Graph neural networks (GNNs) have been proved powerful in graph-oriented tasks. However, many real-world graphs are heterophilous, challenging the homophily assumption of classical GNNs. To solve the universality problem, many studies deepen networks or concatenate intermediate representations, which does not inherently change neighbor aggregation and introduces noise. Recent studies propose new metrics to characterize the homophily, but rarely consider the correlation of the proposed metrics and models. In this paper, we first design a new metric, Neighborhood Homophily (NH), to measure the label complexity or purity in node neighborhoods. Furthermore, we incorporate the metric into the classical graph convolutional network (GCN) architecture and propose Neighborhood Homophily-based Graph Convolutional Network (NHGCN). In this framework, neighbors are grouped by estimated NH values and aggregated from different channels, and the resulting node predictions are then used in turn to estimate and update NH values. The two processes of metric estimation and model inference are alternately optimized to achieve better node classification. NHGCN achieves top overall performance on both homophilous and heterophilous benchmarks, with an improvement of up to 7.4% compared to the current SOTA methods
We propose a new graph convolutional block, called MusGConv, specifically designed for the efficient processing of musical score data and motivated by general perceptual principles. It focuses on two fundamental dimensions of music, pitch and rhythm, and considers both relative and absolute representations of these components. We evaluate our approach on four different musical understanding problems: monophonic voice separation, harmonic analysis, cadence detection, and composer identification which, in abstract terms, translate to different graph learning problems, namely, node classification, link prediction, and graph classification. Our experiments demonstrate that MusGConv improves the performance on three of the aforementioned tasks while being conceptually very simple and efficient. We interpret this as evidence that it is beneficial to include perception-informed processing of fundamental musical concepts when developing graph network applications on musical score data.
Graph convolutional neural networks (GCNs) are powerful tools for learning graph-based knowledge representations from training data. However, they are vulnerable to small perturbations in the input graph, which makes them susceptible to input faults or adversarial attacks. This poses a significant problem for GCNs intended to be used in critical applications, which need to provide certifiably robust services even in the presence of adversarial perturbations. We propose an improved GCN robustness certification technique for node classification in the presence of node feature perturbations. We introduce a novel polyhedra-based abstract interpretation approach to tackle specific challenges of graph data and provide tight upper and lower bounds for the robustness of the GCN. Experiments show that our approach simultaneously improves the tightness of robustness bounds as well as the runtime performance of certification. Moreover, our method can be used during training to further improve the robustness of GCNs.
Graphs are an essential data structure utilized to represent relationships in real-world scenarios. Prior research has established that Graph Neural Networks (GNNs) deliver impressive outcomes in graph-centric tasks, such as link prediction and node classification. Despite these advancements, challenges like data sparsity and limited generalization capabilities continue to persist. Recently, Large Language Models (LLMs) have gained attention in natural language processing. They excel in language comprehension and summarization. Integrating LLMs with graph learning techniques has attracted interest as a way to enhance performance in graph learning tasks. In this survey, we conduct an in-depth review of the latest state-of-the-art LLMs applied in graph learning and introduce a novel taxonomy to categorize existing methods based on their framework design. We detail four unique designs: i) GNNs as Prefix, ii) LLMs as Prefix, iii) LLMs-Graphs Integration, and iv) LLMs-Only, highlighting key methodologies within each category. We explore the strengths and limitations of each framework, and emphasize potential avenues for future research, including overcoming current integration challenges between LLMs and graph learning techniques, and venturing into new application areas. This survey aims to serve as a valuable resource for researchers and practitioners eager to leverage large language models in graph learning, and to inspire continued progress in this dynamic field. We consistently maintain the related open-source materials at \url{https://github.com/HKUDS/Awesome-LLM4Graph-Papers}.
