This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with $\mathcal{O}(n^3)$ runtime and $\mathcal{O}(n^2)$ space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the \textit{online relaxation} technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret $\mathcal{O}(\sqrt{n^{1+\gamma}})$ when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying $\mathcal{O}(k\sqrt{n^{1+\gamma}})$ regret based on this relaxation. The key of FastONL is a \textit{generalized local push} method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is $\mathcal{O}(\text{vol}({\mathcal{S}})\log 1/\epsilon)$ locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.
Graph Neural Networks (GNNs) are gaining extensive attention for their application in graph data. However, the black-box nature of GNNs prevents users from understanding and trusting the models, thus hampering their applicability. Whereas explaining GNNs remains a challenge, most existing methods fall into approximation based and perturbation based approaches with suffer from faithfulness problems and unnatural artifacts, respectively. To tackle these problems, we propose DEGREE \degree to provide a faithful explanation for GNN predictions. By decomposing the information generation and aggregation mechanism of GNNs, DEGREE allows tracking the contributions of specific components of the input graph to the final prediction. Based on this, we further design a subgraph level interpretation algorithm to reveal complex interactions between graph nodes that are overlooked by previous methods. The efficiency of our algorithm can be further improved by utilizing GNN characteristics. Finally, we conduct quantitative and qualitative experiments on synthetic and real-world datasets to demonstrate the effectiveness of DEGREE on node classification and graph classification tasks.
This paper presents a novel transformer architecture for graph representation learning. The core insight of our method is to fully consider the information propagation among nodes and edges in a graph when building the attention module in the transformer blocks. Specifically, we propose a new attention mechanism called Graph Propagation Attention (GPA). It explicitly passes the information among nodes and edges in three ways, i.e. node-to-node, node-to-edge, and edge-to-node, which is essential for learning graph-structured data. On this basis, we design an effective transformer architecture named Graph Propagation Transformer (GPTrans) to further help learn graph data. We verify the performance of GPTrans in a wide range of graph learning experiments on several benchmark datasets. These results show that our method outperforms many state-of-the-art transformer-based graph models with better performance. The code will be released at https://github.com/czczup/GPTrans.
Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making the graph undirected. The reasons for this are historical: 1) many early variants of spectral GNNs explicitly required undirected graphs, and 2) the first benchmarks on homophilic graphs did not find significant gain from using direction. In this paper, we show that in heterophilic settings, treating the graph as directed increases the effective homophily of the graph, suggesting a potential gain from the correct use of directionality information. To this end, we introduce Directed Graph Neural Network (Dir-GNN), a novel general framework for deep learning on directed graphs. Dir-GNN can be used to extend any Message Passing Neural Network (MPNN) to account for edge directionality information by performing separate aggregations of the incoming and outgoing edges. We prove that Dir-GNN matches the expressivity of the Directed Weisfeiler-Lehman test, exceeding that of conventional MPNNs. In extensive experiments, we validate that while our framework leaves performance unchanged on homophilic datasets, it leads to large gains over base models such as GCN, GAT and GraphSage on heterophilic benchmarks, outperforming much more complex methods and achieving new state-of-the-art results.
The prevalence of large-scale graphs poses great challenges in time and storage for training and deploying graph neural networks (GNNs). Several recent works have explored solutions for pruning the large original graph into a small and highly-informative one, such that training and inference on the pruned and large graphs have comparable performance. Although empirically effective, current researches focus on static or non-temporal graphs, which are not directly applicable to dynamic scenarios. In addition, they require labels as ground truth to learn the informative structure, limiting their applicability to new problem domains where labels are hard to obtain. To solve the dilemma, we propose and study the problem of unsupervised graph pruning on dynamic graphs. We approach the problem by our proposed STEP, a self-supervised temporal pruning framework that learns to remove potentially redundant edges from input dynamic graphs. From a technical and industrial viewpoint, our method overcomes the trade-offs between the performance and the time & memory overheads. Our results on three real-world datasets demonstrate the advantages on improving the efficacy, robustness, and efficiency of GNNs on dynamic node classification tasks. Most notably, STEP is able to prune more than 50% of edges on a million-scale industrial graph Alipay (7M nodes, 21M edges) while approximating up to 98% of the original performance. Code is available at https://github.com/EdisonLeeeee/STEP.
