Numerous recent research on graph neural networks (GNNs) has focused on formulating GNN architectures as an optimization problem with the smoothness assumption. However, in node classification tasks, the smoothing effect induced by GNNs tends to assimilate representations and over-homogenize labels of connected nodes, leading to adverse effects such as over-smoothing and misclassification. In this paper, we propose a novel bilevel optimization framework for GNNs inspired by the notion of Bregman distance. We demonstrate that the GNN layer proposed accordingly can effectively mitigate the over-smoothing issue by introducing a mechanism reminiscent of the "skip connection". We validate our theoretical results through comprehensive empirical studies in which Bregman-enhanced GNNs outperform their original counterparts in both homophilic and heterophilic graphs. Furthermore, our experiments also show that Bregman GNNs can produce more robust learning accuracy even when the number of layers is high, suggesting the effectiveness of the proposed method in alleviating the over-smoothing issue.
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis tasks like node classification, link prediction, and visualization. In this paper, we propose a novel force-directed graph embedding method that utilizes the steady acceleration kinetic formula to embed nodes in a way that preserves graph topology and structural features. Our method simulates a set of customized attractive and repulsive forces between all node pairs with respect to their hop distance. These forces are then used in Newton's second law to obtain the acceleration of each node. The method is intuitive, parallelizable, and highly scalable. We evaluate our method on several graph analysis tasks and show that it achieves competitive performance compared to state-of-the-art unsupervised embedding techniques.
Irregular data in real-world are usually organized as heterogeneous graphs (HGs) consisting of multiple types of nodes and edges. To explore useful knowledge from real-world data, both the large-scale encyclopedic HG datasets and corresponding effective learning methods are crucial, but haven't been well investigated. In this paper, we construct a large-scale HG benchmark dataset named UniKG from Wikidata to facilitate knowledge mining and heterogeneous graph representation learning. Overall, UniKG contains more than 77 million multi-attribute entities and 2000 diverse association types, which significantly surpasses the scale of existing HG datasets. To perform effective learning on the large-scale UniKG, two key measures are taken, including (i) the semantic alignment strategy for multi-attribute entities, which projects the feature description of multi-attribute nodes into a common embedding space to facilitate node aggregation in a large receptive field; (ii) proposing a novel plug-and-play anisotropy propagation module (APM) to learn effective multi-hop anisotropy propagation kernels, which extends methods of large-scale homogeneous graphs to heterogeneous graphs. These two strategies enable efficient information propagation among a tremendous number of multi-attribute entities and meantimes adaptively mine multi-attribute association through the multi-hop aggregation in large-scale HGs. We set up a node classification task on our UniKG dataset, and evaluate multiple baseline methods which are constructed by embedding our APM into large-scale homogenous graph learning methods. Our UniKG dataset and the baseline codes have been released at https://github.com/Yide-Qiu/UniKG.
Knowledge graphs enable data scientists to learn end-to-end on heterogeneous knowledge. However, most end-to-end models solely learn from the relational information encoded in graphs' structure: raw values, encoded as literal nodes, are either omitted completely or treated as regular nodes without consideration for their values. In either case we lose potentially relevant information which could have otherwise been exploited by our learning methods. We propose a multimodal message passing network which not only learns end-to-end from the structure of graphs, but also from their possibly divers set of multimodal node features. Our model uses dedicated (neural) encoders to naturally learn embeddings for node features belonging to five different types of modalities, including numbers, texts, dates, images and geometries, which are projected into a joint representation space together with their relational information. We implement and demonstrate our model on node classification and link prediction for artificial and real-worlds datasets, and evaluate the effect that each modality has on the overall performance in an inverse ablation study. Our results indicate that end-to-end multimodal learning from any arbitrary knowledge graph is indeed possible, and that including multimodal information can significantly affect performance, but that much depends on the characteristics of the data.
The recent Long-Range Graph Benchmark (LRGB, Dwivedi et al. 2022) introduced a set of graph learning tasks strongly dependent on long-range interaction between vertices. Empirical evidence suggests that on these tasks Graph Transformers significantly outperform Message Passing GNNs (MPGNNs). In this paper, we carefully reevaluate multiple MPGNN baselines as well as the Graph Transformer GPS (Ramp\'a\v{s}ek et al. 2022) on LRGB. Through a rigorous empirical analysis, we demonstrate that the reported performance gap is overestimated due to suboptimal hyperparameter choices. It is noteworthy that across multiple datasets the performance gap completely vanishes after basic hyperparameter optimization. In addition, we discuss the impact of lacking feature normalization for LRGB's vision datasets and highlight a spurious implementation of LRGB's link prediction metric. The principal aim of our paper is to establish a higher standard of empirical rigor within the graph machine learning community.
