Real-world graphs grow rapidly with edge and vertex insertions over time, motivating the problem of efficiently maintaining robust node representation over evolving graphs. Recent efficient GNNs are designed to decouple recursive message passing from the learning process, and favor Personalized PageRank (PPR) as the underlying feature propagation mechanism. However, most PPR-based GNNs are designed for static graphs, and efficient PPR maintenance remains as an open problem. Further, there is surprisingly little theoretical justification for the choice of PPR, despite its impressive empirical performance. In this paper, we are inspired by the recent PPR formulation as an explicit $\ell_1$-regularized optimization problem and propose a unified dynamic graph learning framework based on sparse node-wise attention. We also present a set of desired properties to justify the choice of PPR in STOA GNNs, and serves as the guideline for future node attention designs. Meanwhile, we take advantage of the PPR-equivalent optimization formulation and employ the proximal gradient method (ISTA) to improve the efficiency of PPR-based GNNs upto 6 times. Finally, we instantiate a simple-yet-effective model (\textsc{GoPPE}) with robust positional encodings by maximizing PPR previously used as attention. The model performs comparably to or better than the STOA baselines and greatly outperforms when the initial node attributes are noisy during graph evolution, demonstrating the effectiveness and robustness of \textsc{GoPPE}.
Incremental graph learning has gained significant attention for its ability to address the catastrophic forgetting problem in graph representation learning. However, traditional methods often rely on a large number of labels for node classification, which is impractical in real-world applications. This makes few-shot incremental learning on graphs a pressing need. Current methods typically require extensive training samples from meta-learning to build memory and perform intensive fine-tuning of GNN parameters, leading to high memory consumption and potential loss of previously learned knowledge. To tackle these challenges, we introduce Mecoin, an efficient method for building and maintaining memory. Mecoin employs Structured Memory Units to cache prototypes of learned categories, as well as Memory Construction Modules to update these prototypes for new categories through interactions between the nodes and the cached prototypes. Additionally, we have designed a Memory Representation Adaptation Module to store probabilities associated with each class prototype, reducing the need for parameter fine-tuning and lowering the forgetting rate. When a sample matches its corresponding class prototype, the relevant probabilities are retrieved from the MRaM. Knowledge is then distilled back into the GNN through a Graph Knowledge Distillation Module, preserving the model's memory. We analyze the effectiveness of Mecoin in terms of generalization error and explore the impact of different distillation strategies on model performance through experiments and VC-dimension analysis. Compared to other related works, Mecoin shows superior performance in accuracy and forgetting rate. Our code is publicly available on the https://github.com/Arvin0313/Mecoin-GFSCIL.git .
We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.
Cognitive diagnosis (CD) utilizes students' existing studying records to estimate their mastery of unknown knowledge concepts, which is vital for evaluating their learning abilities. Accurate CD is extremely challenging because CD is associated with complex relationships and mechanisms among students, knowledge concepts, studying records, etc. However, existing approaches loosely consider these relationships and mechanisms by a non-end-to-end learning framework, resulting in sub-optimal feature extractions and fusions for CD. Different from them, this paper innovatively proposes an End-to-end Graph Neural Networks-based Cognitive Diagnosis (EGNN-CD) model. EGNN-CD consists of three main parts: knowledge concept network (KCN), graph neural networks-based feature extraction (GNNFE), and cognitive ability prediction (CAP). First, KCN constructs CD-related interaction by comprehensively extracting physical information from students, exercises, and knowledge concepts. Second, a four-channel GNNFE is designed to extract high-order and individual features from the constructed KCN. Finally, CAP employs a multi-layer perceptron to fuse the extracted features to predict students' learning abilities in an end-to-end learning way. With such designs, the feature extractions and fusions are guaranteed to be comprehensive and optimal for CD. Extensive experiments on three real datasets demonstrate that our EGNN-CD achieves significantly higher accuracy than state-of-the-art models in CD.
Graph neural network (GNN) has captured wide attention due to its capability of graph representation learning for graph-structured data. However, the distributed data silos limit the performance of GNN. Vertical federated learning (VFL), an emerging technique to process distributed data, successfully makes GNN possible to handle the distributed graph-structured data. Despite the prosperous development of vertical federated graph learning (VFGL), the robustness of VFGL against the adversarial attack has not been explored yet. Although numerous adversarial attacks against centralized GNNs are proposed, their attack performance is challenged in the VFGL scenario. To the best of our knowledge, this is the first work to explore the adversarial attack against VFGL. A query-efficient hybrid adversarial attack framework is proposed to significantly improve the centralized adversarial attacks against VFGL, denoted as NA2, short for Neuron-based Adversarial Attack. Specifically, a malicious client manipulates its local training data to improve its contribution in a stealthy fashion. Then a shadow model is established based on the manipulated data to simulate the behavior of the server model in VFGL. As a result, the shadow model can improve the attack success rate of various centralized attacks with a few queries. Extensive experiments on five real-world benchmarks demonstrate that NA2 improves the performance of the centralized adversarial attacks against VFGL, achieving state-of-the-art performance even under potential adaptive defense where the defender knows the attack method. Additionally, we provide interpretable experiments of the effectiveness of NA2 via sensitive neurons identification and visualization of t-SNE.
Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. Recent advances in GSP have enabled the learning of graph structures from observed signals, but these methods often struggle with time-varying systems and real-time applications. Adaptive filtering techniques, while effective for online learning, have seen limited application in graph topology estimation from a GSP perspective. To this end, we introduce AdaCGP, an online algorithm for adaptive estimation of the Graph Shift Operator (GSO) from multivariate time series. The GSO is estimated from an adaptive time-vertex autoregressive model through recursive update formulae designed to address sparsity, shift-invariance and bias. Through simulations, we show that AdaCGP performs consistently well across various graph topologies, and achieves improvements in excess of 82% for GSO estimation compared to baseline adaptive vector autoregressive models. In addition, our online variable splitting approach for enforcing sparsity enables near-perfect precision in identifying causal connections while maintaining low false positive rates upon optimisation of the forecast error. Finally, AdaCGP's ability to track changes in graph structure is demonstrated on recordings of ventricular fibrillation dynamics in response to an anti-arrhythmic drug. AdaCGP is shown to be able to identify the stability of critical conduction patterns that may be maintaining the arrhythmia in an intuitive way, together with its potential to support diagnosis and treatment strategies.
Graphs play a central role in modeling complex relationships across various domains. Most graph learning methods rely heavily on neighborhood information, raising the question of how to handle cold-start nodes - nodes with no known connections within the graph. These models often overlook the cold-start nodes, making them ineffective for real-world scenarios. To tackle this, we propose G-SPARC, a novel framework addressing cold-start nodes, that leverages generalizable spectral embedding. This framework enables extension to state-of-the-art methods making them suitable for practical applications. By utilizing a key idea of transitioning from graph representation to spectral representation, our approach is generalizable to cold-start nodes, capturing the global structure of the graph without relying on adjacency data. Experimental results demonstrate that our method outperforms existing models on cold-start nodes across various tasks like node classification, node clustering, and link prediction. G-SPARC provides a breakthrough built-in solution to the cold-start problem in graph learning. Our code will be publicly available upon acceptance.
The message-passing mechanism of graph convolutional networks (i.e., GCNs) enables label information to be propagated to a broader range of neighbors, thereby increasing the utilization of labels. However, the label information is not always effectively utilized in the traditional GCN framework. To address this issue, we propose a new two-step framework called ELU-GCN. In the first stage, ELU-GCN conducts graph learning to learn a new graph structure (i.e., ELU-graph), which enables the message passing can effectively utilize label information. In the second stage, we design a new graph contrastive learning on the GCN framework for representation learning by exploring the consistency and mutually exclusive information between the learned ELU graph and the original graph. Moreover, we theoretically demonstrate that the proposed method can ensure the generalization ability of GCNs. Extensive experiments validate the superiority of our method.
Link prediction is a critical problem in graph learning with broad applications such as recommender systems and knowledge graph completion. Numerous research efforts have been directed at solving this problem, including approaches based on similarity metrics and Graph Neural Networks (GNN). However, most existing solutions are still rooted in conventional supervised learning, which makes it challenging to adapt over time to changing customer interests and to address the inherent dilemma of exploitation versus exploration in link prediction. To tackle these challenges, this paper reformulates link prediction as a sequential decision-making process, where each link prediction interaction occurs sequentially. We propose a novel fusion algorithm, PRB (PageRank Bandits), which is the first to combine contextual bandits with PageRank for collaborative exploitation and exploration. We also introduce a new reward formulation and provide a theoretical performance guarantee for PRB. Finally, we extensively evaluate PRB in both online and offline settings, comparing it with bandit-based and graph-based methods. The empirical success of PRB demonstrates the value of the proposed fusion approach. Our code is released at https://github.com/jiaruzouu/PRB.