Node classification tasks on graphs are addressed via fully-trained deep message-passing models that learn a hierarchy of node representations via multiple aggregations of a node's neighbourhood. While effective on graphs that exhibit a high ratio of intra-class edges, this approach poses challenges in the opposite case, i.e. heterophily, where nodes belonging to the same class are usually further apart. In graphs with a high degree of heterophily, the smoothed representations based on close neighbours computed by convolutional models are no longer effective. So far, architectural variations in message-passing models to reduce excessive smoothing or rewiring the input graph to improve longer-range message passing have been proposed. In this paper, we address the challenges of heterophilic graphs with Graph Echo State Network (GESN) for node classification. GESN is a reservoir computing model for graphs, where node embeddings are recursively computed by an untrained message-passing function. Our experiments show that reservoir models are able to achieve better or comparable accuracy with respect to most fully trained deep models that implement ad hoc variations in the architectural bias or perform rewiring as a preprocessing step on the input graph, with an improvement in terms of efficiency/accuracy trade-off. Furthermore, our analysis shows that GESN is able to effectively encode the structural relationships of a graph node, by showing a correlation between iterations of the recursive embedding function and the distribution of shortest paths in a graph.
Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.
Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.
Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.
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 increases, node representations become indistinguishable, which is known as over-smoothing. To address this issue, many residual methods have emerged. In this paper, we focus on the over-smoothing issue and related residual methods. Firstly, we revisit over-smoothing from the perspective of overlapping neighborhood subgraphs, and based on this, we explain how residual methods can alleviate over-smoothing by integrating multiple orders neighborhood subgraphs to avoid the indistinguishability of the single high-order neighborhood subgraphs. Additionally, we reveal the drawbacks of previous residual methods, such as the lack of node adaptability and severe loss of high-order neighborhood subgraph information, and propose a \textbf{Posterior-Sampling-based, Node-Adaptive Residual module (PSNR)}. We theoretically demonstrate that PSNR can alleviate the drawbacks of previous residual methods. Furthermore, extensive experiments verify the superiority of the PSNR module in fully observed node classification and missing feature scenarios. Our code is available at https://github.com/jingbo02/PSNR-GNN.
Heterophily has been considered as an issue that hurts the performance of Graph Neural Networks (GNNs). To address this issue, some existing work uses a graph-level weighted fusion of the information of multi-hop neighbors to include more nodes with homophily. However, the heterophily might differ among nodes, which requires to consider the local topology. Motivated by it, we propose to use the local similarity (LocalSim) to learn node-level weighted fusion, which can also serve as a plug-and-play module. For better fusion, we propose a novel and efficient Initial Residual Difference Connection (IRDC) to extract more informative multi-hop information. Moreover, we provide theoretical analysis on the effectiveness of LocalSim representing node homophily on synthetic graphs. Extensive evaluations over real benchmark datasets show that our proposed method, namely Local Similarity Graph Neural Network (LSGNN), can offer comparable or superior state-of-the-art performance on both homophilic and heterophilic graphs. Meanwhile, the plug-and-play model can significantly boost the performance of existing GNNs. Our code is provided at https://github.com/draym28/LSGNN.
