Graph Neural Networks (GNNs) have achieved great success in modeling graph-structured data. However, recent works show that GNNs are vulnerable to adversarial attacks which can fool the GNN model to make desired predictions of the attacker. In addition, training data of GNNs can be leaked under membership inference attacks. This largely hinders the adoption of GNNs in high-stake domains such as e-commerce, finance and bioinformatics. Though investigations have been made in conducting robust predictions and protecting membership privacy, they generally fail to simultaneously consider the robustness and membership privacy. Therefore, in this work, we study a novel problem of developing robust and membership privacy-preserving GNNs. Our analysis shows that Information Bottleneck (IB) can help filter out noisy information and regularize the predictions on labeled samples, which can benefit robustness and membership privacy. However, structural noises and lack of labels in node classification challenge the deployment of IB on graph-structured data. To mitigate these issues, we propose a novel graph information bottleneck framework that can alleviate structural noises with neighbor bottleneck. Pseudo labels are also incorporated in the optimization to minimize the gap between the predictions on the labeled set and unlabeled set for membership privacy. Extensive experiments on real-world datasets demonstrate that our method can give robust predictions and simultaneously preserve membership privacy.
Graph neural networks have been extensively studied for learning with inter-connected data. Despite this, recent evidence has revealed GNNs' deficiencies related to over-squashing, heterophily, handling long-range dependencies, edge incompleteness and particularly, the absence of graphs altogether. While a plausible solution is to learn new adaptive topology for message passing, issues concerning quadratic complexity hinder simultaneous guarantees for scalability and precision in large networks. In this paper, we introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes, as an important building block for a pioneering Transformer-style network for node classification on large graphs, dubbed as \textsc{NodeFormer}. Specifically, the efficient computation is enabled by a kernerlized Gumbel-Softmax operator that reduces the algorithmic complexity to linearity w.r.t. node numbers for learning latent graph structures from large, potentially fully-connected graphs in a differentiable manner. We also provide accompanying theory as justification for our design. Extensive experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs (with up to 2M nodes) and graph-enhanced applications (e.g., image classification) where input graphs are missing.
Node classification on graphs is a significant task with a wide range of applications, including social analysis and anomaly detection. Even though graph neural networks (GNNs) have produced promising results on this task, current techniques often presume that label information of nodes is accurate, which may not be the case in real-world applications. To tackle this issue, we investigate the problem of learning on graphs with label noise and develop a novel approach dubbed Consistent Graph Neural Network (CGNN) to solve it. Specifically, we employ graph contrastive learning as a regularization term, which promotes two views of augmented nodes to have consistent representations. Since this regularization term cannot utilize label information, it can enhance the robustness of node representations to label noise. Moreover, to detect noisy labels on the graph, we present a sample selection technique based on the homophily assumption, which identifies noisy nodes by measuring the consistency between the labels with their neighbors. Finally, we purify these confident noisy labels to permit efficient semantic graph learning. Extensive experiments on three well-known benchmark datasets demonstrate the superiority of our CGNN over competing approaches.
The contextual stochastic block model (cSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine learning on graphs, the cSBM has been widely used as a synthetic dataset for evaluating the performance of graph-neural networks (GNNs) for semi-supervised node classification. We consider a probabilistic Bayes-optimal formulation of the inference problem and we derive a belief-propagation-based algorithm for the semi-supervised cSBM; we conjecture it is optimal in the considered setting and we provide its implementation. We show that there can be a considerable gap between the accuracy reached by this algorithm and the performance of the GNN architectures proposed in the literature. This suggests that the cSBM, along with the comparison to the performance of the optimal algorithm, readily accessible via our implementation, can be instrumental in the development of more performant GNN architectures.
Self-supervised learning on graphs has made large strides in achieving great performance in various downstream tasks. However, many state-of-the-art methods suffer from a number of impediments, which prevent them from realizing their full potential. For instance, contrastive methods typically require negative sampling, which is often computationally costly. While non-contrastive methods avoid this expensive step, most existing methods either rely on overly complex architectures or dataset-specific augmentations. In this paper, we ask: Can we borrow from classical unsupervised machine learning literature in order to overcome those obstacles? Guided by our key insight that the goal of distance-based clustering closely resembles that of contrastive learning: both attempt to pull representations of similar items together and dissimilar items apart. As a result, we propose CARL-G - a novel clustering-based framework for graph representation learning that uses a loss inspired by Cluster Validation Indices (CVIs), i.e., internal measures of cluster quality (no ground truth required). CARL-G is adaptable to different clustering methods and CVIs, and we show that with the right choice of clustering method and CVI, CARL-G outperforms node classification baselines on 4/5 datasets with up to a 79x training speedup compared to the best-performing baseline. CARL-G also performs at par or better than baselines in node clustering and similarity search tasks, training up to 1,500x faster than the best-performing baseline. Finally, we also provide theoretical foundations for the use of CVI-inspired losses in graph representation learning.
