Continual learning has emerged as a crucial paradigm for learning from sequential data while preserving previous knowledge. In the realm of continual graph learning, where graphs continuously evolve based on streaming graph data, continual graph learning presents unique challenges that require adaptive and efficient graph learning methods in addition to the problem of catastrophic forgetting. The first challenge arises from the interdependencies between different graph data, where previous graphs can influence new data distributions. The second challenge lies in the efficiency concern when dealing with large graphs. To addresses these two problems, we produce an Efficient Continual Graph Learner (E-CGL) in this paper. We tackle the interdependencies issue by demonstrating the effectiveness of replay strategies and introducing a combined sampling strategy that considers both node importance and diversity. To overcome the limitation of efficiency, E-CGL leverages a simple yet effective MLP model that shares weights with a GCN during training, achieving acceleration by circumventing the computationally expensive message passing process. Our method comprehensively surpasses nine baselines on four graph continual learning datasets under two settings, meanwhile E-CGL largely reduces the catastrophic forgetting problem down to an average of -1.1%. Additionally, E-CGL achieves an average of 15.83x training time acceleration and 4.89x inference time acceleration across the four datasets. These results indicate that E-CGL not only effectively manages the correlation between different graph data during continual training but also enhances the efficiency of continual learning on large graphs. The code is publicly available at https://github.com/aubreygjh/E-CGL.
Designing spectral convolutional networks is a formidable task in graph learning. In traditional spectral graph neural networks (GNNs), polynomial-based methods are commonly used to design filters via the Laplacian matrix. In practical applications, however, these polynomial methods encounter inherent limitations, which primarily arise from the the low-order truncation of polynomial filters and the lack of overall modeling of the graph spectrum. This leads to poor performance of existing spectral approaches on real-world graph data, especially when the spectrum is highly concentrated or contains many numerically identical values, as they tend to apply the exact same modulation to signals with the same frequencies. To overcome these issues, in this paper, we propose Graph State Space Network (GrassNet), a novel graph neural network with theoretical support that provides a simple yet effective scheme for designing and learning arbitrary graph spectral filters. In particular, our GrassNet introduces structured state space models (SSMs) to model the correlations of graph signals at different frequencies and derives a unique rectification for each frequency in the graph spectrum. To the best of our knowledge, our work is the first to employ SSMs for the design of GNN spectral filters, and it theoretically offers greater expressive power compared with polynomial filters. Extensive experiments on nine public benchmarks reveal that GrassNet achieves superior performance in real-world graph modeling tasks.
In the fields of computer vision and robotics, accurate pixel-level correspondences are essential for enabling advanced tasks such as structure-from-motion and simultaneous localization and mapping. Recent correspondence pruning methods usually focus on learning local consistency through k-nearest neighbors, which makes it difficult to capture robust context for each correspondence. We propose CorrAdaptor, a novel architecture that introduces a dual-branch structure capable of adaptively adjusting local contexts through both explicit and implicit local graph learning. Specifically, the explicit branch uses KNN-based graphs tailored for initial neighborhood identification, while the implicit branch leverages a learnable matrix to softly assign neighbors and adaptively expand the local context scope, significantly enhancing the model's robustness and adaptability to complex image variations. Moreover, we design a motion injection module to integrate motion consistency into the network to suppress the impact of outliers and refine local context learning, resulting in substantial performance improvements. The experimental results on extensive correspondence-based tasks indicate that our CorrAdaptor achieves state-of-the-art performance both qualitatively and quantitatively. The code and pre-trained models are available at https://github.com/TaoWangzj/CorrAdaptor.
When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to jointly denoise the features and rewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.
