Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations of graph-structured data, demonstrating remarkable performance across various tasks. Recognising their importance, there has been extensive research focused on explaining GNN predictions, aiming to enhance their interpretability and trustworthiness. However, GNNs and their explainers face a notable challenge: graphs are primarily designed to model pair-wise relationships between nodes, which can make it tough to capture higher-order, multi-node interactions. This characteristic can pose difficulties for existing explainers in fully representing multi-node relationships. To address this gap, we present Framework For Higher-Order Representations In Graph Explanations (FORGE), a framework that enables graph explainers to capture such interactions by incorporating higher-order structures, resulting in more accurate and faithful explanations. Extensive evaluation shows that on average real-world datasets from the GraphXAI benchmark and synthetic datasets across various graph explainers, FORGE improves average explanation accuracy by 1.9x and 2.25x, respectively. We perform ablation studies to confirm the importance of higher-order relations in improving explanations, while our scalability analysis demonstrates FORGE's efficacy on large graphs.
In recent years, graph neural networks (GNNs) have become increasingly popular for solving NP-hard combinatorial optimization (CO) problems, such as maximum cut and maximum independent set. The core idea behind these methods is to represent a CO problem as a graph and then use GNNs to learn the node/graph embedding with combinatorial information. Although these methods have achieved promising results, given a specific CO problem, the design of GNN architectures still requires heavy manual work with domain knowledge. Existing automated GNNs are mostly focused on traditional graph learning problems, which is inapplicable to solving NP-hard CO problems. To this end, we present a new class of \textbf{AUTO}mated \textbf{G}NNs for solving \textbf{NP}-hard problems, namely \textbf{AutoGNP}. We represent CO problems by GNNs and focus on two specific problems, i.e., mixed integer linear programming and quadratic unconstrained binary optimization. The idea of AutoGNP is to use graph neural architecture search algorithms to automatically find the best GNNs for a given NP-hard combinatorial optimization problem. Compared with existing graph neural architecture search algorithms, AutoGNP utilizes two-hop operators in the architecture search space. Moreover, AutoGNP utilizes simulated annealing and a strict early stopping policy to avoid local optimal solutions. Empirical results on benchmark combinatorial problems demonstrate the superiority of our proposed model.
Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions across layers and the recursive graph structure have made it challenging to establish a theoretical foundation for learning and generalization. This study introduces the first theoretical investigation of a shallow Graph Transformer for semi-supervised node classification, comprising a self-attention layer with relative positional encoding and a two-layer perceptron. Focusing on a graph data model with discriminative nodes that determine node labels and non-discriminative nodes that are class-irrelevant, we characterize the sample complexity required to achieve a desirable generalization error by training with stochastic gradient descent (SGD). This paper provides the quantitative characterization of the sample complexity and number of iterations for convergence dependent on the fraction of discriminative nodes, the dominant patterns, and the initial model errors. Furthermore, we demonstrate that self-attention and positional encoding enhance generalization by making the attention map sparse and promoting the core neighborhood during training, which explains the superior feature representation of Graph Transformers. Our theoretical results are supported by empirical experiments on synthetic and real-world benchmarks.
In recent years, continual learning (CL) techniques have made significant progress in learning from streaming data while preserving knowledge across sequential tasks, particularly in the realm of euclidean data. To foster fair evaluation and recognize challenges in CL settings, several evaluation frameworks have been proposed, focusing mainly on the single- and multi-label classification task on euclidean data. However, these evaluation frameworks are not trivially applicable when the input data is graph-structured, as they do not consider the topological structure inherent in graphs. Existing continual graph learning (CGL) evaluation frameworks have predominantly focussed on single-label scenarios in the node classification (NC) task. This focus has overlooked the complexities of multi-label scenarios, where nodes may exhibit affiliations with multiple labels, simultaneously participating in multiple tasks. We develop a graph-aware evaluation (\agale) framework that accommodates both single-labeled and multi-labeled nodes, addressing the limitations of previous evaluation frameworks. In particular, we define new incremental settings and devise data partitioning algorithms tailored to CGL datasets. We perform extensive experiments comparing methods from the domains of continual learning, continual graph learning, and dynamic graph learning (DGL). We theoretically analyze \agale and provide new insights about the role of homophily in the performance of compared methods. We release our framework at https://github.com/Tianqi-py/AGALE.
