Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures. Code can be found at \url{https://github.com/hamed1375/Exphormer}.
Graph neural networks have proved to be a key tool for dealing with many problems and domains such as chemistry, natural language processing and social networks. While the structure of the layers is simple, it is difficult to identify the patterns learned by the graph neural network. Several works propose post-hoc methods to explain graph predictions, but few of them try to generate interpretable models. Conversely, the topic of the interpretable models is highly investigated in image recognition. Given the similarity between image and graph domains, we analyze the adaptability of prototype-based neural networks for graph and node classification. In particular, we investigate the use of two interpretable networks, ProtoPNet and TesNet, in the graph domain. We show that the adapted networks manage to reach better or higher accuracy scores than their respective black-box models and comparable performances with state-of-the-art self-explainable models. Showing how to extract ProtoPNet and TesNet explanations on graph neural networks, we further study how to obtain global and local explanations for the trained models. We then evaluate the explanations of the interpretable models by comparing them with post-hoc approaches and self-explainable models. Our findings show that the application of TesNet and ProtoPNet to the graph domain produces qualitative predictions while improving their reliability and transparency.
Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.
This vision paper proposes KGNet, an on-demand graph machine learning (GML) as a service on top of RDF engines to support GML-enabled SPARQL queries. KGNet automates the training of GML models on a KG by identifying a task-specific subgraph. This helps reduce the task-irrelevant KG structure and properties for better scalability and accuracy. While training a GML model on KG, KGNet collects metadata of trained models in the form of an RDF graph called KGMeta, which is interlinked with the relevant subgraphs in KG. Finally, all trained models are accessible via a SPARQL-like query. We call it a GML-enabled query and refer to it as SPARQLML. KGNet supports SPARQLML on top of existing RDF engines as an interface for querying and inferencing over KGs using GML models. The development of KGNet poses research opportunities in several areas, including meta-sampling for identifying task-specific subgraphs, GML pipeline automation with computational constraints, such as limited time and memory budget, and SPARQLML query optimization. KGNet supports different GML tasks, such as node classification, link prediction, and semantic entity matching. We evaluated KGNet using two real KGs of different application domains. Compared to training on the entire KG, KGNet significantly reduced training time and memory usage while maintaining comparable or improved accuracy. The KGNet source-code is available for further study
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 at different regions of the graph. Thus, it is sub-optimal to indifferently embed an entire graph into a single space. In this paper, we explore and analyze two notions of local hyperbolicity, describing the underlying local geometry: geometric (Gromov) and model-based, to determine the preferred space of embedding for each node. The two hyperbolicities' distributions are aligned using the Wasserstein metric such that the calculated geometric hyperbolicity guides the choice of the learned model hyperbolicity. As such our model Joint Space Graph Neural Network (JSGNN) can leverage both Euclidean and hyperbolic spaces during learning by allowing node-specific geometry space selection. We evaluate our model on both node classification and link prediction tasks and observe promising performance compared to baseline models.
Graph Neural Networks (GNNs) have achieved promising results in various tasks such as node classification and graph classification. Recent studies find that GNNs are vulnerable to adversarial attacks. However, effective backdoor attacks on graphs are still an open problem. In particular, backdoor attack poisons the graph by attaching triggers and the target class label to a set of nodes in the training graph. The backdoored GNNs trained on the poisoned graph will then be misled to predict test nodes to target class once attached with triggers. Though there are some initial efforts in graph backdoor attacks, our empirical analysis shows that they may require a large attack budget for effective backdoor attacks and the injected triggers can be easily detected and pruned. Therefore, in this paper, we study a novel problem of unnoticeable graph backdoor attacks with limited attack budget. To fully utilize the attack budget, we propose to deliberately select the nodes to inject triggers and target class labels in the poisoning phase. An adaptive trigger generator is deployed to obtain effective triggers that are difficult to be noticed. Extensive experiments on real-world datasets against various defense strategies demonstrate the effectiveness of our proposed method in conducting effective unnoticeable backdoor attacks.
