayesian framework where a data-dependent prior is introduced for regularization. We apply the proposed stochastic attention modules to various attention-based models, with applications to graph node classification, visual question answering, image captioning, machine translation, and language understanding. Our experiments show the proposed method brings consistent improvements over the corresponding baselines.
Data augmentation helps neural networks generalize better by enlarging the training set, but it remains an open question how to effectively augment graph data to enhance the performance of GNNs (Graph Neural Networks). While most existing graph regularizers focus on manipulating graph topological structures by adding/removing edges, we offer a method to augment node features for better performance. We propose FLAG (Free Large-scale Adversarial Augmentation on Graphs), which iteratively augments node features with gradient-based adversarial perturbations during training. By making the model invariant to small fluctuations in input data, our method helps models generalize to out-of-distribution samples and boosts model performance at test time. FLAG is a general-purpose approach for graph data, which universally works in node classification, link prediction, and graph classification tasks. FLAG is also highly flexible and scalable, and is deployable with arbitrary GNN backbones and large-scale datasets. We demonstrate the efficacy and stability of our method through extensive experiments and ablation studies. We also provide intuitive observations for a deeper understanding of our method.
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social network graph, users in different latent relationships like friends and colleagues, are usually connected via a bare edge that conceals such intrinsic connections. In this paper, we introduce a novel graph convolutional network (GCN), termed as factorizable graph convolutional network(FactorGCN), that explicitly disentangles such intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs, each of which represents a latent and disentangled relation among nodes. The features of the nodes are then aggregated separately in each factorized latent space to produce disentangled features, which further leads to better performances for downstream tasks. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets, and demonstrate that it yields truly encouraging results in terms of both disentangling and feature aggregation. Code is publicly available at https://github.com/ihollywhy/FactorGCN.PyTorch.
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. 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. 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. 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, and a relative increase in precision of 1.6% on the MolPCBA dataset. An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.
Knowledge Graphs (KG) are of vital importance for multiple applications on the web, including information retrieval, recommender systems, and metadata annotation. Regardless of whether they are built manually by domain experts or with automatic pipelines, KGs are often incomplete. Recent work has begun to explore the use of textual descriptions available in knowledge graphs to learn vector representations of entities in order to preform link prediction. However, the extent to which these representations learned for link prediction generalize to other tasks is unclear. This is important given the cost of learning such representations. Ideally, we would prefer representations that do not need to be trained again when transferring to a different task, while retaining reasonable performance. In this work, we propose a holistic evaluation protocol for entity representations learned via a link prediction objective. We consider the inductive link prediction and entity classification tasks, which involve entities not seen during training. We also consider an information retrieval task for entity-oriented search. We evaluate an architecture based on a pretrained language model, that exhibits strong generalization to entities not observed during training, and outperforms related state-of-the-art methods (22% MRR improvement in link prediction on average). We further provide evidence that the learned representations transfer well to other tasks without fine-tuning. In the entity classification task we obtain an average improvement of 16% in accuracy compared with baselines that also employ pre-trained models. In the information retrieval task, we obtain significant improvements of up to 8.8% in NDCG@10 for natural language queries. We thus show that the learned representations are not limited KG-specific tasks, and have greater generalization properties than evaluated in previous work.