Graph data, also known as complex network data, is omnipresent across various domains and applications. Prior graph neural network models primarily focused on extracting task-specific structural features through supervised learning objectives, but they fell short in capturing the inherent semantic and structural features of the entire graph. In this paper, we introduce the semantic-structural attention-enhanced graph convolutional network (SSA-GCN), which not only models the graph structure but also extracts generalized unsupervised features to enhance vertex classification performance. The SSA-GCN's key contributions lie in three aspects: firstly, it derives semantic information through unsupervised feature extraction from a knowledge graph perspective; secondly, it obtains structural information through unsupervised feature extraction from a complex network perspective; and finally, it integrates these features through a cross-attention mechanism. By leveraging these features, we augment the graph convolutional network, thereby enhancing the model's generalization capabilities. Our experiments on the Cora and CiteSeer datasets demonstrate the performance improvements achieved by our proposed method. Furthermore, our approach also exhibits excellent accuracy under privacy settings, making it a robust and effective solution for graph data analysis.
Graph neural networks have achieved remarkable success in learning graph representations, especially graph Transformer, which has recently shown superior performance on various graph mining tasks. However, graph Transformer generally treats nodes as tokens, which results in quadratic complexity regarding the number of nodes during self-attention computation. The graph MLP Mixer addresses this challenge by using the efficient MLP Mixer technique from computer vision. However, the time-consuming process of extracting graph tokens limits its performance. In this paper, we present a novel architecture named ChebMixer, a newly graph MLP Mixer that uses fast Chebyshev polynomials-based spectral filtering to extract a sequence of tokens. Firstly, we produce multiscale representations of graph nodes via fast Chebyshev polynomial-based spectral filtering. Next, we consider each node's multiscale representations as a sequence of tokens and refine the node representation with an effective MLP Mixer. Finally, we aggregate the multiscale representations of nodes through Chebyshev interpolation. Owing to the powerful representation capabilities and fast computational properties of MLP Mixer, we can quickly extract more informative node representations to improve the performance of downstream tasks. The experimental results prove our significant improvements in a variety of scenarios ranging from graph node classification to medical image segmentation.
Over the past few years, federated learning has become widely used in various classical machine learning fields because of its collaborative ability to train data from multiple sources without compromising privacy. However, in the area of graph neural networks, the nodes and network structures of graphs held by clients are different in many practical applications, and the aggregation method that directly shares model gradients cannot be directly applied to this scenario. Therefore, this work proposes a federated aggregation method FLGNN applied to various graph federation scenarios and investigates the aggregation effect of parameter sharing at each layer of the graph neural network model. The effectiveness of the federated aggregation method FLGNN is verified by experiments on real datasets. Additionally, for the privacy security of FLGNN, this paper designs membership inference attack experiments and differential privacy defense experiments. The results show that FLGNN performs good robustness, and the success rate of privacy theft is further reduced by adding differential privacy defense methods.
Large language models (LLMs) have achieved great success in many fields, and recent works have studied exploring LLMs for graph discriminative tasks such as node classification. However, the abilities of LLMs for graph generation remain unexplored in the literature. Graph generation requires the LLM to generate graphs with given properties, which has valuable real-world applications such as drug discovery, while tends to be more challenging. In this paper, we propose LLM4GraphGen to explore the ability of LLMs for graph generation with systematical task designs and extensive experiments. Specifically, we propose several tasks tailored with comprehensive experiments to address key questions regarding LLMs' understanding of different graph structure rules, their ability to capture structural type distributions, and their utilization of domain knowledge for property-based graph generation. Our evaluations demonstrate that LLMs, particularly GPT-4, exhibit preliminary abilities in graph generation tasks, including rule-based and distribution-based generation. We also observe that popular prompting methods, such as few-shot and chain-of-thought prompting, do not consistently enhance performance. Besides, LLMs show potential in generating molecules with specific properties. These findings may serve as foundations for designing good LLMs based models for graph generation and provide valuable insights and further research.
Open-world semi-supervised learning (Open-world SSL) for node classification, that classifies unlabeled nodes into seen classes or multiple novel classes, is a practical but under-explored problem in the graph community. As only seen classes have human labels, they are usually better learned than novel classes, and thus exhibit smaller intra-class variances within the embedding space (named as imbalance of intra-class variances between seen and novel classes). Based on empirical and theoretical analysis, we find the variance imbalance can negatively impact the model performance. Pre-trained feature encoders can alleviate this issue via producing compact representations for novel classes. However, creating general pre-trained encoders for various types of graph data has been proven to be challenging. As such, there is a demand for an effective method that does not rely on pre-trained graph encoders. In this paper, we propose an IMbalance-Aware method named OpenIMA for Open-world semi-supervised node classification, which trains the node classification model from scratch via contrastive learning with bias-reduced pseudo labels. Extensive experiments on seven popular graph benchmarks demonstrate the effectiveness of OpenIMA, and the source code has been available on GitHub.