Recent progress in Graph Neural Networks (GNNs) has greatly enhanced the ability to model complex molecular structures for predicting properties. Nevertheless, molecular data encompasses more than just graph structures, including textual and visual information that GNNs do not handle well. To bridge this gap, we present an innovative framework that utilizes multimodal molecular data to extract insights from Large Language Models (LLMs). We introduce GALLON (Graph Learning from Large Language Model Distillation), a framework that synergizes the capabilities of LLMs and GNNs by distilling multimodal knowledge into a unified Multilayer Perceptron (MLP). This method integrates the rich textual and visual data of molecules with the structural analysis power of GNNs. Extensive experiments reveal that our distilled MLP model notably improves the accuracy and efficiency of molecular property predictions.
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered sequence of static graph snapshots observed at discrete time points. Sequence models such as RNNs or Transformers have long been the predominant backbone networks for modeling such temporal graphs. Yet, despite the promising results, RNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Recently, state space models (SSMs), which are framed as discretized representations of an underlying continuous-time linear dynamical system, have garnered substantial attention and achieved breakthrough advancements in independent sequence modeling. In this work, we undertake a principled investigation that extends SSM theory to temporal graphs by integrating structural information into the online approximation objective via the adoption of a Laplacian regularization term. The emergent continuous-time system introduces novel algorithmic challenges, thereby necessitating our development of GraphSSM, a graph state space model for modeling the dynamics of temporal graphs. Extensive experimental results demonstrate the effectiveness of our GraphSSM framework across various temporal graph benchmarks.
Graph neural networks are recognized for their strong performance across various applications, with the backpropagation algorithm playing a central role in the development of most GNN models. However, despite its effectiveness, BP has limitations that challenge its biological plausibility and affect the efficiency, scalability and parallelism of training neural networks for graph-based tasks. While several non-BP training algorithms, such as the direct feedback alignment, have been successfully applied to fully-connected and convolutional network components for handling Euclidean data, directly adapting these non-BP frameworks to manage non-Euclidean graph data in GNN models presents significant challenges. These challenges primarily arise from the violation of the i.i.d. assumption in graph data and the difficulty in accessing prediction errors for all samples (nodes) within the graph. To overcome these obstacles, in this paper we propose DFA-GNN, a novel forward learning framework tailored for GNNs with a case study of semi-supervised learning. The proposed method breaks the limitations of BP by using a dedicated forward training mechanism. Specifically, DFA-GNN extends the principles of DFA to adapt to graph data and unique architecture of GNNs, which incorporates the information of graph topology into the feedback links to accommodate the non-Euclidean characteristics of graph data. Additionally, for semi-supervised graph learning tasks, we developed a pseudo error generator that spreads residual errors from training data to create a pseudo error for each unlabeled node. These pseudo errors are then utilized to train GNNs using DFA. Extensive experiments on 10 public benchmarks reveal that our learning framework outperforms not only previous non-BP methods but also the standard BP methods, and it exhibits excellent robustness against various types of noise and attacks.
Dynamic graph learning equips the edges with time attributes and allows multiple links between two nodes, which is a crucial technology for understanding evolving data scenarios like traffic prediction and recommendation systems. Existing works obtain the evolving patterns mainly depending on the most recent neighbor sequences. However, we argue that whether two nodes will have interaction with each other in the future is highly correlated with the same interaction that happened in the past. Only considering the recent neighbors overlooks the phenomenon of repeat behavior and fails to accurately capture the temporal evolution of interactions. To fill this gap, this paper presents RepeatMixer, which considers evolving patterns of first and high-order repeat behavior in the neighbor sampling strategy and temporal information learning. Firstly, we define the first-order repeat-aware nodes of the source node as the destination nodes that have interacted historically and extend this concept to high orders as nodes in the destination node's high-order neighbors. Then, we extract neighbors of the source node that interacted before the appearance of repeat-aware nodes with a slide window strategy as its neighbor sequence. Next, we leverage both the first and high-order neighbor sequences of source and destination nodes to learn temporal patterns of interactions via an MLP-based encoder. Furthermore, considering the varying temporal patterns on different orders, we introduce a time-aware aggregation mechanism that adaptively aggregates the temporal representations from different orders based on the significance of their interaction time sequences. Experimental results demonstrate the superiority of RepeatMixer over state-of-the-art models in link prediction tasks, underscoring the effectiveness of the proposed repeat-aware neighbor sampling strategy.
Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node's representation in an input graph by aggregating messages from the node's neighbors, which necessitates a memory complexity of the order of the number of graph edges. This complexity might quickly become prohibitive for large graphs provided they are not very sparse. In this paper, we propose a novel approach to alleviate this problem by approximating the input graph as an intersecting community graph (ICG) -- a combination of intersecting cliques. The key insight is that the number of communities required to approximate a graph does not depend on the graph size. We develop a new constructive version of the Weak Graph Regularity Lemma to efficiently construct an approximating ICG for any input graph. We then devise an efficient graph learning algorithm operating directly on ICG in linear memory and time with respect to the number of nodes (rather than edges). This offers a new and fundamentally different pipeline for learning on very large non-sparse graphs, whose applicability is demonstrated empirically on node classification tasks and spatio-temporal data processing.
Task planning in language agents is emerging as an important research topic alongside the development of large language models (LLMs). It aims to break down complex user requests in natural language into solvable sub-tasks, thereby fulfilling the original requests. In this context, the sub-tasks can be naturally viewed as a graph, where the nodes represent the sub-tasks, and the edges denote the dependencies among them. Consequently, task planning is a decision-making problem that involves selecting a connected path or subgraph within the corresponding graph and invoking it. In this paper, we explore graph learning-based methods for task planning, a direction that is orthogonal to the prevalent focus on prompt design. Our interest in graph learning stems from a theoretical discovery: the biases of attention and auto-regressive loss impede LLMs' ability to effectively navigate decision-making on graphs, which is adeptly addressed by graph neural networks (GNNs). This theoretical insight led us to integrate GNNs with LLMs to enhance overall performance. Extensive experiments demonstrate that GNN-based methods surpass existing solutions even without training, and minimal training can further enhance their performance. The performance gain increases with a larger task graph size.
Graph Prompt Learning (GPL) bridges significant disparities between pretraining and downstream applications to alleviate the knowledge transfer bottleneck in real-world graph learning. While GPL offers superior effectiveness in graph knowledge transfer and computational efficiency, the security risks posed by backdoor poisoning effects embedded in pretrained models remain largely unexplored. Our study provides a comprehensive analysis of GPL's vulnerability to backdoor attacks. We introduce \textit{CrossBA}, the first cross-context backdoor attack against GPL, which manipulates only the pretraining phase without requiring knowledge of downstream applications. Our investigation reveals both theoretically and empirically that tuning trigger graphs, combined with prompt transformations, can seamlessly transfer the backdoor threat from pretrained encoders to downstream applications. Through extensive experiments involving 3 representative GPL methods across 5 distinct cross-context scenarios and 5 benchmark datasets of node and graph classification tasks, we demonstrate that \textit{CrossBA} consistently achieves high attack success rates while preserving the functionality of downstream applications over clean input. We also explore potential countermeasures against \textit{CrossBA} and conclude that current defenses are insufficient to mitigate \textit{CrossBA}. Our study highlights the persistent backdoor threats to GPL systems, raising trustworthiness concerns in the practices of GPL techniques.
The smoothing issue in graph learning leads to indistinguishable node representations, posing significant challenges for graph-related tasks. However, our experiments reveal that this problem can uncover underlying properties of node anomaly detection (NAD) that previous research has missed. We introduce Individual Smoothing Patterns (ISP) and Neighborhood Smoothing Patterns (NSP), which indicate that the representations of anomalous nodes are harder to smooth than those of normal ones. In addition, we explore the theoretical implications of these patterns, demonstrating the potential benefits of ISP and NSP for NAD tasks. Motivated by these findings, we propose SmoothGNN, a novel unsupervised NAD framework. First, we design a learning component to explicitly capture ISP for detecting node anomalies. Second, we design a spectral graph neural network to implicitly learn ISP to enhance detection. Third, we design an effective coefficient based on our findings that NSP can serve as coefficients for node representations, aiding in the identification of anomalous nodes. Furthermore, we devise a novel anomaly measure to calculate loss functions and anomalous scores for nodes, reflecting the properties of NAD using ISP and NSP. Extensive experiments on 9 real datasets show that SmoothGNN outperforms the best rival by an average of 14.66% in AUC and 7.28% in Average Precision, with 75x running time speedup, validating the effectiveness and efficiency of our framework.