Federated Graph Learning (FGL) aims to collaboratively and privately optimize graph models on divergent data for different tasks. A critical challenge in FGL is to enable effective yet efficient federated optimization against multifaceted graph heterogeneity to enhance mutual performance. However, existing FGL works primarily address graph data heterogeneity and perform incapable of graph task heterogeneity. To address the challenge, we propose a Federated Graph Prompt Learning (FedGPL) framework to efficiently enable prompt-based asymmetric graph knowledge transfer between multifaceted heterogeneous federated participants. Generally, we establish a split federated framework to preserve universal and domain-specific graph knowledge, respectively. Moreover, we develop two algorithms to eliminate task and data heterogeneity for advanced federated knowledge preservation. First, a Hierarchical Directed Transfer Aggregator (HiDTA) delivers cross-task beneficial knowledge that is hierarchically distilled according to the directional transferability. Second, a Virtual Prompt Graph (VPG) adaptively generates graph structures to enhance data utility by distinguishing dominant subgraphs and neutralizing redundant ones. We conduct theoretical analyses and extensive experiments to demonstrate the significant accuracy and efficiency effectiveness of FedGPL against multifaceted graph heterogeneity compared to state-of-the-art baselines on large-scale federated graph datasets.
Deep neural networks (DNNs) achieve state-of-the-art performance on many tasks, but this often requires increasingly larger model sizes, which in turn leads to more complex internal representations. Explainability techniques (XAI) have made remarkable progress in the interpretability of ML models. However, the non-relational nature of Graph neural networks (GNNs) make it difficult to reuse already existing XAI methods. While other works have focused on instance-based explanation methods for GNNs, very few have investigated model-based methods and, to our knowledge, none have tried to probe the embedding of the GNNs for well-known structural graph properties. In this paper we present a model agnostic explainability pipeline for GNNs employing diagnostic classifiers. This pipeline aims to probe and interpret the learned representations in GNNs across various architectures and datasets, refining our understanding and trust in these models.
Learning the graph topology of a complex network is challenging due to limited data availability and imprecise data models. A common remedy in existing works is to incorporate priors such as sparsity or modularity which highlight on the structural property of graph topology. We depart from these approaches to develop priors that are directly inspired by complex network dynamics. Focusing on social networks with actions modeled by equilibriums of linear quadratic games, we postulate that the social network topologies are optimized with respect to a social welfare function. Utilizing this prior knowledge, we propose a network games induced regularizer to assist graph learning. We then formulate the graph topology learning problem as a bilevel program. We develop a two-timescale gradient algorithm to tackle the latter. We draw theoretical insights on the optimal graph structure of the bilevel program and show that they agree with the topology in several man-made networks. Empirically, we demonstrate the proposed formulation gives rise to reliable estimate of graph topology.
Graph Neural Networks (GNNs) have become essential in interpreting relational data across various domains, yet, they often struggle to generalize to unseen graph data that differs markedly from training instances. In this paper, we introduce a novel framework called General Retrieval-Augmented Graph Learning (RAGraph), which brings external graph data into the general graph foundation model to improve model generalization on unseen scenarios. On the top of our framework is a toy graph vector library that we established, which captures key attributes, such as features and task-specific label information. During inference, the RAGraph adeptly retrieves similar toy graphs based on key similarities in downstream tasks, integrating the retrieved data to enrich the learning context via the message-passing prompting mechanism. Our extensive experimental evaluations demonstrate that RAGraph significantly outperforms state-of-the-art graph learning methods in multiple tasks such as node classification, link prediction, and graph classification across both dynamic and static datasets. Furthermore, extensive testing confirms that RAGraph consistently maintains high performance without the need for task-specific fine-tuning, highlighting its adaptability, robustness, and broad applicability.
Graph learning is naturally well suited for use in symbolic, object-centric planning due to its ability to exploit relational structures exhibited in planning domains and to take as input planning instances with arbitrary numbers of objects. Numeric planning is an extension of symbolic planning in which states may now also exhibit numeric variables. In this work, we propose data-efficient and interpretable machine learning models for learning to solve numeric planning tasks. This involves constructing a new graph kernel for graphs with both continuous and categorical attributes, as well as new optimisation methods for learning heuristic functions for numeric planning. Experiments show that our graph kernels are vastly more efficient and generalise better than graph neural networks for numeric planning, and also yield competitive coverage performance compared to domain-independent numeric planners. Code is available at https://github.com/DillonZChen/goose
Recently, graph prompt learning has garnered increasing attention in adapting pre-trained GNN models for downstream graph learning tasks. However, existing works generally conduct prompting over all graph elements (e.g., nodes, edges, node attributes, etc.), which is suboptimal and obviously redundant. To address this issue, we propose exploiting sparse representation theory for graph prompting and present Graph Sparse Prompting (GSP). GSP aims to adaptively and sparsely select the optimal elements (e.g., certain node attributes) to achieve compact prompting for downstream tasks. Specifically, we propose two kinds of GSP models, termed Graph Sparse Feature Prompting (GSFP) and Graph Sparse multi-Feature Prompting (GSmFP). Both GSFP and GSmFP provide a general scheme for tuning any specific pre-trained GNNs that can achieve attribute selection and compact prompt learning simultaneously. A simple yet effective algorithm has been designed for solving GSFP and GSmFP models. Experiments on 16 widely-used benchmark datasets validate the effectiveness and advantages of the proposed GSFPs.