Cross-network node classification (CNNC), which aims to classify nodes in a label-deficient target network by transferring the knowledge from a source network with abundant labels, draws increasing attention recently. To address CNNC, we propose a domain-adaptive message passing graph neural network (DM-GNN), which integrates graph neural network (GNN) with conditional adversarial domain adaptation. DM-GNN is capable of learning informative representations for node classification that are also transferrable across networks. Firstly, a GNN encoder is constructed by dual feature extractors to separate ego-embedding learning from neighbor-embedding learning so as to jointly capture commonality and discrimination between connected nodes. Secondly, a label propagation node classifier is proposed to refine each node's label prediction by combining its own prediction and its neighbors' prediction. In addition, a label-aware propagation scheme is devised for the labeled source network to promote intra-class propagation while avoiding inter-class propagation, thus yielding label-discriminative source embeddings. Thirdly, conditional adversarial domain adaptation is performed to take the neighborhood-refined class-label information into account during adversarial domain adaptation, so that the class-conditional distributions across networks can be better matched. Comparisons with eleven state-of-the-art methods demonstrate the effectiveness of the proposed DM-GNN.
Our study reveals new theoretical insights into over-smoothing and feature over-correlation in graph neural networks. Specifically, we demonstrate that with increased depth, node representations become dominated by a low-dimensional subspace that depends on the aggregation function but not on the feature transformations. For all aggregation functions, the rank of the node representations collapses, resulting in over-smoothing for particular aggregation functions. Our study emphasizes the importance for future research to focus on rank collapse rather than over-smoothing. Guided by our theory, we propose a sum of Kronecker products as a beneficial property that provably prevents over-smoothing, over-correlation, and rank collapse. We empirically demonstrate the shortcomings of existing models in fitting target functions of node classification tasks.
To handle graphs in which features or connectivities are evolving over time, a series of temporal graph neural networks (TGNNs) have been proposed. Despite the success of these TGNNs, the previous TGNN evaluations reveal several limitations regarding four critical issues: 1) inconsistent datasets, 2) inconsistent evaluation pipelines, 3) lacking workload diversity, and 4) lacking efficient comparison. Overall, there lacks an empirical study that puts TGNN models onto the same ground and compares them comprehensively. To this end, we propose BenchTemp, a general benchmark for evaluating TGNN models on various workloads. BenchTemp provides a set of benchmark datasets so that different TGNN models can be fairly compared. Further, BenchTemp engineers a standard pipeline that unifies the TGNN evaluation. With BenchTemp, we extensively compare the representative TGNN models on different tasks (e.g., link prediction and node classification) and settings (transductive and inductive), w.r.t. both effectiveness and efficiency metrics. We have made BenchTemp publicly available at https://github.com/qianghuangwhu/benchtemp.
Graph representation learning (GRL) has become a prominent tool for furthering the understanding of complex networks providing tools for network embedding, link prediction, and node classification. In this paper, we propose the Hybrid Membership-Latent Distance Model (HM-LDM) by exploring how a Latent Distance Model (LDM) can be constrained to a latent simplex. By controlling the edge lengths of the corners of the simplex, the volume of the latent space can be systematically controlled. Thereby communities are revealed as the space becomes more constrained, with hard memberships being recovered as the simplex volume goes to zero. We further explore a recent likelihood formulation for signed networks utilizing the Skellam distribution to account for signed weighted networks and extend the HM-LDM to the signed Hybrid Membership-Latent Distance Model (sHM-LDM). Importantly, the induced likelihood function explicitly attracts nodes with positive links and deters nodes from having negative interactions. We demonstrate the utility of HM-LDM and sHM-LDM on several real networks. We find that the procedures successfully identify prominent distinct structures, as well as how nodes relate to the extracted aspects providing favorable performances in terms of link prediction when compared to prominent baselines. Furthermore, the learned soft memberships enable easily interpretable network visualizations highlighting distinct patterns.