Anomaly detection in continuous-time dynamic graphs is an emerging field yet under-explored in the context of learning algorithms. In this paper, we pioneer structured analyses of link-level anomalies and graph representation learning for identifying categorically anomalous graph links. First, we introduce a fine-grained taxonomy for edge-level anomalies leveraging structural, temporal, and contextual graph properties. Based on these properties, we introduce a method for generating and injecting typed anomalies into graphs. Next, we introduce a novel method to generate continuous-time dynamic graphs featuring consistencies across either or combinations of time, structure, and context. To enable temporal graph learning methods to detect specific types of anomalous links rather than the bare existence of a link, we extend the generic link prediction setting by: (1) conditioning link existence on contextual edge attributes; and (2) refining the training regime to accommodate diverse perturbations in the negative edge sampler. Comprehensive benchmarks on synthetic and real-world datasets -- featuring synthetic and labeled organic anomalies and employing six state-of-the-art link prediction methods -- validate our taxonomy and generation processes for anomalies and benign graphs, as well as our approach to adapting methods for anomaly detection. Our results reveal that different learning methods excel in capturing different aspects of graph normality and detecting different types of anomalies. We conclude with a comprehensive list of findings highlighting opportunities for future research.
The burgeoning volume of graph data presents significant computational challenges in training graph neural networks (GNNs), critically impeding their efficiency in various applications. To tackle this challenge, graph condensation (GC) has emerged as a promising acceleration solution, focusing on the synthesis of a compact yet representative graph for efficiently training GNNs while retaining performance. Despite the potential to promote scalable use of GNNs, existing GC methods are limited to aligning the condensed graph with merely the observed static graph distribution. This limitation significantly restricts the generalization capacity of condensed graphs, particularly in adapting to dynamic distribution changes. In real-world scenarios, however, graphs are dynamic and constantly evolving, with new nodes and edges being continually integrated. Consequently, due to the limited generalization capacity of condensed graphs, applications that employ GC for efficient GNN training end up with sub-optimal GNNs when confronted with evolving graph structures and distributions in dynamic real-world situations. To overcome this issue, we propose open-world graph condensation (OpenGC), a robust GC framework that integrates structure-aware distribution shift to simulate evolving graph patterns and exploit the temporal environments for invariance condensation. This approach is designed to extract temporal invariant patterns from the original graph, thereby enhancing the generalization capabilities of the condensed graph and, subsequently, the GNNs trained on it. Extensive experiments on both real-world and synthetic evolving graphs demonstrate that OpenGC outperforms state-of-the-art (SOTA) GC methods in adapting to dynamic changes in open-world graph environments.
We present a novel end-to-end framework that generates highly compact (typically 6-15 dimensions), discrete (int4 type), and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs. By employing vector quantization, we compress continuous node embeddings from multiple layers of a Graph Neural Network (GNN) into discrete codes, applicable under both self-supervised and supervised learning paradigms. These node IDs capture high-level abstractions of graph data and offer interpretability that traditional GNN embeddings lack. Extensive experiments on 34 datasets, encompassing node classification, graph classification, link prediction, and attributed graph clustering tasks, demonstrate that the generated node IDs significantly enhance speed and memory efficiency while achieving competitive performance compared to current state-of-the-art methods.
Fairness-aware Graph Neural Networks (GNNs) often face a challenging trade-off, where prioritizing fairness may require compromising utility. In this work, we re-examine fairness through the lens of spectral graph theory, aiming to reconcile fairness and utility within the framework of spectral graph learning. We explore the correlation between sensitive features and spectrum in GNNs, using theoretical analysis to delineate the similarity between original sensitive features and those after convolution under different spectra. Our analysis reveals a reduction in the impact of similarity when the eigenvectors associated with the largest magnitude eigenvalue exhibit directional similarity. Based on these theoretical insights, we propose FUGNN, a novel spectral graph learning approach that harmonizes the conflict between fairness and utility. FUGNN ensures algorithmic fairness and utility by truncating the spectrum and optimizing eigenvector distribution during the encoding process. The fairness-aware eigenvector selection reduces the impact of convolution on sensitive features while concurrently minimizing the sacrifice of utility. FUGNN further optimizes the distribution of eigenvectors through a transformer architecture. By incorporating the optimized spectrum into the graph convolution network, FUGNN effectively learns node representations. Experiments on six real-world datasets demonstrate the superiority of FUGNN over baseline methods. The codes are available at https://github.com/yushuowiki/FUGNN.