Graph neural networks (GNNs) have shown great success in learning from graph-based data. The key mechanism of current GNNs is message passing, where a node's feature is updated based on the information passing from its local neighbourhood. A limitation of this mechanism is that node features become increasingly dominated by the information aggregated from the neighbourhood as we use more rounds of message passing. Consequently, as the GNN layers become deeper, adjacent node features tends to be similar, making it more difficult for GNNs to distinguish adjacent nodes, thereby, limiting the performance of GNNs. In this paper, we propose conditional local feature encoding (CLFE) to help prevent the problem of node features being dominated by the information from local neighbourhood. The idea of our method is to extract the node hidden state embedding from message passing process and concatenate it with the nodes feature from previous stage, then we utilise linear transformation to form a CLFE based on the concatenated vector. The CLFE will form the layer output to better preserve node-specific information, thus help to improve the performance of GNN models. To verify the feasibility of our method, we conducted extensive experiments on seven benchmark datasets for four graph domain tasks: super-pixel graph classification, node classification, link prediction, and graph regression. The experimental results consistently demonstrate that our method improves model performance across a variety of baseline GNN models for all four tasks.
Spectral graph convolutional network (SGCN) is a kind of graph neural networks (GNN) based on graph signal filters, and has shown compelling expressivity for modeling graph-structured data. Most SGCNs adopt polynomial filters and learn the coefficients from the training data. Many of them focus on which polynomial basis leads to optimal expressive power and models' architecture is little discussed. In this paper, we propose a general form in terms of spectral graph convolution, where the coefficients of polynomial basis are stored in a third-order tensor. Then, we show that the convolution block in existing SGCNs can be derived by performing a certain coefficient decomposition operation on the coefficient tensor. Based on the generalized view, we develop novel spectral graph convolutions CoDeSGC-CP and -Tucker by tensor decomposition CP and Tucker on the coefficient tensor. Extensive experimental results demonstrate that the proposed convolutions achieve favorable performance improvements.
Heterogeneous graphs are ubiquitous to model complex data. There are urgent needs on powerful heterogeneous graph neural networks to effectively support important applications. We identify a potential semantic mixing issue in existing message passing processes, where the representations of the neighbors of a node $v$ are forced to be transformed to the feature space of $v$ for aggregation, though the neighbors are in different types. That is, the semantics in different node types are entangled together into node $v$'s representation. To address the issue, we propose SlotGAT with separate message passing processes in slots, one for each node type, to maintain the representations in their own node-type feature spaces. Moreover, in a slot-based message passing layer, we design an attention mechanism for effective slot-wise message aggregation. Further, we develop a slot attention technique after the last layer of SlotGAT, to learn the importance of different slots in downstream tasks. Our analysis indicates that the slots in SlotGAT can preserve different semantics in various feature spaces. The superiority of SlotGAT is evaluated against 13 baselines on 6 datasets for node classification and link prediction. Our code is at https://github.com/scottjiao/SlotGAT_ICML23/.
Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: (1) We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. (2) We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. (3) Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.
In the context of machine learning for graphs, many researchers have empirically observed that Deep Graph Networks (DGNs) perform favourably on node classification tasks when the graph structure is homophilic (\ie adjacent nodes are similar). In this paper, we introduce Lying-GCN, a new DGN inspired by opinion dynamics that can adaptively work in both the heterophilic and the homophilic setting. At each layer, each agent (node) shares its own opinions (node embeddings) with its neighbours. Instead of sharing its opinion directly as in GCN, we introduce a mechanism which allows agents to lie. Such a mechanism is adaptive, thus the agents learn how and when to lie according to the task that should be solved. We provide a characterisation of our proposal in terms of dynamical systems, by studying the spectral property of the coefficient matrix of the system. While the steady state of the system collapses to zero, we believe the lying mechanism is still usable to solve node classification tasks. We empirically prove our belief on both synthetic and real-world datasets, by showing that the lying mechanism allows to increase the performances in the heterophilic setting without harming the results in the homophilic one.
Graph Neural Networks (GNNs) have shown great performance in various tasks, with the core idea of learning from data labels and aggregating messages within the neighborhood of nodes. However, the common challenges in graphs are twofold: insufficient accurate (high-quality) labels and limited neighbors for nodes, resulting in weak GNNs. Existing graph augmentation methods typically address only one of these challenges, often adding training costs or relying on oversimplified or knowledge-intensive strategies, limiting their generalization. To simultaneously address both challenges faced by graphs in a generalized way, we propose an elegant method called IntraMix. Considering the incompatibility of vanilla Mixup with the complex topology of graphs, IntraMix innovatively employs Mixup among inaccurate labeled data of the same class, generating high-quality labeled data at minimal cost. Additionally, it finds data with high confidence of being clustered into the same group as the generated data to serve as their neighbors, thereby enriching the neighborhoods of graphs. IntraMix efficiently tackles both issues faced by graphs and challenges the prior notion of the limited effectiveness of Mixup in node classification. IntraMix is a theoretically grounded plug-in-play method that can be readily applied to all GNNs. Extensive experiments demonstrate the effectiveness of IntraMix across various GNNs and datasets. Our code is available at: https://github.com/Zhengsh123/IntraMix.