Graph Contrastive Learning (GCL) is an effective way to learn generalized graph representations in a self-supervised manner, and has grown rapidly in recent years. However, the underlying community semantics has not been well explored by most previous GCL methods. Research that attempts to leverage communities in GCL regards them as having the same influence on the graph, leading to extra representation errors. To tackle this issue, we define ''community strength'' to measure the difference of influence among communities. Under this premise, we propose a Community-Strength-enhanced Graph Contrastive Learning (CSGCL) framework to preserve community strength throughout the learning process. Firstly, we present two novel graph augmentation methods, Communal Attribute Voting (CAV) and Communal Edge Dropping (CED), where the perturbations of node attributes and edges are guided by community strength. Secondly, we propose a dynamic ''Team-up'' contrastive learning scheme, where community strength is used to progressively fine-tune the contrastive objective. We report extensive experiment results on three downstream tasks: node classification, node clustering, and link prediction. CSGCL achieves state-of-the-art performance compared with other GCL methods, validating that community strength brings effectiveness and generality to graph representations. Our code is available at https://github.com/HanChen-HUST/CSGCL.
There has been rapid growth in biomedical literature, yet capturing the heterogeneity of the bibliographic information of these articles remains relatively understudied. Although graph mining research via heterogeneous graph neural networks has taken center stage, it remains unclear whether these approaches capture the heterogeneity of the PubMed database, a vast digital repository containing over 33 million articles. We introduce PubMed Graph Benchmark (PGB), a new benchmark dataset for evaluating heterogeneous graph embeddings for biomedical literature. The benchmark contains rich metadata including abstract, authors, citations, MeSH terms, MeSH hierarchy, and some other information. The benchmark contains three different evaluation tasks encompassing systematic reviews, node classification, and node clustering. In PGB, we aggregate the metadata associated with the biomedical articles from PubMed into a unified source and make the benchmark publicly available for any future works.
In node classification using graph neural networks (GNNs), a typical model generates logits for different class labels at each node. A softmax layer often outputs a label prediction based on the largest logit. We demonstrate that it is possible to infer hidden graph structural information from the dataset using these logits. We introduce the key notion of label non-uniformity, which is derived from the Wasserstein distance between the softmax distribution of the logits and the uniform distribution. We demonstrate that nodes with small label non-uniformity are harder to classify correctly. We theoretically analyze how the label non-uniformity varies across the graph, which provides insights into boosting the model performance: increasing training samples with high non-uniformity or dropping edges to reduce the maximal cut size of the node set of small non-uniformity. These mechanisms can be easily added to a base GNN model. Experimental results demonstrate that our approach improves the performance of many benchmark base models.
Homophily principle, i.e., nodes with the same labels are more likely to be connected, has been believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over Neural Networks on node classification tasks. Recent research suggests that, even in the absence of homophily, the advantage of GNNs still exists as long as nodes from the same class share similar neighborhood patterns. However, this argument only considers intra-class Node Distinguishability (ND) but neglects inter-class ND, which provides incomplete understanding of homophily on GNNs. In this paper, we first demonstrate such deficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea and study ND deeply, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and negative generalized Jeffreys divergence, to quantify ND. With the metrics, we visualize and analyze how graph filters, node degree distributions and class variances influence ND, and investigate the combined effect of intra- and inter-class ND. Besides, we discovered the mid-homophily pitfall, which occurs widely in graph datasets. Furthermore, we verified that, in real-work tasks, the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels. Grounded in this observation, we propose a new hypothesis-testing based performance metric beyond homophily, which is non-linear, feature-based and can provide statistical threshold value for GNNs' the superiority. Experiments indicate that it is significantly more effective than the existing homophily metrics on revealing the advantage and disadvantage of graph-aware modes on both synthetic and benchmark real-world datasets.
Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to its powerful graph data modelling capabilities, various graph embedding models and libraries have been proposed to learn embeddings and help researchers ease conducting experiments. In this paper, we introduce a novel graph representation framework covering various graph embedding models, ranging from shallow to state-of-the-art models, namely Connector. First, we consider graph generation by constructing various types of graphs with different structural relations, including homogeneous, signed, heterogeneous, and knowledge graphs. Second, we introduce various graph representation learning models, ranging from shallow to deep graph embedding models. Finally, we plan to build an efficient open-source framework that can provide deep graph embedding models to represent structural relations in graphs. The framework is available at https://github.com/NSLab-CUK/Connector.