Given the ubiquity of graph data, it is intriguing to ask: Is it possible to train a graph foundation model on a broad range of graph data across diverse domains? A major hurdle toward this goal lies in the fact that graphs from different domains often exhibit profoundly divergent characteristics. Although there have been some initial efforts in integrating multi-domain graphs for pre-training, they primarily rely on textual descriptions to align the graphs, limiting their application to text-attributed graphs. Moreover, different source domains may conflict or interfere with each other, and their relevance to the target domain can vary significantly. To address these issues, we propose MDGPT, a text free Multi-Domain Graph Pre-Training and adaptation framework designed to exploit multi-domain knowledge for graph learning. First, we propose a set of domain tokens to to align features across source domains for synergistic pre-training. Second, we propose a dual prompts, consisting of a unifying prompt and a mixing prompt, to further adapt the target domain with unified multi-domain knowledge and a tailored mixture of domain-specific knowledge. Finally, we conduct extensive experiments involving six public datasets to evaluate and analyze MDGPT, which outperforms prior art by up to 37.9%.
We propose a heterogeneous graph mamba network (HGMN) as the first exploration in leveraging the selective state space models (SSSMs) for heterogeneous graph learning. Compared with the literature, our HGMN overcomes two major challenges: (i) capturing long-range dependencies among heterogeneous nodes and (ii) adapting SSSMs to heterogeneous graph data. Our key contribution is a general graph architecture that can solve heterogeneous nodes in real-world scenarios, followed an efficient flow. Methodologically, we introduce a two-level efficient tokenization approach that first captures long-range dependencies within identical node types, and subsequently across all node types. Empirically, we conduct comparisons between our framework and 19 state-of-the-art methods on the heterogeneous benchmarks. The extensive comparisons demonstrate that our framework outperforms other methods in both the accuracy and efficiency dimensions.
The MRI-derived brain network serves as a pivotal instrument in elucidating both the structural and functional aspects of the brain, encompassing the ramifications of diseases and developmental processes. However, prevailing methodologies, often focusing on synchronous BOLD signals from functional MRI (fMRI), may not capture directional influences among brain regions and rarely tackle temporal functional dynamics. In this study, we first construct the brain-effective network via the dynamic causal model. Subsequently, we introduce an interpretable graph learning framework termed Spatio-Temporal Embedding ODE (STE-ODE). This framework incorporates specifically designed directed node embedding layers, aiming at capturing the dynamic interplay between structural and effective networks via an ordinary differential equation (ODE) model, which characterizes spatial-temporal brain dynamics. Our framework is validated on several clinical phenotype prediction tasks using two independent publicly available datasets (HCP and OASIS). The experimental results clearly demonstrate the advantages of our model compared to several state-of-the-art methods.
Graph Neural Networks (GNNs) have demonstrated superior performance across various graph learning tasks but face significant computational challenges when applied to large-scale graphs. One effective approach to mitigate these challenges is graph sparsification, which involves removing non-essential edges to reduce computational overhead. However, previous graph sparsification methods often rely on a single global sparsity setting and uniform pruning criteria, failing to provide customized sparsification schemes for each node's complex local context. In this paper, we introduce Mixture-of-Graphs (MoG), leveraging the concept of Mixture-of-Experts (MoE), to dynamically select tailored pruning solutions for each node. Specifically, MoG incorporates multiple sparsifier experts, each characterized by unique sparsity levels and pruning criteria, and selects the appropriate experts for each node. Subsequently, MoG performs a mixture of the sparse graphs produced by different experts on the Grassmann manifold to derive an optimal sparse graph. One notable property of MoG is its entirely local nature, as it depends on the specific circumstances of each individual node. Extensive experiments on four large-scale OGB datasets and two superpixel datasets, equipped with five GNN backbones, demonstrate that MoG (I) identifies subgraphs at higher sparsity levels ($8.67\%\sim 50.85\%$), with performance equal to or better than the dense graph, (II) achieves $1.47-2.62\times$ speedup in GNN inference with negligible performance drop, and (III) boosts ``top-student'' GNN performance ($1.02\%\uparrow$ on RevGNN+\textsc{ogbn-proteins} and $1.74\%\uparrow$ on DeeperGCN+\textsc{ogbg-ppa}).