Graph Neural Network (GNN) training and inference involve significant challenges of scalability with respect to both model sizes and number of layers, resulting in degradation of efficiency and accuracy for large and deep GNNs. We present an end-to-end solution that aims to address these challenges for efficient GNNs in resource constrained environments while avoiding the oversmoothing problem in deep GNNs. We introduce a quantization based approach for all stages of GNNs, from message passing in training to node classification, compressing the model and enabling efficient processing. The proposed GNN quantizer learns quantization ranges and reduces the model size with comparable accuracy even under low-bit quantization. To scale with the number of layers, we devise a message propagation mechanism in training that controls layer-wise changes of similarities between neighboring nodes. This objective is incorporated into a Lagrangian function with constraints and a differential multiplier method is utilized to iteratively find optimal embeddings. This mitigates oversmoothing and suppresses the quantization error to a bound. Significant improvements are demonstrated over state-of-the-art quantization methods and deep GNN approaches in both full-precision and quantized models. The proposed quantizer demonstrates superior performance in INT2 configurations across all stages of GNN, achieving a notable level of accuracy. In contrast, existing quantization approaches fail to generate satisfactory accuracy levels. Finally, the inference with INT2 and INT4 representations exhibits a speedup of 5.11 $\times$ and 4.70 $\times$ compared to full precision counterparts, respectively.
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks including node classification and link prediction. However, these methods often suffer from data imbalance, a common issue in graph data where certain segments possess abundant data while others are scarce, thereby leading to biased learning outcomes. This necessitates the emerging field of imbalanced learning on graphs, which aims to correct these data distribution skews for more accurate and representative learning outcomes. In this survey, we embark on a comprehensive review of the literature on imbalanced learning on graphs. We begin by providing a definitive understanding of the concept and related terminologies, establishing a strong foundational understanding for readers. Following this, we propose two comprehensive taxonomies: (1) the problem taxonomy, which describes the forms of imbalance we consider, the associated tasks, and potential solutions; (2) the technique taxonomy, which details key strategies for addressing these imbalances, and aids readers in their method selection process. Finally, we suggest prospective future directions for both problems and techniques within the sphere of imbalanced learning on graphs, fostering further innovation in this critical area.
Class imbalance is prevalent in real-world node classification tasks and poses great challenges for graph learning models. Most existing studies are rooted in a class-rebalancing (CR) perspective and address class imbalance with class-wise reweighting or resampling. In this work, we approach the root cause of class-imbalance bias from an topological paradigm. Specifically, we theoretically reveal two fundamental phenomena in the graph topology that greatly exacerbate the predictive bias stemming from class imbalance. On this basis, we devise a lightweight topological augmentation framework BAT to mitigate the class-imbalance bias without class rebalancing. Being orthogonal to CR, BAT can function as an efficient plug-and-play module that can be seamlessly combined with and significantly boost existing CR techniques. Systematic experiments on real-world imbalanced graph learning tasks show that BAT can deliver up to 46.27% performance gain and up to 72.74% bias reduction over existing techniques. Code, examples, and documentations are available at https://github.com/ZhiningLiu1998/BAT.
Unsupervised GAD methods assume the lack of anomaly labels, i.e., whether a node is anomalous or not. One common observation we made from previous unsupervised methods is that they not only assume the absence of such anomaly labels, but also the absence of class labels (the class a node belongs to used in a general node classification task). In this work, we study the utility of class labels for unsupervised GAD; in particular, how they enhance the detection of structural anomalies. To this end, we propose a Class Label-aware Graph Anomaly Detection framework (CLAD) that utilizes a limited amount of labeled nodes to enhance the performance of unsupervised GAD. Extensive experiments on ten datasets demonstrate the superior performance of CLAD in comparison to existing unsupervised GAD methods, even in the absence of ground-truth class label information. The source code for CLAD is available at \url{https://github.com/jhkim611/CLAD}.
Graph transformers need strong inductive biases to derive meaningful attention scores. Yet, current methods often fall short in capturing longer ranges, hierarchical structures, or community structures, which are common in various graphs such as molecules, social networks, and citation networks. This paper presents a Hierarchical Distance Structural Encoding (HDSE) method to model node distances in a graph, focusing on its multi-level, hierarchical nature. We introduce a novel framework to seamlessly integrate HDSE into the attention mechanism of existing graph transformers, allowing for simultaneous application with other positional encodings. To apply graph transformers with HDSE to large-scale graphs, we further propose a high-level HDSE that effectively biases the linear transformers towards graph hierarchies. We theoretically prove the superiority of HDSE over shortest path distances in terms of expressivity and generalization. Empirically, we demonstrate that graph transformers with HDSE excel in graph classification, regression on 7 graph-level datasets, and node classification on 11 large-scale graphs, including those with up to a billion nodes.
