In representation learning on graph-structured data, many popular graph neural networks (GNNs) fail to capture long-range dependencies, leading to performance degradation. Furthermore, this weakness is magnified when the concerned graph is characterized by heterophily (low homophily). To solve this issue, this paper proposes a novel graph learning framework called the graph convolutional network with self-attention (GCN-SA). The proposed scheme exhibits an exceptional generalization capability in node-level representation learning. The proposed GCN-SA contains two enhancements corresponding to edges and node features. For edges, we utilize a self-attention mechanism to design a stable and effective graph-structure-learning module that can capture the internal correlation between any pair of nodes. This graph-structure-learning module can identify reliable neighbors for each node from the entire graph. Regarding the node features, we modify the transformer block to make it more applicable to enable GCN to fuse valuable information from the entire graph. These two enhancements work in distinct ways to help our GCN-SA capture long-range dependencies, enabling it to perform representation learning on graphs with varying levels of homophily. The experimental results on benchmark datasets demonstrate the effectiveness of the proposed GCN-SA. Compared to other outstanding GNN counterparts, the proposed GCN-SA is competitive.
Graph Structure Learning (GSL) focuses on capturing intrinsic dependencies and interactions among nodes in graph-structured data by generating novel graph structures. Graph Neural Networks (GNNs) have emerged as promising GSL solutions, utilizing recursive message passing to encode node-wise inter-dependencies. However, many existing GSL methods heavily depend on explicit graph structural information as supervision signals, leaving them susceptible to challenges such as data noise and sparsity. In this work, we propose GraphEdit, an approach that leverages large language models (LLMs) to learn complex node relationships in graph-structured data. By enhancing the reasoning capabilities of LLMs through instruction-tuning over graph structures, we aim to overcome the limitations associated with explicit graph structural information and enhance the reliability of graph structure learning. Our approach not only effectively denoises noisy connections but also identifies node-wise dependencies from a global perspective, providing a comprehensive understanding of the graph structure. We conduct extensive experiments on multiple benchmark datasets to demonstrate the effectiveness and robustness of GraphEdit across various settings. We have made our model implementation available at: https://github.com/HKUDS/GraphEdit.
We investigate the replay buffer in rehearsal-based approaches for graph continual learning (GCL) methods. Existing rehearsal-based GCL methods select the most representative nodes for each class and store them in a replay buffer for later use in training subsequent tasks. However, we discovered that considering only the class representativeness of each replayed node makes the replayed nodes to be concentrated around the center of each class, incurring a potential risk of overfitting to nodes residing in those regions, which aggravates catastrophic forgetting. Moreover, as the rehearsal-based approach heavily relies on a few replayed nodes to retain knowledge obtained from previous tasks, involving the replayed nodes that have irrelevant neighbors in the model training may have a significant detrimental impact on model performance. In this paper, we propose a GCL model named DSLR, specifically, we devise a coverage-based diversity (CD) approach to consider both the class representativeness and the diversity within each class of the replayed nodes. Moreover, we adopt graph structure learning (GSL) to ensure that the replayed nodes are connected to truly informative neighbors. Extensive experimental results demonstrate the effectiveness and efficiency of DSLR. Our source code is available at https://github.com/seungyoon-Choi/DSLR_official.
Anomaly detection in multivariate time series (MTS) has been widely studied in one-class classification (OCC) setting. The training samples in OCC are assumed to be normal, which is difficult to guarantee in practical situations. Such a case may degrade the performance of OCC-based anomaly detection methods which fit the training distribution as the normal distribution. In this paper, we propose MTGFlow, an unsupervised anomaly detection approach for MTS anomaly detection via dynamic Graph and entity-aware normalizing Flow. MTGFlow first estimates the density of the entire training samples and then identifies anomalous instances based on the density of the test samples within the fitted distribution. This relies on a widely accepted assumption that anomalous instances exhibit more sparse densities than normal ones, with no reliance on the clean training dataset. However, it is intractable to directly estimate the density due to complex dependencies among entities and their diverse inherent characteristics. To mitigate this, we utilize the graph structure learning model to learn interdependent and evolving relations among entities, which effectively captures complex and accurate distribution patterns of MTS. In addition, our approach incorporates the unique characteristics of individual entities by employing an entity-aware normalizing flow. This enables us to represent each entity as a parameterized normal distribution. Furthermore, considering that some entities present similar characteristics, we propose a cluster strategy that capitalizes on the commonalities of entities with similar characteristics, resulting in more precise and detailed density estimation. We refer to this cluster-aware extension as MTGFlow_cluster. Extensive experiments are conducted on six widely used benchmark datasets, in which MTGFlow and MTGFlow cluster demonstrate their superior detection performance.