End-to-end training with global optimization have popularized graph neural networks (GNNs) for node classification, yet inadvertently introduced vulnerabilities to adversarial edge-perturbing attacks. Adversaries can exploit the inherent opened interfaces of GNNs' input and output, perturbing critical edges and thus manipulating the classification results. Current defenses, due to their persistent utilization of global-optimization-based end-to-end training schemes, inherently encapsulate the vulnerabilities of GNNs. This is specifically evidenced in their inability to defend against targeted secondary attacks. In this paper, we propose the Graph Agent Network (GAgN) to address the aforementioned vulnerabilities of GNNs. GAgN is a graph-structured agent network in which each node is designed as an 1-hop-view agent. Through the decentralized interactions between agents, they can learn to infer global perceptions to perform tasks including inferring embeddings, degrees and neighbor relationships for given nodes. This empowers nodes to filtering adversarial edges while carrying out classification tasks. Furthermore, agents' limited view prevents malicious messages from propagating globally in GAgN, thereby resisting global-optimization-based secondary attacks. We prove that single-hidden-layer multilayer perceptrons (MLPs) are theoretically sufficient to achieve these functionalities. Experimental results show that GAgN effectively implements all its intended capabilities and, compared to state-of-the-art defenses, achieves optimal classification accuracy on the perturbed datasets.
Graph Neural Network (GNN) research has highlighted a relationship between high homophily (i.e., the tendency of nodes of the same class to connect) and strong predictive performance in node classification. However, recent work has found the relationship to be more nuanced, demonstrating that simple GNNs can learn in certain heterophilous settings. To resolve these conflicting findings and align closer to real-world datasets, we go beyond the assumption of a global graph homophily level and study the performance of GNNs when the local homophily level of a node deviates from the global homophily level. Through theoretical and empirical analysis, we systematically demonstrate how shifts in local homophily can introduce performance degradation, leading to performance discrepancies across local homophily levels. We ground the practical implications of this work through granular analysis on five real-world datasets with varying global homophily levels, demonstrating that (a) GNNs can fail to generalize to test nodes that deviate from the global homophily of a graph, and (b) high local homophily does not necessarily confer high performance for a node. We further show that GNNs designed for globally heterophilous graphs can alleviate performance discrepancy by improving performance across local homophily levels, offering a new perspective on how these GNNs achieve stronger global performance.
Few-shot Node Classification (FSNC) is a challenge in graph representation learning where only a few labeled nodes per class are available for training. To tackle this issue, meta-learning has been proposed to transfer structural knowledge from base classes with abundant labels to target novel classes. However, existing solutions become ineffective or inapplicable when base classes have no or limited labeled nodes. To address this challenge, we propose an innovative method dubbed Virtual Node Tuning (VNT). Our approach utilizes a pretrained graph transformer as the encoder and injects virtual nodes as soft prompts in the embedding space, which can be optimized with few-shot labels in novel classes to modulate node embeddings for each specific FSNC task. A unique feature of VNT is that, by incorporating a Graph-based Pseudo Prompt Evolution (GPPE) module, VNT-GPPE can handle scenarios with sparse labels in base classes. Experimental results on four datasets demonstrate the superiority of the proposed approach in addressing FSNC with unlabeled or sparsely labeled base classes, outperforming existing state-of-the-art methods and even fully supervised baselines.
We present a new effective and scalable framework for training GNNs in node classification tasks, based on the effective resistance, a powerful tool solidly rooted in graph theory. Our approach progressively refines the GNN weights on an extensive sequence of random spanning trees, suitably transformed into path graphs that retain essential topological and node information of the original graph. The sparse nature of these path graphs substantially lightens the computational burden of GNN training. This not only enhances scalability but also effectively addresses common issues like over-squashing, over-smoothing, and performance deterioration caused by overfitting in small training set regimes. We carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we apply our framework to graph convolutional networks, showing simultaneous improvement of both training speed and test accuracy over a wide pool of representative baselines.