Graph convolutional networks (GCNs) have been very effective in addressing the issue of various graph-structured related tasks. However, recent research has shown that GCNs are vulnerable to a new type of threat called a backdoor attack, where the adversary can inject a hidden backdoor into GCNs so that the attacked model performs well on benign samples, but its prediction will be maliciously changed to the attacker-specified target label if the hidden backdoor is activated by the attacker-defined trigger. A semantic backdoor attack is a new type of backdoor attack on deep neural networks (DNNs), where a naturally occurring semantic feature of samples can serve as a backdoor trigger such that the infected DNN models will misclassify testing samples containing the predefined semantic feature even without the requirement of modifying the testing samples. Since the backdoor trigger is a naturally occurring semantic feature of the samples, semantic backdoor attacks are more imperceptible and pose a new and serious threat. In this paper, we investigate whether such semantic backdoor attacks are possible for GCNs and propose a semantic backdoor attack against GCNs (SBAG) under the context of graph classification to reveal the existence of this security vulnerability in GCNs. SBAG uses a certain type of node in the samples as a backdoor trigger and injects a hidden backdoor into GCN models by poisoning training data. The backdoor will be activated, and the GCN models will give malicious classification results specified by the attacker even on unmodified samples as long as the samples contain enough trigger nodes. We evaluate SBAG on four graph datasets and the experimental results indicate that SBAG is effective.
Graph neural networks (GNNs) have achieved champion in wide applications. Neural message passing is a typical key module for feature propagation by aggregating neighboring features. In this work, we propose a new message passing based on multiscale framelet transforms, called Framelet Message Passing. Different from traditional spatial methods, it integrates framelet representation of neighbor nodes from multiple hops away in node message update. We also propose a continuous message passing using neural ODE solvers. It turns both discrete and continuous cases can provably achieve network stability and limit oversmoothing due to the multiscale property of framelets. Numerical experiments on real graph datasets show that the continuous version of the framelet message passing significantly outperforms existing methods when learning heterogeneous graphs and achieves state-of-the-art performance on classic node classification tasks with low computational costs.
Graph neural networks (GNNs) fuel diverse machine learning tasks involving graph-structured data, ranging from predicting protein structures to serving personalized recommendations. Real-world graph data must often be stored distributed across many machines not just because of capacity constraints, but because of compliance with data residency or privacy laws. In such setups, network communication is costly and becomes the main bottleneck to train GNNs. Optimizations for distributed GNN training have targeted data-level improvements so far -- via caching, network-aware partitioning, and sub-sampling -- that work for data center-like setups where graph data is accessible to a single entity and data transfer costs are ignored. We present RETEXO, the first framework which eliminates the severe communication bottleneck in distributed GNN training while respecting any given data partitioning configuration. The key is a new training procedure, lazy message passing, that reorders the sequence of training GNN elements. RETEXO achieves 1-2 orders of magnitude reduction in network data costs compared to standard GNN training, while retaining accuracy. RETEXO scales gracefully with increasing decentralization and decreasing bandwidth. It is the first framework that can be used to train GNNs at all network decentralization levels -- including centralized data-center networks, wide area networks, proximity networks, and edge networks.
Graph neural networks (GNNs) have shown high potential for a variety of real-world, challenging applications, but one of the major obstacles in GNN research is the lack of large-scale flexible datasets. Most existing public datasets for GNNs are relatively small, which limits the ability of GNNs to generalize to unseen data. The few existing large-scale graph datasets provide very limited labeled data. This makes it difficult to determine if the GNN model's low accuracy for unseen data is inherently due to insufficient training data or if the model failed to generalize. Additionally, datasets used to train GNNs need to offer flexibility to enable a thorough study of the impact of various factors while training GNN models. In this work, we introduce the Illinois Graph Benchmark (IGB), a research dataset tool that the developers can use to train, scrutinize and systematically evaluate GNN models with high fidelity. IGB includes both homogeneous and heterogeneous academic graphs of enormous sizes, with more than 40% of their nodes labeled. Compared to the largest graph datasets publicly available, the IGB provides over 162X more labeled data for deep learning practitioners and developers to create and evaluate models with higher accuracy. The IGB dataset is a collection of academic graphs designed to be flexible, enabling the study of various GNN architectures, embedding generation techniques, and analyzing system performance issues for node classification tasks. IGB is open-sourced, supports DGL and PyG frameworks, and comes with releases of the raw text that we believe foster emerging language models and GNN research projects. An early public version of IGB is available at https://github.com/IllinoisGraphBenchmark/IGB-Datasets.