We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph Gram Index (GGI) to measure such instability which is invariant to permutation, orthogonal transformation, translation and order of evaluation. This allows us to study the varying instability behaviour of GNN embeddings on large graphs for both node classification and link prediction.
Graph neural networks (GNNs) are increasingly used in critical human applications for predicting node labels in attributed graphs. Their ability to aggregate features from nodes' neighbors for accurate classification also has the capacity to exacerbate existing biases in data or to introduce new ones towards members from protected demographic groups. Thus, it is imperative to quantify how GNNs may be biased and to what extent their harmful effects may be mitigated. To this end, we propose two new GNN-agnostic interventions namely, (i) PFR-AX which decreases the separability between nodes in protected and non-protected groups, and (ii) PostProcess which updates model predictions based on a blackbox policy to minimize differences between error rates across demographic groups. Through a large set of experiments on four datasets, we frame the efficacies of our approaches (and three variants) in terms of their algorithmic fairness-accuracy tradeoff and benchmark our results against three strong baseline interventions on three state-of-the-art GNN models. Our results show that no single intervention offers a universally optimal tradeoff, but PFR-AX and PostProcess provide granular control and improve model confidence when correctly predicting positive outcomes for nodes in protected groups.
Graph representation learning (GRL) methods, such as graph neural networks and graph transformer models, have been successfully used to analyze graph-structured data, mainly focusing on node classification and link prediction tasks. However, the existing studies mostly only consider local connectivity while ignoring long-range connectivity and the roles of nodes. In this paper, we propose Unified Graph Transformer Networks (UGT) that effectively integrate local and global structural information into fixed-length vector representations. First, UGT learns local structure by identifying the local substructures and aggregating features of the $k$-hop neighborhoods of each node. Second, we construct virtual edges, bridging distant nodes with structural similarity to capture the long-range dependencies. Third, UGT learns unified representations through self-attention, encoding structural distance and $p$-step transition probability between node pairs. Furthermore, we propose a self-supervised learning task that effectively learns transition probability to fuse local and global structural features, which could then be transferred to other downstream tasks. Experimental results on real-world benchmark datasets over various downstream tasks showed that UGT significantly outperformed baselines that consist of state-of-the-art models. In addition, UGT reaches the expressive power of the third-order Weisfeiler-Lehman isomorphism test (3d-WL) in distinguishing non-isomorphic graph pairs. The source code is available at https://github.com/NSLab-CUK/Unified-Graph-Transformer.
Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding "slow nodes" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.
Graph Active Learning (GAL), which aims to find the most informative nodes in graphs for annotation to maximize the Graph Neural Networks (GNNs) performance, has attracted many research efforts but remains non-trivial challenges. One major challenge is that existing GAL strategies may introduce semantic confusion to the selected training set, particularly when graphs are noisy. Specifically, most existing methods assume all aggregating features to be helpful, ignoring the semantically negative effect between inter-class edges under the message-passing mechanism. In this work, we present Semantic-aware Active learning framework for Graphs (SAG) to mitigate the semantic confusion problem. Pairwise similarities and dissimilarities of nodes with semantic features are introduced to jointly evaluate the node influence. A new prototype-based criterion and query policy are also designed to maintain diversity and class balance of the selected nodes, respectively. Extensive experiments on the public benchmark graphs and a real-world financial dataset demonstrate that SAG significantly improves node classification performances and consistently outperforms previous methods. Moreover, comprehensive analysis and ablation study also verify the effectiveness of the proposed framework.
In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with better node classification predictions of message-passing methods. More recently, however, researchers pointed out that such dichotomy is too simplistic as we can construct node classification tasks where graphs are completely heterophilic but the performances remain high. Most of these works have also proposed new quantitative metrics to understand when a graph structure is useful, which implicitly or explicitly assume the correlation between node features and target labels. Our work empirically investigates what happens when this strong assumption does not hold, by formalising two generative processes for node classification tasks that allow us to build and study ad-hoc problems. To quantitatively measure the influence of the node features on the target labels, we also use a metric we call Feature Informativeness. We construct six synthetic tasks and evaluate the performance of six models, including structure-agnostic ones. Our findings reveal that previously defined metrics are not adequate when we relax the above assumption. Our contribution to the workshop aims at presenting novel research findings that could help advance our understanding of the field.