Graph Neural Networks (GNNs) have emerged as the de facto standard for representation learning on graphs, owing to their ability to effectively integrate graph topology and node attributes. However, the inherent suboptimal nature of node connections, resulting from the complex and contingent formation process of graphs, presents significant challenges in modeling them effectively. To tackle this issue, Graph Structure Learning (GSL), a family of data-centric learning approaches, has garnered substantial attention in recent years. The core concept behind GSL is to jointly optimize the graph structure and the corresponding GNN models. Despite the proposal of numerous GSL methods, the progress in this field remains unclear due to inconsistent experimental protocols, including variations in datasets, data processing techniques, and splitting strategies. In this paper, we introduce OpenGSL, the first comprehensive benchmark for GSL, aimed at addressing this gap. OpenGSL enables a fair comparison among state-of-the-art GSL methods by evaluating them across various popular datasets using uniform data processing and splitting strategies. Through extensive experiments, we observe that existing GSL methods do not consistently outperform vanilla GNN counterparts. We also find that there is no significant correlation between the homophily of the learned structure and task performance, challenging the common belief. Moreover, we observe that the learned graph structure demonstrates a strong generalization ability across different GNN models, despite the high computational and space consumption. We hope that our open-sourced library will facilitate rapid and equitable evaluation and inspire further innovative research in this field. The code of the benchmark can be found in https://github.com/OpenGSL/OpenGSL.
Graph neural networks (GNNs) demonstrate outstanding performance in a broad range of applications. While the majority of GNN applications assume that a graph structure is given, some recent methods substantially expanded the applicability of GNNs by showing that they may be effective even when no graph structure is explicitly provided. The GNN parameters and a graph structure are jointly learned. Previous studies adopt different experimentation setups, making it difficult to compare their merits. In this paper, we propose a benchmarking strategy for graph structure learning using a unified framework. Our framework, called Unified Graph Structure Learning (UGSL), reformulates existing models into a single model. We implement a wide range of existing models in our framework and conduct extensive analyses of the effectiveness of different components in the framework. Our results provide a clear and concise understanding of the different methods in this area as well as their strengths and weaknesses. The benchmark code is available at https://github.com/google-research/google-research/tree/master/ugsl.
Graph clustering is a fundamental task in graph analysis, and recent advances in utilizing graph neural networks (GNNs) have shown impressive results. Despite the success of existing GNN-based graph clustering methods, they often overlook the quality of graph structure, which is inherent in real-world graphs due to their sparse and multifarious nature, leading to subpar performance. Graph structure learning allows refining the input graph by adding missing links and removing spurious connections. However, previous endeavors in graph structure learning have predominantly centered around supervised settings, and cannot be directly applied to our specific clustering tasks due to the absence of ground-truth labels. To bridge the gap, we propose a novel method called \textbf{ho}mophily-enhanced structure \textbf{le}arning for graph clustering (HoLe). Our motivation stems from the observation that subtly enhancing the degree of homophily within the graph structure can significantly improve GNNs and clustering outcomes. To realize this objective, we develop two clustering-oriented structure learning modules, i.e., hierarchical correlation estimation and cluster-aware sparsification. The former module enables a more accurate estimation of pairwise node relationships by leveraging guidance from latent and clustering spaces, while the latter one generates a sparsified structure based on the similarity matrix and clustering assignments. Additionally, we devise a joint optimization approach alternating between training the homophily-enhanced structure learning and GNN-based clustering, thereby enforcing their reciprocal effects. Extensive experiments on seven benchmark datasets of various types and scales, across a range of clustering metrics, demonstrate the superiority of HoLe against state-of-the-art baselines.