Graph-based anomaly detection is currently an important research topic in the field of graph neural networks (GNNs). We find that in graph anomaly detection, the homophily distribution differences between different classes are significantly greater than those in homophilic and heterophilic graphs. For the first time, we introduce a new metric called Class Homophily Variance, which quantitatively describes this phenomenon. To mitigate its impact, we propose a novel GNN model named Homophily Edge Generation Graph Neural Network (HedGe). Previous works typically focused on pruning, selecting or connecting on original relationships, and we refer to these methods as modifications. Different from these works, our method emphasizes generating new relationships with low class homophily variance, using the original relationships as an auxiliary. HedGe samples homophily adjacency matrices from scratch using a self-attention mechanism, and leverages nodes that are relevant in the feature space but not directly connected in the original graph. Additionally, we modify the loss function to punish the generation of unnecessary heterophilic edges by the model. Extensive comparison experiments demonstrate that HedGe achieved the best performance across multiple benchmark datasets, including anomaly detection and edgeless node classification. The proposed model also improves the robustness under the novel Heterophily Attack with increased class homophily variance on other graph classification tasks.
Graph neural networks (GNNs) have attracted significant attention for their outstanding performance in graph learning and node classification tasks. However, their vulnerability to adversarial attacks, particularly through susceptible nodes, poses a challenge in decision-making. The need for robust graph summarization is evident in adversarial challenges resulting from the propagation of attacks throughout the entire graph. In this paper, we address both performance and adversarial robustness in graph input by introducing the novel technique SHERD (Subgraph Learning Hale through Early Training Representation Distances). SHERD leverages information from layers of a partially trained graph convolutional network (GCN) to detect susceptible nodes during adversarial attacks using standard distance metrics. The method identifies "vulnerable (bad)" nodes and removes such nodes to form a robust subgraph while maintaining node classification performance. Through our experiments, we demonstrate the increased performance of SHERD in enhancing robustness by comparing the network's performance on original and subgraph inputs against various baselines alongside existing adversarial attacks. Our experiments across multiple datasets, including citation datasets such as Cora, Citeseer, and Pubmed, as well as microanatomical tissue structures of cell graphs in the placenta, highlight that SHERD not only achieves substantial improvement in robust performance but also outperforms several baselines in terms of node classification accuracy and computational complexity.
The generalization performance of deep neural networks in classification tasks is a major concern in machine learning research. Despite widespread techniques used to diminish the over-fitting issue such as data augmentation, pseudo-labeling, regularization, and ensemble learning, this performance still needs to be enhanced with other approaches. In recent years, it has been theoretically demonstrated that the loss function characteristics i.e. its Lipschitzness and maximum value affect the generalization performance of deep neural networks which can be utilized as a guidance to propose novel distance measures. In this paper, by analyzing the aforementioned characteristics, we introduce a distance called Reduced Jeffries-Matusita as a loss function for training deep classification models to reduce the over-fitting issue. In our experiments, we evaluate the new loss function in two different problems: image classification in computer vision and node classification in the context of graph learning. The results show that the new distance measure stabilizes the training process significantly, enhances the generalization ability, and improves the performance of the models in the Accuracy and F1-score metrics, even if the training set size is small.
We formulate an XAI-based model improvement approach for Graph Neural Networks (GNNs) for node classification, called Explanation Enhanced Graph Learning (EEGL). The goal is to improve predictive performance of GNN using explanations. EEGL is an iterative self-improving algorithm, which starts with a learned "vanilla" GNN, and repeatedly uses frequent subgraph mining to find relevant patterns in explanation subgraphs. These patterns are then filtered further to obtain application-dependent features corresponding to the presence of certain subgraphs in the node neighborhoods. Giving an application-dependent algorithm for such a subgraph-based extension of the Weisfeiler-Leman (1-WL) algorithm has previously been posed as an open problem. We present experimental evidence, with synthetic and real-world data, which show that EEGL outperforms related approaches in predictive performance and that it has a node-distinguishing power beyond that of vanilla GNNs. We also analyze EEGL's training dynamics.