Graph-based semi-supervised node classification has been shown to become a state-of-the-art approach in many applications with high research value and significance. Most existing methods are only based on the original intrinsic or artificially established graph structure which may not accurately reflect the "true" correlation among data and are not optimal for semi-supervised node classification in the downstream graph neural networks. Besides, while existing graph-based methods mostly utilize the explicit graph structure, some implicit information, for example, the density information, can also provide latent information that can be further exploited. To address these limitations, this paper proposes the Dual Hypergraph Neural Network (DualHGNN), a new dual connection model integrating both hypergraph structure learning and hypergraph representation learning simultaneously in a unified architecture. The DualHGNN first leverages a multi-view hypergraph learning network to explore the optimal hypergraph structure from multiple views, constrained by a consistency loss proposed to improve its generalization. Then, DualHGNN employs a density-aware hypergraph attention network to explore the high-order semantic correlation among data points based on the density-aware attention mechanism. Extensive experiments are conducted in various benchmark datasets, and the results demonstrate the effectiveness of the proposed approach.
Fairness in graph neural networks has been actively studied recently. However, existing works often do not explicitly consider the role of message passing in introducing or amplifying the bias. In this paper, we first investigate the problem of bias amplification in message passing. We empirically and theoretically demonstrate that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced. Guided by such analyses, we propose BeMap, a fair message passing method, that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups. Extensive experiments on node classification demonstrate the efficacy of BeMap in mitigating bias while maintaining classification accuracy. The code is available at https://github.com/xiaolin-cs/BeMap.
We introduce a randomized topological augmentor based on Schur complements for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the technique generates unbiased approximations of its Schur complements and treats the corresponding graphs as augmented views. We discuss the benefits of our approach, provide theoretical justifications and present connections with graph diffusion. Unlike previous efforts, we study the empirical effectiveness of the augmentor in a controlled fashion by varying the design choices for subsequent GCL phases, such as encoding and contrasting. Extensive experiments on node and graph classification benchmarks demonstrate that our technique consistently outperforms pre-defined and adaptive augmentation approaches to achieve state-of-the-art results.
Graph Neural Networks (GNNs) have shown remarkable performance on graph-structured data. However, recent empirical studies suggest that GNNs are very susceptible to distribution shift. There is still significant ambiguity about why graph-based models seem more vulnerable to these shifts. In this work we provide a thorough theoretical analysis on it by quantifying the magnitude of conditional shift between the input features and the output label. Our findings show that both graph heterophily and model architecture exacerbate conditional shifts, leading to performance degradation. To address this, we propose an approach that involves estimating and minimizing the conditional shift for unsupervised domain adaptation on graphs. In our controlled synthetic experiments, our algorithm demonstrates robustness towards distribution shift, resulting in up to 10% absolute ROC AUC improvement versus the second-best algorithm. Furthermore, comprehensive experiments on both node classification and graph classification show its robust performance under various distribution shifts.
Knowledge graph embedding models (KGEMs) have gained considerable traction in recent years. These models learn a vector representation of knowledge graph entities and relations, a.k.a. knowledge graph embeddings (KGEs). Learning versatile KGEs is desirable as it makes them useful for a broad range of tasks. However, KGEMs are usually trained for a specific task, which makes their embeddings task-dependent. In parallel, the widespread assumption that KGEMs actually create a semantic representation of the underlying entities and relations (e.g., project similar entities closer than dissimilar ones) has been challenged. In this work, we design heuristics for generating protographs -- small, modified versions of a KG that leverage RDF/S information. The learnt protograph-based embeddings are meant to encapsulate the semantics of a KG, and can be leveraged in learning KGEs that, in turn, also better capture semantics. Extensive experiments on various evaluation benchmarks demonstrate the soundness of this approach, which we call Modular and Agnostic SCHema-based Integration of protograph Embeddings (MASCHInE). In particular, MASCHInE helps produce more versatile KGEs that yield substantially better performance for entity clustering and node classification tasks. For link prediction, using MASCHinE substantially increases the number of semantically valid predictions with equivalent rank-based performance.
Graph neural networks (GNNs) have achieved remarkable advances in graph-oriented tasks. However, real-world graphs invariably contain a certain proportion of heterophilous nodes, challenging the homophily assumption of traditional GNNs and hindering their performance. Most existing studies continue to design generic models with shared weights between heterophilous and homophilous nodes. Despite the incorporation of high-order messages or multi-channel architectures, these efforts often fall short. A minority of studies attempt to train different node groups separately but suffer from inappropriate separation metrics and low efficiency. In this paper, we first propose a new metric, termed Neighborhood Confusion (NC), to facilitate a more reliable separation of nodes. We observe that node groups with different levels of NC values exhibit certain differences in intra-group accuracy and visualized embeddings. These pave the way for Neighborhood Confusion-guided Graph Convolutional Network (NCGCN), in which nodes are grouped by their NC values and accept intra-group weight sharing and message passing. Extensive experiments on both homophilous and heterophilous benchmarks demonstrate that our framework can effectively separate nodes and yield significant performance improvement compared to the latest methods. The source code will be available in https://github.com/GISec-Team/NCGNN.
Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the weight of its propagation. Despite their popularity, the discussion on deep graph attention and its unique challenges has been limited. In this work, we investigate some problematic phenomena related to deep graph attention, including vulnerability to over-smoothed features and smooth cumulative attention. Through theoretical and empirical analyses, we show that various attention-based GNNs suffer from these problems. Motivated by our findings, we propose AEROGNN, a novel GNN architecture designed for deep graph attention. AERO-GNN provably mitigates the proposed problems of deep graph attention, which is further empirically demonstrated with (a) its adaptive and less smooth attention functions and (b) higher performance at deep layers (up to 64). On 9 out of 12 node classification benchmarks, AERO-GNN outperforms the baseline GNNs, highlighting the advantages of deep graph attention. Our code is available at https://github.com/syleeheal/AERO-GNN.
While Graph Neural Networks (GNNs) are remarkably successful in a variety of high-impact applications, we demonstrate that, in link prediction, the common practices of including the edges being predicted in the graph at training and/or test have outsized impact on the performance of low-degree nodes. We theoretically and empirically investigate how these practices impact node-level performance across different degrees. Specifically, we explore three issues that arise: (I1) overfitting; (I2) distribution shift; and (I3) implicit test leakage. The former two issues lead to poor generalizability to the test data, while the latter leads to overestimation of the model's performance and directly impacts the deployment of GNNs. To address these issues in a systematic way, we introduce an effective and efficient GNN training framework, SpotTarget, which leverages our insight on low-degree nodes: (1) at training time, it excludes a (training) edge to be predicted if it is incident to at least one low-degree node; and (2) at test time, it excludes all test edges to be predicted (thus, mimicking real scenarios of using GNNs, where the test data is not included in the graph). SpotTarget helps researchers and practitioners adhere to best practices for learning from graph data, which are frequently overlooked even by the most widely-used frameworks. Our experiments on various real-world datasets show that SpotTarget makes GNNs up to 15x more accurate in sparse graphs, and significantly improves their performance for low-degree nodes in dense graphs.
Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node classification tasks. At the theory's core is grouping nodes connected by significant information flow at a given time scale. Representations of the graph at different scales encode interaction information at different ranges. We specifically experiment using representations at the characteristic scale of the graph's mesoscopic structures. We provide the models with the original graph and the graph represented at the characteristic resolution scale and compare them to models that can only access the original graph. Our results showed that models with access to both the original graph and the characteristic scale graph can achieve statistically significant improvements in test accuracy.
Heterogeneous Graph Neural Networks (HGNNs) have gained significant popularity in various heterogeneous graph learning tasks. However, most existing HGNNs rely on spatial domain-based methods to aggregate information, i.e., manually selected meta-paths or some heuristic modules, lacking theoretical guarantees. Furthermore, these methods cannot learn arbitrary valid heterogeneous graph filters within the spectral domain, which have limited expressiveness. To tackle these issues, we present a positive spectral heterogeneous graph convolution via positive noncommutative polynomials. Then, using this convolution, we propose PSHGCN, a novel Positive Spectral Heterogeneous Graph Convolutional Network. PSHGCN offers a simple yet effective method for learning valid heterogeneous graph filters. Moreover, we demonstrate the rationale of PSHGCN in the graph optimization framework. We conducted an extensive experimental study to show that PSHGCN can learn diverse heterogeneous graph filters and outperform all baselines on open benchmarks. Notably, PSHGCN exhibits remarkable scalability, efficiently handling large real-world graphs comprising millions of nodes and edges. Our codes are available at https://github.com/ivam-he/PSHGCN.
We study the problem of learning features through self-supervision that are generalisable to multiple graphs. State-of-the-art graph self-supervision restricts training to only one graph, resulting in graph-specific models that are incompatible with different but related graphs. We hypothesize that training with more than one graph that belong to the same family can improve the quality of the learnt representations. However, learning universal features from disparate node/edge features in different graphs is non-trivial. To address this challenge, we first homogenise the disparate features with graph-specific encoders that transform the features into a common space. A universal representation learning module then learns generalisable features on this common space. We show that compared to traditional self-supervision with one graph, our approach results in (1) better performance on downstream node classification, (2) learning features that can be re-used for unseen graphs of the same family, (3) more efficient training and (4) compact yet generalisable models. We also show ability of the proposed framework to deliver these benefits for relatively larger graphs. In this paper, we present a principled way to design foundation graph models that learn from more than one graph in an end-to-end manner, while bridging the gap between self-supervised and supervised performance.