Graph structure learning is a well-established problem that aims at optimizing graph structures adaptive to specific graph datasets to help message passing neural networks (i.e., GNNs) to yield effective and robust node embeddings. However, the common limitation of existing models lies in the underlying \textit{closed-world assumption}: the testing graph is the same as the training graph. This premise requires independently training the structure learning model from scratch for each graph dataset, which leads to prohibitive computation costs and potential risks for serious over-fitting. To mitigate these issues, this paper explores a new direction that moves forward to learn a universal structure learning model that can generalize across graph datasets in an open world. We first introduce the mathematical definition of this novel problem setting, and describe the model formulation from a probabilistic data-generative aspect. Then we devise a general framework that coordinates a single graph-shared structure learner and multiple graph-specific GNNs to capture the generalizable patterns of optimal message-passing topology across datasets. The well-trained structure learner can directly produce adaptive structures for unseen target graphs without any fine-tuning. Across diverse datasets and various challenging cross-graph generalization protocols, our experiments show that even without training on target graphs, the proposed model i) significantly outperforms expressive GNNs trained on input (non-optimized) topology, and ii) surprisingly performs on par with state-of-the-art models that independently optimize adaptive structures for specific target graphs, with notably orders-of-magnitude acceleration for training on the target graph.
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.
Temporal Graph Learning, which aims to model the time-evolving nature of graphs, has gained increasing attention and achieved remarkable performance recently. However, in reality, graph structures are often incomplete and noisy, which hinders temporal graph networks (TGNs) from learning informative representations. Graph contrastive learning uses data augmentation to generate plausible variations of existing data and learn robust representations. However, rule-based augmentation approaches may be suboptimal as they lack learnability and fail to leverage rich information from downstream tasks. To address these issues, we propose a Time-aware Graph Structure Learning (TGSL) approach via sequence prediction on temporal graphs, which learns better graph structures for downstream tasks through adding potential temporal edges. In particular, it predicts time-aware context embedding based on previously observed interactions and uses the Gumble-Top-K to select the closest candidate edges to this context embedding. Additionally, several candidate sampling strategies are proposed to ensure both efficiency and diversity. Furthermore, we jointly learn the graph structure and TGNs in an end-to-end manner and perform inference on the refined graph. Extensive experiments on temporal link prediction benchmarks demonstrate that TGSL yields significant gains for the popular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive learning methods on temporal graphs. We release the code at https://github.com/ViktorAxelsen/TGSL.
Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph structure learning (GSL) frameworks still lack robustness and interpretability. This paper proposes a general GSL framework, SE-GSL, through structural entropy and the graph hierarchy abstracted in the encoding tree. Particularly, we exploit the one-dimensional structural entropy to maximize embedded information content when auxiliary neighbourhood attributes are fused to enhance the original graph. A new scheme of constructing optimal encoding trees is proposed to minimize the uncertainty and noises in the graph whilst assuring proper community partition in hierarchical abstraction. We present a novel sample-based mechanism for restoring the graph structure via node structural entropy distribution. It increases the connectivity among nodes with larger uncertainty in lower-level communities. SE-GSL is compatible with various GNN models and enhances the robustness towards noisy and heterophily structures. Extensive experiments show significant improvements in the effectiveness and robustness of structure learning and node representation learning.
Accurate traffic prediction is essential for effective urban management and the improvement of transportation efficiency. Recently, data-driven traffic prediction methods have been widely adopted, with better performance than traditional approaches. However, they often require large amounts of data for effective training, which becomes challenging given the prevalence of data scarcity in regions with inadequate sensing infrastructures. To address this issue, we propose a Semantic-Fused Multi-Granularity Transfer Learning (SFMGTL) model to achieve knowledge transfer across cities with fused semantics at different granularities. In detail, we design a semantic fusion module to fuse various semantics while conserving static spatial dependencies via reconstruction losses. Then, a fused graph is constructed based on node features through graph structure learning. Afterwards, we implement hierarchical node clustering to generate graphs with different granularity. To extract feasible meta-knowledge, we further introduce common and private memories and obtain domain-invariant features via adversarial training. It is worth noting that our work jointly addresses semantic fusion and multi-granularity issues in transfer learning. We conduct extensive experiments on six real-world datasets to verify the effectiveness of our SFMGTL model by comparing it with other state-of-the-art baselines. Afterwards, we also perform ablation and case studies, demonstrating that our model possesses substantially fewer parameters compared to baseline models. Moreover, we illustrate how knowledge transfer aids the model in accurately predicting demands, especially during peak hours. The codes can be found at https://github.com/zeonchen/SFMGTL.