Textual graphs are ubiquitous in real-world applications, featuring rich text information with complex relationships, which enables advanced research across various fields. Textual graph representation learning aims to generate low-dimensional feature embeddings from textual graphs that can improve the performance of downstream tasks. A high-quality feature embedding should effectively capture both the structural and the textual information in a textual graph. However, most textual graph dataset benchmarks rely on word2vec techniques to generate feature embeddings, which inherently limits their capabilities. Recent works on textual graph representation learning can be categorized into two folds: supervised and unsupervised methods. Supervised methods finetune a language model on labeled nodes, which have limited capabilities when labeled data is scarce. Unsupervised methods, on the other hand, extract feature embeddings by developing complex training pipelines. To address these limitations, we propose a novel unified unsupervised learning autoencoder framework, named Node Level Graph AutoEncoder (NodeGAE). We employ language models as the backbone of the autoencoder, with pretraining on text reconstruction. Additionally, we add an auxiliary loss term to make the feature embeddings aware of the local graph structure. Our method maintains simplicity in the training process and demonstrates generalizability across diverse textual graphs and downstream tasks. We evaluate our method on two core graph representation learning downstream tasks: node classification and link prediction. Comprehensive experiments demonstrate that our approach substantially enhances the performance of diverse graph neural networks (GNNs) across multiple textual graph datasets.
Battery life estimation is critical for optimizing battery performance and guaranteeing minimal degradation for better efficiency and reliability of battery-powered systems. The existing methods to predict the Remaining Useful Life(RUL) of Lithium-ion Batteries (LiBs) neglect the relational dependencies of the battery parameters to model the nonlinear degradation trajectories. We present the Battery GraphNets framework that jointly learns to incorporate a discrete dependency graph structure between battery parameters to capture the complex interactions and the graph-learning algorithm to model the intrinsic battery degradation for RUL prognosis. The proposed method outperforms several popular methods by a significant margin on publicly available battery datasets and achieves SOTA performance. We report the ablation studies to support the efficacy of our approach.
Learning electronic health records (EHRs) has received emerging attention because of its capability to facilitate accurate medical diagnosis. Since the EHRs contain enriched information specifying complex interactions between entities, modeling EHRs with graphs is shown to be effective in practice. The EHRs, however, present a great degree of heterogeneity, sparsity, and complexity, which hamper the performance of most of the models applied to them. Moreover, existing approaches modeling EHRs often focus on learning the representations for a single task, overlooking the multi-task nature of EHR analysis problems and resulting in limited generalizability across different tasks. In view of these limitations, we propose a novel framework for EHR modeling, namely MulT-EHR (Multi-Task EHR), which leverages a heterogeneous graph to mine the complex relations and model the heterogeneity in the EHRs. To mitigate the large degree of noise, we introduce a denoising module based on the causal inference framework to adjust for severe confounding effects and reduce noise in the EHR data. Additionally, since our model adopts a single graph neural network for simultaneous multi-task prediction, we design a multi-task learning module to leverage the inter-task knowledge to regularize the training process. Extensive empirical studies on MIMIC-III and MIMIC-IV datasets validate that the proposed method consistently outperforms the state-of-the-art designs in four popular EHR analysis tasks -- drug recommendation, and predictions of the length of stay, mortality, and readmission. Thorough ablation studies demonstrate the robustness of our method upon variations to key components and hyperparameters.
Dynamic graph learning aims to uncover evolutionary laws in real-world systems, enabling accurate social recommendation (link prediction) or early detection of cancer cells (classification). Inspired by the success of state space models, e.g., Mamba, for efficiently capturing long-term dependencies in language modeling, we propose DyG-Mamba, a new continuous state space model (SSM) for dynamic graph learning. Specifically, we first found that using inputs as control signals for SSM is not suitable for continuous-time dynamic network data with irregular sampling intervals, resulting in models being insensitive to time information and lacking generalization properties. Drawing inspiration from the Ebbinghaus forgetting curve, which suggests that memory of past events is strongly correlated with time intervals rather than specific details of the events themselves, we directly utilize irregular time spans as control signals for SSM to achieve significant robustness and generalization. Through exhaustive experiments on 12 datasets for dynamic link prediction and dynamic node classification tasks, we found that DyG-Mamba achieves state-of-the-art performance on most of the datasets, while also demonstrating significantly improved computation and memory efficiency.