Personalized Federated Graph Learning (pFGL) facilitates the decentralized training of Graph Neural Networks (GNNs) without compromising privacy while accommodating personalized requirements for non-IID participants. In cross-domain scenarios, structural heterogeneity poses significant challenges for pFGL. Nevertheless, previous pFGL methods incorrectly share non-generic knowledge globally and fail to tailor personalized solutions locally under domain structural shift. We innovatively reveal that the spectral nature of graphs can well reflect inherent domain structural shifts. Correspondingly, our method overcomes it by sharing generic spectral knowledge. Moreover, we indicate the biased message-passing schemes for graph structures and propose the personalized preference module. Combining both strategies, we propose our pFGL framework FedSSP which Shares generic Spectral knowledge while satisfying graph Preferences. Furthermore, We perform extensive experiments on cross-dataset and cross-domain settings to demonstrate the superiority of our framework. The code is available at https://github.com/OakleyTan/FedSSP.
Distribution shifts on graphs -- the discrepancies in data distribution between training and employing a graph machine learning model -- are ubiquitous and often unavoidable in real-world scenarios. These shifts may severely deteriorate model performance, posing significant challenges for reliable graph machine learning. Consequently, there has been a surge in research on graph machine learning under distribution shifts, aiming to train models to achieve satisfactory performance on out-of-distribution (OOD) test data. In our survey, we provide an up-to-date and forward-looking review of deep graph learning under distribution shifts. Specifically, we cover three primary scenarios: graph OOD generalization, training-time graph OOD adaptation, and test-time graph OOD adaptation. We begin by formally formulating the problems and discussing various types of distribution shifts that can affect graph learning, such as covariate shifts and concept shifts. To provide a better understanding of the literature, we introduce a systematic taxonomy that classifies existing methods into model-centric and data-centric approaches, investigating the techniques used in each category. We also summarize commonly used datasets in this research area to facilitate further investigation. Finally, we point out promising research directions and the corresponding challenges to encourage further study in this vital domain. We also provide a continuously updated reading list at https://github.com/kaize0409/Awesome-Graph-OOD.
This paper addresses the problem of optimizing the allocation of labeling resources for semi-supervised belief representation learning in social networks. The objective is to strategically identify valuable messages on social media graphs that are worth labeling within a constrained budget, ultimately maximizing the task's performance. Despite the progress in unsupervised or semi-supervised methods in advancing belief and ideology representation learning on social networks and the remarkable efficacy of graph learning techniques, the availability of high-quality curated labeled social data can greatly benefit and further improve performances. Consequently, allocating labeling efforts is a critical research problem in scenarios where labeling resources are limited. This paper proposes a graph data augmentation-inspired perturbation-based active learning strategy (PerbALGraph) that progressively selects messages for labeling according to an automatic estimator, obviating human guidance. This estimator is based on the principle that messages in the network that exhibit heightened sensitivity to structural features of the observational data indicate landmark quality that significantly influences semi-supervision processes. We design the estimator to be the prediction variance under a set of designed graph perturbations, which is model-agnostic and application-independent. Extensive experiment results demonstrate the effectiveness of the proposed strategy for belief representation learning tasks.
Although recent advancements in end-to-end learning-based link prediction (LP) methods have shown remarkable capabilities, the significance of traditional similarity-based LP methods persists in unsupervised scenarios where there are no known link labels. However, the selection of node features for similarity computation in similarity-based LP can be challenging. Less informative node features can result in suboptimal LP performance. To address these challenges, we integrate self-supervised graph learning techniques into similarity-based LP and propose a novel method: Self-Supervised Similarity-based LP (3SLP). 3SLP is suitable for the unsupervised condition of similarity-based LP without the assistance of known link labels. Specifically, 3SLP introduces a dual-view contrastive node representation learning (DCNRL) with crafted data augmentation and node representation learning. DCNRL is dedicated to developing more informative node representations, replacing the node attributes as inputs in the similarity-based LP backbone. Extensive experiments over benchmark datasets demonstrate the salient improvement of 3SLP, outperforming the baseline of traditional similarity-based LP by up to 21.2% (AUC).
Causal discovery in real-world systems, such as biological networks, is often complicated by feedback loops and incomplete data. Standard algorithms, which assume acyclic structures or fully observed data, struggle with these challenges. To address this gap, we propose MissNODAG, a differentiable framework for learning both the underlying cyclic causal graph and the missingness mechanism from partially observed data, including data missing not at random. Our framework integrates an additive noise model with an expectation-maximization procedure, alternating between imputing missing values and optimizing the observed data likelihood, to uncover both the cyclic structures and the missingness mechanism. We demonstrate the effectiveness of MissNODAG through synthetic experiments and an application to real-world gene perturbation data.