Graph neural networks (GNNs) have achieved great success in node classification tasks. However, existing GNNs naturally bias towards the majority classes with more labelled data and ignore those minority classes with relatively few labelled ones. The traditional techniques often resort over-sampling methods, but they may cause overfitting problem. More recently, some works propose to synthesize additional nodes for minority classes from the labelled nodes, however, there is no any guarantee if those generated nodes really stand for the corresponding minority classes. In fact, improperly synthesized nodes may result in insufficient generalization of the algorithm. To resolve the problem, in this paper we seek to automatically augment the minority classes from the massive unlabelled nodes of the graph. Specifically, we propose \textit{GraphSR}, a novel self-training strategy to augment the minority classes with significant diversity of unlabelled nodes, which is based on a Similarity-based selection module and a Reinforcement Learning(RL) selection module. The first module finds a subset of unlabelled nodes which are most similar to those labelled minority nodes, and the second one further determines the representative and reliable nodes from the subset via RL technique. Furthermore, the RL-based module can adaptively determine the sampling scale according to current training data. This strategy is general and can be easily combined with different GNNs models. Our experiments demonstrate the proposed approach outperforms the state-of-the-art baselines on various class-imbalanced datasets.
Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the property of the polynomial basis. Consequently, two natural and fundamental questions arise: Can we learn a suitable polynomial basis from the training data? Can we determine the optimal polynomial basis for a given graph and node features? In this paper, we propose two spectral GNN models that provide positive answers to the questions posed above. First, inspired by Favard's Theorem, we propose the FavardGNN model, which learns a polynomial basis from the space of all possible orthonormal bases. Second, we examine the supposedly unsolvable definition of optimal polynomial basis from Wang & Zhang (2022) and propose a simple model, OptBasisGNN, which computes the optimal basis for a given graph structure and graph signal. Extensive experiments are conducted to demonstrate the effectiveness of our proposed models. Our code is available at https://github.com/yuziGuo/FarOptBasis.
Node classification is a classical graph machine learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs where edges tend to connect nodes of the same class. Graphs without this property are called heterophilous, and it is typically assumed that specialized methods are required to achieve strong performance on such graphs. In this work, we challenge this assumption. First, we show that the standard datasets used for evaluating heterophily-specific models have serious drawbacks, making results obtained by using them unreliable. The most significant of these drawbacks is the presence of a large number of duplicate nodes in the datasets Squirrel and Chameleon, which leads to train-test data leakage. We show that removing duplicate nodes strongly affects GNN performance on these datasets. Then, we propose a set of heterophilous graphs of varying properties that we believe can serve as a better benchmark for evaluating the performance of GNNs under heterophily. We show that standard GNNs achieve strong results on these heterophilous graphs, almost always outperforming specialized models. Our datasets and the code for reproducing our experiments are available at https://github.com/yandex-research/heterophilous-graphs
Graph convolutional networks (GCNs) were a great step towards extending deep learning to unstructured data such as graphs. But GCNs still need a constructed graph to work with. To solve this problem, classical graphs such as $k$-nearest neighbor are usually used to initialize the GCN. Although it is computationally efficient to construct $k$-nn graphs, the constructed graph might not be very useful for learning. In a $k$-nn graph, points are restricted to have a fixed number of edges, and all edges in the graph have equal weights. We present a new way to construct the graph and initialize the GCN. It is based on random projection forest (rpForest). rpForest enables us to assign varying weights on edges indicating varying importance, which enhanced the learning. The number of trees is a hyperparameter in rpForest. We performed spectral analysis to help us setting this parameter in the right range. In the experiments, initializing the GCN using rpForest provides better results compared to $k$-nn initialization.
Graph Neural Networks (GNNs) are increasingly becoming the favorite method for graph learning. They exploit the semi-supervised nature of deep learning, and they bypass computational bottlenecks associated with traditional graph learning methods. In addition to the feature matrix $X$, GNNs need an adjacency matrix $A$ to perform feature propagation. In many cases, the adjacency matrix $A$ is missing. We introduce a graph construction scheme that constructs the adjacency matrix $A$ using unsupervised and supervised information. Unsupervised information characterizes the neighborhood around points. We used Principal Axis trees (PA-trees) as a source for unsupervised information, where we create edges between points falling onto the same leaf node. For supervised information, we used the concept of penalty and intrinsic graphs. A penalty graph connects points with different class labels, whereas an intrinsic graph connects points with the same class labels. We used the penalty and intrinsic graphs to remove or add edges to the graph constructed via PA-tree. We tested this graph construction scheme on two well-known GNNs: 1) Graph Convolutional Network (GCN) and 2) Simple Graph Convolution (SGC). The experiments show that it is better to use SGC because it is faster and delivers better or the same results as GCN. We also test the effect of oversmoothing on both GCN and SGC. We found out that the level of smoothing has to be carefully selected for SGC to avoid oversmoothing.