Unified graph representation learning aims to produce node embeddings, which can be applied to multiple downstream applications. However, existing studies based on graph neural networks and language models either suffer from the limitations of numerous training needed toward specific downstream predictions or have shallow semantic features. In this work, we propose a novel Path-LLM model to learn unified graph representation, which leverages a powerful large language model (LLM) to incorporate our proposed path features. Our Path-LLM framework consists of several well-designed techniques. First, we develop a new mechanism of long-to-short shortest path (L2SP) selection, which covers essential connections between different dense groups. An in-depth comparison of different path selection plans is offered to illustrate the strength of our designed L2SP. Then, we design path textualization to obtain L2SP-based training texts. Next, we feed the texts into a self-supervised LLM training process to learn embeddings. Extensive experiments on benchmarks validate the superiority of Path-LLM against the state-of-the-art WalkLM method on two classical graph learning tasks (node classification and link prediction) and one NP-hard graph query processing task (keyword search), meanwhile saving more than 90% of training paths.
The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders practical implementation. In this article, we address this challenge by proposing a method that constructs feature vectors based on fundamental graph structural properties. We demonstrate that these features, despite their simplicity, are powerful enough to capture the intrinsic characteristics of graphs within the same class. We explore the efficacy of our approach using three distinct machine learning methods, highlighting how our feature-based classification leverages the inherent structural similarities of graphs within the same class to achieve accurate classification. A key advantage of our approach is its simplicity, which makes it accessible and adaptable to a broad range of applications, including social network analysis, bioinformatics, and cybersecurity. Furthermore, we conduct extensive experiments to validate the performance of our method, showing that it not only reveals a competitive performance but in some cases surpasses the accuracy of more complex, state-of-the-art techniques. Our findings suggest that a focus on fundamental graph features can provide a robust and efficient alternative for graph classification, offering significant potential for both research and practical applications.
This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for regression tasks was benchmarked against a collection of linear models through a combination of simulated and real-world data training studies. First, a selection of five arbitrarily designed multi-step surrogate functions were developed to reflect various features commonly found within experimental processes. A graph transformer network outperformed all tested linear models in scenarios that featured hidden interactions between process steps and sequence dependent features, while retaining equivalent performance in sequence agnostic scenarios. Then, a similar comparison was applied to real-world literature data on algorithm guided colloidal atomic layer deposition. Using the complete reaction sequence as training data, the graph neural network outperformed all linear models in predicting the three spectral properties for most training set sizes. Further implementation of graph neural networks and geometric representation of scientific processes for the prediction of experiment outcomes could lead to algorithm driven navigation of higher dimension parameter spaces and efficient exploration of more dynamic systems.
As the volume and complexity increase, graph-structured data commonly need to be split and stored across distributed systems. To enable data mining on subgraphs within these distributed systems, federated graph learning has been proposed, allowing collaborative training of Graph Neural Networks (GNNs) across clients without sharing raw node features. However, when dealing with graph structures that involve high-order relationships between nodes, known as hypergraphs, existing federated graph learning methods are less effective. In this study, we introduce FedHGL, an innovative federated hypergraph learning algorithm. FedHGL is designed to collaboratively train a comprehensive hypergraph neural network across multiple clients, facilitating mining tasks on subgraphs of a hypergraph where relationships are not merely pairwise. To address the high-order information loss between subgraphs caused by distributed storage, we introduce a pre-propagation hyperedge completion operation before the federated training process. In this pre-propagation step, cross-client feature aggregation is performed and distributed at the central server to ensure that this information can be utilized by the clients. Furthermore, by incorporating local differential privacy (LDP) mechanisms, we ensure that the original node features are not disclosed during this aggregation process. Experimental results on seven real-world datasets confirm the effectiveness of our approach and demonstrate its performance advantages over traditional federated graph learning methods.
Graph Neural Networks (GNNs) are important across different domains, such as social network analysis and recommendation systems, due to their ability to model complex relational data. This paper introduces subgraph queries as a new task for deep graph learning. Unlike traditional graph prediction tasks that focus on individual components like link prediction or node classification, subgraph queries jointly predict the components of a target subgraph based on evidence that is represented by an observed subgraph. For instance, a subgraph query can predict a set of target links and/or node labels. To answer subgraph queries, we utilize a probabilistic deep Graph Generative Model. Specifically, we inductively train a Variational Graph Auto-Encoder (VGAE) model, augmented to represent a joint distribution over links, node features and labels. Bayesian optimization is used to tune a weighting for the relative importance of links, node features and labels in a specific domain. We describe a deterministic and a sampling-based inference method for estimating subgraph probabilities from the VGAE generative graph distribution, without retraining, in zero-shot fashion. For evaluation, we apply the inference methods on a range of subgraph queries on six benchmark datasets. We find that inference from a model achieves superior predictive performance, surpassing independent prediction baselines with improvements in AUC scores ranging from 0.06 to 0.2 points, depending on the dataset.