How can we learn effective node representations on textual graphs? Graph Neural Networks (GNNs) that use Language Models (LMs) to encode textual information of graphs achieve state-of-the-art performance in many node classification tasks. Yet, combining GNNs with LMs has not been widely explored for practical deployments due to its scalability issues. In this work, we tackle this challenge by developing a Graph-Aware Distillation framework (GRAD) to encode graph structures into an LM for graph-free, fast inference. Different from conventional knowledge distillation, GRAD jointly optimizes a GNN teacher and a graph-free student over the graph's nodes via a shared LM. This encourages the graph-free student to exploit graph information encoded by the GNN teacher while at the same time, enables the GNN teacher to better leverage textual information from unlabeled nodes. As a result, the teacher and the student models learn from each other to improve their overall performance. Experiments in eight node classification benchmarks in both transductive and inductive settings showcase GRAD's superiority over existing distillation approaches for textual graphs.
Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open research problem. Recent works have proposed extensions to standard GNN architectures to improve performance on heterophilous graphs, trading off model simplicity for prediction accuracy. However, these models fail to capture basic graph properties, such as neighborhood label distribution, which are fundamental for learning. In this work, we propose GCN for Heterophily (GCNH), a simple yet effective GNN architecture applicable to both heterophilous and homophilous scenarios. GCNH learns and combines separate representations for a node and its neighbors, using one learned importance coefficient per layer to balance the contributions of center nodes and neighborhoods. We conduct extensive experiments on eight real-world graphs and a set of synthetic graphs with varying degrees of heterophily to demonstrate how the design choices for GCNH lead to a sizable improvement over a vanilla GCN. Moreover, GCNH outperforms state-of-the-art models of much higher complexity on four out of eight benchmarks, while producing comparable results on the remaining datasets. Finally, we discuss and analyze the lower complexity of GCNH, which results in fewer trainable parameters and faster training times than other methods, and show how GCNH mitigates the oversmoothing problem.
Graph Neural Networks (GNNs) have shown state-of-the-art improvements in node classification tasks on graphs. While these improvements have been largely demonstrated in a multi-class classification scenario, a more general and realistic scenario in which each node could have multiple labels has so far received little attention. The first challenge in conducting focused studies on multi-label node classification is the limited number of publicly available multi-label graph datasets. Therefore, as our first contribution, we collect and release three real-world biological datasets and develop a multi-label graph generator to generate datasets with tunable properties. While high label similarity (high homophily) is usually attributed to the success of GNNs, we argue that a multi-label scenario does not follow the usual semantics of homophily and heterophily so far defined for a multi-class scenario. As our second contribution, we define homophily and Cross-Class Neighborhood Similarity for the multi-label scenario and provide a thorough analyses of the collected $9$ multi-label datasets. Finally, we perform a large-scale comparative study with $8$ methods and $9$ datasets and analyse the performances of the methods to assess the progress made by current state of the art in the multi-label node classification scenario. We release our benchmark at https://github.com/Tianqi-py/MLGNC.
The presence of a large number of bots on social media leads to adverse effects. Although Random forest algorithm is widely used in bot detection and can significantly enhance the performance of weak classifiers, it cannot utilize the interaction between accounts. This paper proposes a Random Forest boosted Graph Neural Network for social bot detection, called RF-GNN, which employs graph neural networks (GNNs) as the base classifiers to construct a random forest, effectively combining the advantages of ensemble learning and GNNs to improve the accuracy and robustness of the model. Specifically, different subgraphs are constructed as different training sets through node sampling, feature selection, and edge dropout. Then, GNN base classifiers are trained using various subgraphs, and the remaining features are used for training Fully Connected Netural Network (FCN). The outputs of GNN and FCN are aligned in each branch. Finally, the outputs of all branches are aggregated to produce the final result. Moreover, RF-GNN is compatible with various widely-used GNNs for node classification. Extensive experimental results demonstrate that the proposed method obtains better performance than other state-of-the-art methods.