In recent years, Graph Neural Networks (GNNs) have been popular in the graph classification task. Currently, shallow GNNs are more common due to the well-known over-smoothing problem facing deeper GNNs. However, they are sub-optimal without utilizing the information from distant nodes, i.e., the long-range dependencies. The mainstream methods in the graph classification task can extract the long-range dependencies either by designing the pooling operations or incorporating the higher-order neighbors, while they have evident drawbacks by modifying the original graph structure, which may result in information loss in graph structure learning. In this paper, by justifying the smaller influence of the over-smoothing problem in the graph classification task, we evoke the importance of stacking-based GNNs and then employ them to capture the long-range dependencies without modifying the original graph structure. To achieve this, two design needs are given for stacking-based GNNs, i.e., sufficient model depth and adaptive skip-connection schemes. By transforming the two design needs into designing data-specific inter-layer connections, we propose a novel approach with the help of neural architecture search (NAS), which is dubbed LRGNN (Long-Range Graph Neural Networks). Extensive experiments on five datasets show that the proposed LRGNN can achieve the best performance, and obtained data-specific GNNs with different depth and skip-connection schemes, which can better capture the long-range dependencies.
Spatio-temporal modeling as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the underlying heterogeneity and non-stationarity implied in the graph streams, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two benchmark datasets (METR-LA and PEMS-BAY) and a large-scale spatio-temporal dataset that contains a variaty of non-stationary phenomena. Our model outperformed the state-of-the-arts to a large degree on all three datasets (over 27% MAE and 34% RMSE). Besides, through a series of qualitative evaluations, we demonstrate that our model can explicitly disentangle locations and time slots with different patterns and be robustly adaptive to different anomalous situations. Codes and datasets are available at https://github.com/deepkashiwa20/MegaCRN.
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many studies on structure learning with various types of data, the structure learning on the dynamic graph has not been explored yet, and thus we study the learning problem of node feature generation mechanism on such ubiquitous dynamic graph data. In a dynamic graph, we propose to simultaneously estimate contemporaneous relationships and time-lagged interaction relationships between the node features. These two kinds of relationships form a DAG, which could effectively characterize the feature generation process in a concise way. To learn such a DAG, we cast the learning problem as a continuous score-based optimization problem, which consists of a differentiable score function to measure the validity of the learned DAGs and a smooth acyclicity constraint to ensure the acyclicity of the learned DAGs. These two components are translated into an unconstraint augmented Lagrangian objective which could be minimized by mature continuous optimization techniques. The resulting algorithm, named GraphNOTEARS, outperforms baselines on simulated data across a wide range of settings that may encounter in real-world applications. We also apply the proposed approach on two dynamic graphs constructed from the real-world Yelp dataset, demonstrating our method could learn the connections between node features, which conforms with the domain knowledge.
Traffic forecasting as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the spatio-temporal heterogeneity and non-stationarity implied in the traffic stream, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two benchmark datasets (i.e., METR-LA and PEMS-BAY) and a new large-scale traffic speed dataset called EXPY-TKY that covers 1843 expressway road links in Tokyo. Our model outperformed the state-of-the-arts on all three datasets. Besides, through a series of qualitative evaluations, we demonstrate that our model can explicitly disentangle the road links and time slots with different patterns and be robustly adaptive to any anomalous traffic situations. Codes and datasets are available at https://github.com/deepkashiwa20/MegaCRN.
Multivariate biosignals are prevalent in many medical domains, such as electroencephalography, polysomnography, and electrocardiography. Modeling spatiotemporal dependencies in multivariate biosignals is challenging due to (1) long-range temporal dependencies and (2) complex spatial correlations between the electrodes. To address these challenges, we propose representing multivariate biosignals as time-dependent graphs and introduce GraphS4mer, a general graph neural network (GNN) architecture that improves performance on biosignal classification tasks by modeling spatiotemporal dependencies in biosignals. Specifically, (1) we leverage the Structured State Space architecture, a state-of-the-art deep sequence model, to capture long-range temporal dependencies in biosignals and (2) we propose a graph structure learning layer in GraphS4mer to learn dynamically evolving graph structures in the data. We evaluate our proposed model on three distinct biosignal classification tasks and show that GraphS4mer consistently improves over existing models, including (1) seizure detection from electroencephalographic signals, outperforming a previous GNN with self-supervised pre-training by 3.1 points in AUROC; (2) sleep staging from polysomnographic signals, a 4.1 points improvement in macro-F1 score compared to existing sleep staging models; and (3) 12-lead electrocardiogram classification, outperforming previous state-of-the-art models by 2.7 points in macro-F1 score.