Graph clustering, a classical task in graph learning, involves partitioning the nodes of a graph into distinct clusters. This task has applications in various real-world scenarios, such as anomaly detection, social network analysis, and community discovery. Current graph clustering methods commonly rely on module pre-training to obtain a reliable prior distribution for the model, which is then used as the optimization objective. However, these methods often overlook deeper supervised signals, leading to sub-optimal reliability of the prior distribution. To address this issue, we propose a novel deep graph clustering method called CGCN. Our approach introduces contrastive signals and deep structural information into the pre-training process. Specifically, CGCN utilizes a contrastive learning mechanism to foster information interoperability among multiple modules and allows the model to adaptively adjust the degree of information aggregation for different order structures. Our CGCN method has been experimentally validated on multiple real-world graph datasets, showcasing its ability to boost the dependability of prior clustering distributions acquired through pre-training. As a result, we observed notable enhancements in the performance of the model.
This paper addresses the challenge of out-of-distribution (OOD) generalization in graph machine learning, a field rapidly advancing yet grappling with the discrepancy between source and target data distributions. Traditional graph learning algorithms, based on the assumption of uniform distribution between training and test data, falter in real-world scenarios where this assumption fails, resulting in suboptimal performance. A principal factor contributing to this suboptimal performance is the inherent simplicity bias of neural networks trained through Stochastic Gradient Descent (SGD), which prefer simpler features over more complex yet equally or more predictive ones. This bias leads to a reliance on spurious correlations, adversely affecting OOD performance in various tasks such as image recognition, natural language understanding, and graph classification. Current methodologies, including subgraph-mixup and information bottleneck approaches, have achieved partial success but struggle to overcome simplicity bias, often reinforcing spurious correlations. To tackle this, we propose DIVE, training a collection of models to focus on all label-predictive subgraphs by encouraging the models to foster divergence on the subgraph mask, which circumvents the limitation of a model solely focusing on the subgraph corresponding to simple structural patterns. Specifically, we employs a regularizer to punish overlap in extracted subgraphs across models, thereby encouraging different models to concentrate on distinct structural patterns. Model selection for robust OOD performance is achieved through validation accuracy. Tested across four datasets from GOOD benchmark and one dataset from DrugOOD benchmark, our approach demonstrates significant improvement over existing methods, effectively addressing the simplicity bias and enhancing generalization in graph machine learning.
Graph learning methods have been extensively applied in diverse application areas. However, what kind of inherent graph properties e.g. graph proximity, graph structural information has been encoded into graph representation learning for downstream tasks is still under-explored. In this paper, we propose a novel graph probing framework (GraphProbe) to investigate and interpret whether the family of graph learning methods has encoded different levels of knowledge in graph representation learning. Based on the intrinsic properties of graphs, we design three probes to systematically investigate the graph representation learning process from different perspectives, respectively the node-wise level, the path-wise level, and the structural level. We construct a thorough evaluation benchmark with nine representative graph learning methods from random walk based approaches, basic graph neural networks and self-supervised graph methods, and probe them on six benchmark datasets for node classification, link prediction and graph classification. The experimental evaluation verify that GraphProbe can estimate the capability of graph representation learning. Remaking results have been concluded: GCN and WeightedGCN methods are relatively versatile methods achieving better results with respect to different tasks.