A Knowledge Graph (KG) is a heterogeneous graph encompassing a diverse range of node and edge types. Heterogeneous Graph Neural Networks (HGNNs) are popular for training machine learning tasks like node classification and link prediction on KGs. However, HGNN methods exhibit excessive complexity influenced by the KG's size, density, and the number of node and edge types. AI practitioners handcraft a subgraph of a KG G relevant to a specific task. We refer to this subgraph as a task-oriented subgraph (TOSG), which contains a subset of task-related node and edge types in G. Training the task using TOSG instead of G alleviates the excessive computation required for a large KG. Crafting the TOSG demands a deep understanding of the KG's structure and the task's objectives. Hence, it is challenging and time-consuming. This paper proposes KG-TOSA, an approach to automate the TOSG extraction for task-oriented HGNN training on a large KG. In KG-TOSA, we define a generic graph pattern that captures the KG's local and global structure relevant to a specific task. We explore different techniques to extract subgraphs matching our graph pattern: namely (i) two techniques sampling around targeted nodes using biased random walk or influence scores, and (ii) a SPARQL-based extraction method leveraging RDF engines' built-in indices. Hence, it achieves negligible preprocessing overhead compared to the sampling techniques. We develop a benchmark of real KGs of large sizes and various tasks for node classification and link prediction. Our experiments show that KG-TOSA helps state-of-the-art HGNN methods reduce training time and memory usage by up to 70% while improving the model performance, e.g., accuracy and inference time.
Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods.
Linear Graph Convolutional Networks (GCNs) are used to classify the node in the graph data. However, we note that most existing linear GCN models perform neural network operations in Euclidean space, which do not explicitly capture the tree-like hierarchical structure exhibited in real-world datasets that modeled as graphs. In this paper, we attempt to introduce hyperbolic space into linear GCN and propose a novel framework for Lorentzian linear GCN. Specifically, we map the learned features of graph nodes into hyperbolic space, and then perform a Lorentzian linear feature transformation to capture the underlying tree-like structure of data. Experimental results on standard citation networks datasets with semi-supervised learning show that our approach yields new state-of-the-art results of accuracy 74.7$\%$ on Citeseer and 81.3$\%$ on PubMed datasets. Furthermore, we observe that our approach can be trained up to two orders of magnitude faster than other nonlinear GCN models on PubMed dataset. Our code is publicly available at https://github.com/llqy123/LLGC-master.
Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts.
Deep Graph Neural Networks struggle with oversmoothing. This paper introduces a novel, physics-inspired GNN model designed to mitigate this issue. Our approach integrates with existing GNN architectures, introducing an entropy-aware message passing term. This term performs gradient ascent on the entropy during node aggregation, thereby preserving a certain degree of entropy in the embeddings. We conduct a comparative analysis of our model against state-of-the-art GNNs across various common datasets.
Low precision training can significantly reduce the computational overhead of training deep neural networks (DNNs). Though many such techniques exist, cyclic precision training (CPT), which dynamically adjusts precision throughout training according to a cyclic schedule, achieves particularly impressive improvements in training efficiency, while actually improving DNN performance. Existing CPT implementations take common learning rate schedules (e.g., cyclical cosine schedules) and use them for low precision training without adequate comparisons to alternative scheduling options. We define a diverse suite of CPT schedules and analyze their performance across a variety of DNN training regimes, some of which are unexplored in the low precision training literature (e.g., node classification with graph neural networks). From these experiments, we discover alternative CPT schedules that offer further improvements in training efficiency and model performance, as well as derive a set of best practices for choosing CPT schedules. Going further, we find that a correlation exists between model performance and training cost, and that changing the underlying CPT schedule can control the tradeoff between these two variables. To explain the direct correlation between model performance and training cost, we draw a connection between quantized training and critical learning periods, suggesting that aggressive quantization is a form of learning impairment that can permanently damage model performance.
Graph-based methods, pivotal for label inference over interconnected objects in many real-world applications, often encounter generalization challenges, if the graph used for model training differs significantly from the graph used for testing. This work delves into Graph Domain Adaptation (GDA) to address the unique complexities of distribution shifts over graph data, where interconnected data points experience shifts in features, labels, and in particular, connecting patterns. We propose a novel, theoretically principled method, Pairwise Alignment (Pair-Align) to counter graph structure shift by mitigating conditional structure shift (CSS) and label shift (LS). Pair-Align uses edge weights to recalibrate the influence among neighboring nodes to handle CSS and adjusts the classification loss with label weights to handle LS. Our method demonstrates superior performance in real-world applications, including node classification with region shift in social networks, and the pileup mitigation task in particle colliding experiments. For the first application, we also curate the largest dataset by far for GDA studies. Our method shows strong performance in synthetic and other existing benchmark datasets.