Multimodal recommender systems utilizing multimodal features (e.g., images and textual descriptions) typically show better recommendation accuracy than general recommendation models based solely on user-item interactions. Generally, prior work fuses multimodal features into item ID embeddings to enrich item representations, thus failing to capture the latent semantic item-item structures. In this context, LATTICE proposes to learn the latent structure between items explicitly and achieves state-of-the-art performance for multimodal recommendations. However, we argue the latent graph structure learning of LATTICE is both inefficient and unnecessary. Experimentally, we demonstrate that freezing its item-item structure before training can also achieve competitive performance. Based on this finding, we propose a simple yet effective model, dubbed as FREEDOM, that FREEzes the item-item graph and DenOises the user-item interaction graph simultaneously for Multimodal recommendation. Theoretically, we examine the design of FREEDOM through a graph spectral perspective and demonstrate that it possesses a tighter upper bound on the graph spectrum. In denoising the user-item interaction graph, we devise a degree-sensitive edge pruning method, which rejects possibly noisy edges with a high probability when sampling the graph. We evaluate the proposed model on three real-world datasets and show that FREEDOM can significantly outperform current strongest baselines. Compared with LATTICE, FREEDOM achieves an average improvement of 19.07% in recommendation accuracy while reducing its memory cost up to 6$\times$ on large graphs. The source code is available at: https://github.com/enoche/FREEDOM.
Graph structure learning (GSL), which aims to learn the adjacency matrix for graph neural networks (GNNs), has shown great potential in boosting the performance of GNNs. Most existing GSL works apply a joint learning framework where the estimated adjacency matrix and GNN parameters are optimized for downstream tasks. However, as GSL is essentially a link prediction task, whose goal may largely differ from the goal of the downstream task. The inconsistency of these two goals limits the GSL methods to learn the potential optimal graph structure. Moreover, the joint learning framework suffers from scalability issues in terms of time and space during the process of estimation and optimization of the adjacency matrix. To mitigate these issues, we propose a graph structure refinement (GSR) framework with a pretrain-finetune pipeline. Specifically, The pre-training phase aims to comprehensively estimate the underlying graph structure by a multi-view contrastive learning framework with both intra- and inter-view link prediction tasks. Then, the graph structure is refined by adding and removing edges according to the edge probabilities estimated by the pre-trained model. Finally, the fine-tuning GNN is initialized by the pre-trained model and optimized toward downstream tasks. With the refined graph structure remaining static in the fine-tuning space, GSR avoids estimating and optimizing graph structure in the fine-tuning phase which enjoys great scalability and efficiency. Moreover, the fine-tuning GNN is boosted by both migrating knowledge and refining graphs. Extensive experiments are conducted to evaluate the effectiveness (best performance on six benchmark datasets), efficiency, and scalability (13.8x faster using 32.8% GPU memory compared to the best GSL baseline on Cora) of the proposed model.
We introduce pyGSL, a Python library that provides efficient implementations of state-of-the-art graph structure learning models along with diverse datasets to evaluate them on. The implementations are written in GPU-friendly ways, allowing one to scale to much larger network tasks. A common interface is introduced for algorithm unrolling methods, unifying implementations of recent state-of-the-art techniques and allowing new methods to be quickly developed by avoiding the need to rebuild the underlying unrolling infrastructure. Implementations of differentiable graph structure learning models are written in PyTorch, allowing us to leverage the rich software ecosystem that exists e.g., around logging, hyperparameter search, and GPU-communication. This also makes it easy to incorporate these models as components in larger gradient based learning systems where differentiable estimates of graph structure may be useful, e.g. in latent graph learning. Diverse datasets and performance metrics allow consistent comparisons across models in this fast growing field. The full code repository can be found on https://github.com/maxwass/pyGSL.