Network embedding has numerous practical applications and has received extensive attention in graph learning, which aims at mapping vertices into a low-dimensional and continuous dense vector space by preserving the underlying structural properties of the graph. Many network embedding methods have been proposed, among which factorization of the Personalized PageRank (PPR for short) matrix has been empirically and theoretically well supported recently. However, several fundamental issues cannot be addressed. (1) Existing methods invoke a seminal Local Push subroutine to approximate \textit{a single} row or column of the PPR matrix. Thus, they have to execute $n$ ($n$ is the number of nodes) Local Push subroutines to obtain a provable PPR matrix, resulting in prohibitively high computational costs for large $n$. (2) The PPR matrix has limited power in capturing the structural similarity between vertices, leading to performance degradation. To overcome these dilemmas, we propose PSNE, an efficient spectral s\textbf{P}arsification method for \textbf{S}caling \textbf{N}etwork \textbf{E}mbedding, which can fast obtain the embedding vectors that retain strong structural similarities. Specifically, PSNE first designs a matrix polynomial sparser to accelerate the calculation of the PPR matrix, which has a theoretical guarantee in terms of the Frobenius norm. Subsequently, PSNE proposes a simple but effective multiple-perspective strategy to enhance further the representation power of the obtained approximate PPR matrix. Finally, PSNE applies a randomized singular value decomposition algorithm on the sparse and multiple-perspective PPR matrix to get the target embedding vectors. Experimental evaluation of real-world and synthetic datasets shows that our solutions are indeed more efficient, effective, and scalable compared with ten competitors.
Graph out-of-distribution (OOD) generalization remains a major challenge in graph learning since graph neural networks (GNNs) often suffer from severe performance degradation under distribution shifts. Invariant learning, aiming to extract invariant features across varied distributions, has recently emerged as a promising approach for OOD generation. Despite the great success of invariant learning in OOD problems for Euclidean data (i.e., images), the exploration within graph data remains constrained by the complex nature of graphs. Existing studies, such as data augmentation or causal intervention, either suffer from disruptions to invariance during the graph manipulation process or face reliability issues due to a lack of supervised signals for causal parts. In this work, we propose a novel framework, called Invariant Graph Learning based on Information bottleneck theory (InfoIGL), to extract the invariant features of graphs and enhance models' generalization ability to unseen distributions. Specifically, InfoIGL introduces a redundancy filter to compress task-irrelevant information related to environmental factors. Cooperating with our designed multi-level contrastive learning, we maximize the mutual information among graphs of the same class in the downstream classification tasks, preserving invariant features for prediction to a great extent. An appealing feature of InfoIGL is its strong generalization ability without depending on supervised signal of invariance. Experiments on both synthetic and real-world datasets demonstrate that our method achieves state-of-the-art performance under OOD generalization for graph classification tasks. The source code is available at https://github.com/maowenyu-11/InfoIGL.
Recent research on the robustness of Graph Neural Networks (GNNs) under noises or attacks has attracted great attention due to its importance in real-world applications. Most previous methods explore a single noise source, recovering corrupt node embedding by reliable structures bias or developing structure learning with reliable node features. However, the noises and attacks may come from both structures and features in graphs, making the graph denoising a dilemma and challenging problem. In this paper, we develop a unified graph denoising (UGD) framework to unravel the deadlock between structure and feature denoising. Specifically, a high-order neighborhood proximity evaluation method is proposed to recognize noisy edges, considering features may be perturbed simultaneously. Moreover, we propose to refine noisy features with reconstruction based on a graph auto-encoder. An iterative updating algorithm is further designed to optimize the framework and acquire a clean graph, thus enabling robust graph learning for downstream tasks. Our UGD framework is self-supervised and can be easily implemented as a plug-and-play module. We carry out extensive experiments, which proves the effectiveness and advantages of our method. Code is avalaible at https://github.com/YoungTimmy/UGD.
Rethink convolution-based graph neural networks (GNN) -- they characteristically suffer from limited expressiveness, over-smoothing, and over-squashing, and require specialized sparse kernels for efficient computation. Here, we design a simple graph learning module entirely free of convolution operators, coined random walk with unifying memory (RUM) neural network, where an RNN merges the topological and semantic graph features along the random walks terminating at each node. Relating the rich literature on RNN behavior and graph topology, we theoretically show and experimentally verify that RUM attenuates the aforementioned symptoms and is more expressive than the Weisfeiler-Lehman (WL) isomorphism test. On a variety of node- and graph-level classification and regression tasks, RUM not only achieves competitive performance, but is also robust, memory-efficient, scalable, and faster than the simplest convolutional GNNs.