This paper introduces a new class of explanation structures, called robust counterfactual witnesses (RCWs), to provide robust, both counterfactual and factual explanations for graph neural networks. Given a graph neural network M, a robust counterfactual witness refers to the fraction of a graph G that are counterfactual and factual explanation of the results of M over G, but also remains so for any "disturbed" G by flipping up to k of its node pairs. We establish the hardness results, from tractable results to co-NP-hardness, for verifying and generating robust counterfactual witnesses. We study such structures for GNN-based node classification, and present efficient algorithms to verify and generate RCWs. We also provide a parallel algorithm to verify and generate RCWs for large graphs with scalability guarantees. We experimentally verify our explanation generation process for benchmark datasets, and showcase their applications.
We propose training-free graph neural networks (TFGNNs), which can be used without training and can also be improved with optional training, for transductive node classification. We first advocate labels as features (LaF), which is an admissible but not explored technique. We show that LaF provably enhances the expressive power of graph neural networks. We design TFGNNs based on this analysis. In the experiments, we confirm that TFGNNs outperform existing GNNs in the training-free setting and converge with much fewer training iterations than traditional GNNs.
Previous graph neural networks (GNNs) usually assume that the graph data is with clean labels for representation learning, but it is not true in real applications. In this paper, we propose a new multi-teacher distillation method based on bi-level optimization (namely BO-NNC), to conduct noisy node classification on the graph data. Specifically, we first employ multiple self-supervised learning methods to train diverse teacher models, and then aggregate their predictions through a teacher weight matrix. Furthermore, we design a new bi-level optimization strategy to dynamically adjust the teacher weight matrix based on the training progress of the student model. Finally, we design a label improvement module to improve the label quality. Extensive experimental results on real datasets show that our method achieves the best results compared to state-of-the-art methods.
Spectral graph neural networks are proposed to harness spectral information inherent in graph-structured data through the application of polynomial-defined graph filters, recently achieving notable success in graph-based web applications. Existing studies reveal that various polynomial choices greatly impact spectral GNN performance, underscoring the importance of polynomial selection. However, this selection process remains a critical and unresolved challenge. Although prior work suggests a connection between the approximation capabilities of polynomials and the efficacy of spectral GNNs, there is a lack of theoretical insights into this relationship, rendering polynomial selection a largely heuristic process. To address the issue, this paper examines polynomial selection from an error-sum of function slices perspective. Inspired by the conventional signal decomposition, we represent graph filters as a sum of disjoint function slices. Building on this, we then bridge the polynomial capability and spectral GNN efficacy by proving that the construction error of graph convolution layer is bounded by the sum of polynomial approximation errors on function slices. This result leads us to develop an advanced filter based on trigonometric polynomials, a widely adopted option for approximating narrow signal slices. The proposed filter remains provable parameter efficiency, with a novel Taylor-based parameter decomposition that achieves streamlined, effective implementation. With this foundation, we propose TFGNN, a scalable spectral GNN operating in a decoupled paradigm. We validate the efficacy of TFGNN via benchmark node classification tasks, along with an example graph anomaly detection application to show its practical utility.
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.
In this paper, we propose the Graph-Learning-Dual Graph Convolutional Neural Network called GLDGCN based on the classic Graph Convolutional Neural Network(GCN) by introducing dual convolutional layer and graph learning layer. We apply GLDGCN to the semi-supervised node classification task. Compared with the baseline methods, we achieve higher classification accuracy on three citation networks Citeseer, Cora and Pubmed, and we also analyze and discussabout selection of the hyperparameters and network depth. GLDGCN also perform well on the classic social network KarateClub and the new Wiki-CS dataset. For the insufficient ability of our algorithm to process large graphs during the experiment, we also introduce subgraph clustering and stochastic gradient descent methods into GCN and design a semi-supervised node classification algorithm based on the CLustering Graph Convolutional neural Network, which enables GCN to process large graph and improves its application value. We complete semi-supervised node classification experiments on two classic large graph which are PPI dataset (more than 50,000 nodes) and Reddit dataset (more than 200,000 nodes), and also perform well.