Knowledge graphs (KGs) are a powerful approach for integrating heterogeneous data and making inferences in biology and many other domains, but a coherent solution for constructing, exchanging, and facilitating the downstream use of knowledge graphs is lacking. Here we present KG-Hub, a platform that enables standardized construction, exchange, and reuse of knowledge graphs. Features include a simple, modular extract-transform-load (ETL) pattern for producing graphs compliant with Biolink Model (a high-level data model for standardizing biological data), easy integration of any OBO (Open Biological and Biomedical Ontologies) ontology, cached downloads of upstream data sources, versioned and automatically updated builds with stable URLs, web-browsable storage of KG artifacts on cloud infrastructure, and easy reuse of transformed subgraphs across projects. Current KG-Hub projects span use cases including COVID-19 research, drug repurposing, microbial-environmental interactions, and rare disease research. KG-Hub is equipped with tooling to easily analyze and manipulate knowledge graphs. KG-Hub is also tightly integrated with graph machine learning (ML) tools which allow automated graph machine learning, including node embeddings and training of models for link prediction and node classification.
Node classification is a substantial problem in graph-based fraud detection. Many existing works adopt Graph Neural Networks (GNNs) to enhance fraud detectors. While promising, currently most GNN-based fraud detectors fail to generalize to the low homophily setting. Besides, label utilization has been proved to be significant factor for node classification problem. But we find they are less effective in fraud detection tasks due to the low homophily in graphs. In this work, we propose GAGA, a novel Group AGgregation enhanced TrAnsformer, to tackle the above challenges. Specifically, the group aggregation provides a portable method to cope with the low homophily issue. Such an aggregation explicitly integrates the label information to generate distinguishable neighborhood information. Along with group aggregation, an attempt towards end-to-end trainable group encoding is proposed which augments the original feature space with the class labels. Meanwhile, we devise two additional learnable encodings to recognize the structural and relational context. Then, we combine the group aggregation and the learnable encodings into a Transformer encoder to capture the semantic information. Experimental results clearly show that GAGA outperforms other competitive graph-based fraud detectors by up to 24.39% on two trending public datasets and a real-world industrial dataset from Anonymous. Even more, the group aggregation is demonstrated to outperform other label utilization methods (e.g., C&S, BoT/UniMP) in the low homophily setting.
Graph Neural Networks (GNNs) have proven to be powerful in many graph-based applications. However, they fail to generalize well under heterophilic setups, where neighbor nodes have different labels. To address this challenge, we employ a confidence ratio as a hyper-parameter, assuming that some of the edges are disassortative (heterophilic). Here, we propose a two-phased algorithm. Firstly, we determine edge coefficients through subgraph matching using a supplementary module. Then, we apply GNNs with a modified label propagation mechanism to utilize the edge coefficients effectively. Specifically, our supplementary module identifies a certain proportion of task-irrelevant edges based on a given confidence ratio. Using the remaining edges, we employ the widely used optimal transport to measure the similarity between two nodes with their subgraphs. Finally, using the coefficients as supplementary information on GNNs, we improve the label propagation mechanism which can prevent two nodes with smaller weights from being closer. The experiments on benchmark datasets show that our model alleviates over-smoothing and improves performance.
Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only one-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperforms state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.
Graph convolutional networks (GCNs) are currently the most promising paradigm for dealing with graph-structure data, while recent studies have also shown that GCNs are vulnerable to adversarial attacks. Thus developing GCN models that are robust to such attacks become a hot research topic. However, the structural purification learning-based or robustness constraints-based defense GCN methods are usually designed for specific data or attacks, and introduce additional objective that is not for classification. Extra training overhead is also required in their design. To address these challenges, we conduct in-depth explorations on mid-frequency signals on graphs and propose a simple yet effective Mid-pass filter GCN (Mid-GCN). Theoretical analyses guarantee the robustness of signals through the mid-pass filter, and we also shed light on the properties of different frequency signals under adversarial attacks. Extensive experiments on six benchmark graph data further verify the effectiveness of our designed Mid-GCN in node classification accuracy compared to state-of-the-art GCNs under various adversarial attack strategies.