Graph transformers (GTs) have emerged as a promising architecture that is theoretically more expressive than message-passing graph neural networks (GNNs). However, typical GT models have at least quadratic complexity and thus cannot scale to large graphs. While there are several linear GTs recently proposed, they still lag behind GNN counterparts on several popular graph datasets, which poses a critical concern on their practical expressivity. To balance the trade-off between expressivity and scalability of GTs, we propose Polynormer, a polynomial-expressive GT model with linear complexity. Polynormer is built upon a novel base model that learns a high-degree polynomial on input features. To enable the base model permutation equivariant, we integrate it with graph topology and node features separately, resulting in local and global equivariant attention models. Consequently, Polynormer adopts a linear local-to-global attention scheme to learn high-degree equivariant polynomials whose coefficients are controlled by attention scores. Polynormer has been evaluated on $13$ homophilic and heterophilic datasets, including large graphs with millions of nodes. Our extensive experiment results show that Polynormer outperforms state-of-the-art GNN and GT baselines on most datasets, even without the use of nonlinear activation functions.
Graph learning has become essential in various domains, including recommendation systems and social network analysis. Graph Neural Networks (GNNs) have emerged as promising techniques for encoding structural information and improving performance in tasks like link prediction and node classification. However, a key challenge remains: the difficulty of generalizing to unseen graph data with different properties. In this work, we propose a novel graph foundation model, called OpenGraph, to address this challenge. Our approach tackles several technical obstacles. Firstly, we enhance data augmentation using a large language model (LLM) to overcome data scarcity in real-world scenarios. Secondly, we introduce a unified graph tokenizer that enables the model to generalize effectively to diverse graph data, even when encountering unseen properties during training. Thirdly, our developed scalable graph transformer captures node-wise dependencies within the global topological context. Extensive experiments validate the effectiveness of our framework. By adapting OpenGraph to new graph characteristics and comprehending diverse graphs, our approach achieves remarkable zero-shot graph learning performance across various settings. We release the model implementation at https://github.com/HKUDS/OpenGraph.
We address the challenge of federated learning on graph-structured data distributed across multiple clients. Specifically, we focus on the prevalent scenario of interconnected subgraphs, where interconnections between different clients play a critical role. We present a novel framework for this scenario, named FedStruct, that harnesses deep structural dependencies. To uphold privacy, unlike existing methods, FedStruct eliminates the necessity of sharing or generating sensitive node features or embeddings among clients. Instead, it leverages explicit global graph structure information to capture inter-node dependencies. We validate the effectiveness of FedStruct through experimental results conducted on six datasets for semi-supervised node classification, showcasing performance close to the centralized approach across various scenarios, including different data partitioning methods, varying levels of label availability, and number of clients.
Open-set graph learning is a practical task that aims to classify the known class nodes and to identify unknown class samples as unknowns. Conventional node classification methods usually perform unsatisfactorily in open-set scenarios due to the complex data they encounter, such as out-of-distribution (OOD) data and in-distribution (IND) noise. OOD data are samples that do not belong to any known classes. They are outliers if they occur in training (OOD noise), and open-set samples if they occur in testing. IND noise are training samples which are assigned incorrect labels. The existence of IND noise and OOD noise is prevalent, which usually cause the ambiguity problem, including the intra-class variety problem and the inter-class confusion problem. Thus, to explore robust open-set learning methods is necessary and difficult, and it becomes even more difficult for non-IID graph data.To this end, we propose a unified framework named ROG$_{PL}$ to achieve robust open-set learning on complex noisy graph data, by introducing prototype learning. In specific, ROG$_{PL}$ consists of two modules, i.e., denoising via label propagation and open-set prototype learning via regions. The first module corrects noisy labels through similarity-based label propagation and removes low-confidence samples, to solve the intra-class variety problem caused by noise. The second module learns open-set prototypes for each known class via non-overlapped regions and remains both interior and border prototypes to remedy the inter-class confusion problem.The two modules are iteratively updated under the constraints of classification loss and prototype diversity loss. To the best of our knowledge, the proposed ROG$_{PL}$ is the first robust open-set node classification method for graph data with complex noise.