Graph Convolutional Networks (GCNs) have shown excellent performance in dealing with various graph structures such as node classification, graph classification and other tasks. However,recent studies have shown that GCNs are vulnerable to a novel threat known as backdoor attacks. However, all existing backdoor attacks in the graph domain require modifying the training samples to accomplish the backdoor injection, which may not be practical in many realistic scenarios where adversaries have no access to modify the training samples and may leads to the backdoor attack being detected easily. In order to explore the backdoor vulnerability of GCNs and create a more practical and stealthy backdoor attack method, this paper proposes a clean-graph backdoor attack against GCNs (CBAG) in the node classification task,which only poisons the training labels without any modification to the training samples, revealing that GCNs have this security vulnerability. Specifically, CBAG designs a new trigger exploration method to find important feature dimensions as the trigger patterns to improve the attack performance. By poisoning the training labels, a hidden backdoor is injected into the GCNs model. Experimental results show that our clean graph backdoor can achieve 99% attack success rate while maintaining the functionality of the GCNs model on benign samples.
While graph neural networks (GNNs) have become the de-facto standard for graph-based node classification, they impose a strong assumption on the availability of sufficient labeled samples. This assumption restricts the classification performance of prevailing GNNs on many real-world applications suffering from low-data regimes. Specifically, features extracted from scarce labeled nodes could not provide sufficient supervision for the unlabeled samples, leading to severe over-fitting. In this work, we point out that leveraging subgraphs to capture long-range dependencies can augment the representation of a node with homophily properties, thus alleviating the low-data regime. However, prior works leveraging subgraphs fail to capture the long-range dependencies among nodes. To this end, we present a novel self-supervised learning framework, called multi-view subgraph neural networks (Muse), for handling long-range dependencies. In particular, we propose an information theory-based identification mechanism to identify two types of subgraphs from the views of input space and latent space, respectively. The former is to capture the local structure of the graph, while the latter captures the long-range dependencies among nodes. By fusing these two views of subgraphs, the learned representations can preserve the topological properties of the graph at large, including the local structure and long-range dependencies, thus maximizing their expressiveness for downstream node classification tasks. Experimental results show that Muse outperforms the alternative methods on node classification tasks with limited labeled data.
Graph structured data, specifically text-attributed graphs (TAG), effectively represent relationships among varied entities. Such graphs are essential for semi-supervised node classification tasks. Graph Neural Networks (GNNs) have emerged as a powerful tool for handling this graph-structured data. Although gradient descent is commonly utilized for training GNNs for node classification, this study ventures into alternative methods, eliminating the iterative optimization processes. We introduce TrainlessGNN, a linear GNN model capitalizing on the observation that text encodings from the same class often cluster together in a linear subspace. This model constructs a weight matrix to represent each class's node attribute subspace, offering an efficient approach to semi-supervised node classification on TAG. Extensive experiments reveal that our trainless models can either match or even surpass their conventionally trained counterparts, demonstrating the possibility of refraining from gradient descent in certain configurations.
Recently, the optimization of polynomial filters within Spectral Graph Neural Networks (GNNs) has emerged as a prominent research focus. Existing spectral GNNs mainly emphasize polynomial properties in filter design, introducing computational overhead and neglecting the integration of crucial graph structure information. We argue that incorporating graph information into basis construction can enhance understanding of polynomial basis, and further facilitate simplified polynomial filter design. Motivated by this, we first propose a Positive and Negative Coupling Analysis (PNCA) framework, where the concepts of positive and negative activation are defined and their respective and mixed effects are analysed. Then, we explore PNCA from the message propagation perspective, revealing the subtle information hidden in the activation process. Subsequently, PNCA is used to analyze the mainstream polynomial filters, and a novel simple basis that decouples the positive and negative activation and fully utilizes graph structure information is designed. Finally, a simple GNN (called GSCNet) is proposed based on the new basis. Experimental results on the benchmark datasets for node classification verify that our GSCNet obtains better or comparable results compared with existing state-of-the-art GNNs while demanding relatively less computational time.