Conditional molecular generation, aiming to generate 2D and 3D molecules that satisfy given properties, has achieved remarkable progress, thanks to the advances in deep generative models such as graph diffusion. However, existing methods generally assume that the given conditions for training and testing are consistent, failing to handle the realistic challenge when there exist distribution shifts between training and testing conditions. Invariant learning is a mainstream paradigm for addressing distribution shifts, but fusing invariant learning principles with conditional molecular generation faces three core challenges: (1) existing invariant learning methods focus on discriminative tasks and cannot be directly adapted to molecule generative tasks; (2) how to distinguish between invariant subgraph and variant subgraph of a molecule graph, which is treated as an integrated input; (3) how to fuse invariant subgraphs, variant subgraphs, and property conditions for effective generation. To tackle these challenges, we propose Invariant Conditional MOLecular generation (IC-MOL), a framework that combines invariant learning with graph diffusion to improve the generalization ability of conditional molecular generation under distribution shifts. Specifically, we first disentangle molecular graphs into invariant and variant subgraphs while maintaining SE(3) equivariance, an important inductive bias for molecular generation. On this basis, we further design a two-phase graph diffusion generation model. In the first phase, we generate an invariant molecular consistent with the target property. In the second phase, we propose a cross-attention mechanism to fuse variant subgraph representations and property conditions to guide the generation of complete molecules while maintaining property alignment. Extensive experiments on the benchmark dataset show that IC-MOL consistently outperforms state-of-the-art baselines across six property conditions under distribution shifts.

Graph Foundation Models (GFMs) are pre-trained on diverse source domains and adapted to unseen targets, enabling broad generalization for graph machine learning. Despite that GFMs have attracted considerable attention recently, their vulnerability to backdoor attacks remains largely underexplored. A compromised GFM can introduce backdoor behaviors into downstream applications, posing serious security risks. However, launching backdoor attacks against GFMs is non-trivial due to three key challenges. (1) Effectiveness: Attackers lack knowledge of the downstream task during pre-training, complicating the assurance that triggers reliably induce misclassifications into desired classes. (2) Stealthiness: The variability in node features across domains complicates trigger insertion that remains stealthy. (3) Persistence: Downstream fine-tuning may erase backdoor behaviors by updating model parameters. To address these challenges, we propose GFM-BA, a novel Backdoor Attack model against Graph Foundation Models. Specifically, we first design a label-free trigger association module that links the trigger to a set of prototype embeddings, eliminating the need for knowledge about downstream tasks to perform backdoor injection. Then, we introduce a node-adaptive trigger generator, dynamically producing node-specific triggers, reducing the risk of trigger detection while reliably activating the backdoor. Lastly, we develop a persistent backdoor anchoring module that firmly anchors the backdoor to fine-tuning-insensitive parameters, enhancing the persistence of the backdoor under downstream adaptation. Extensive experiments demonstrate the effectiveness, stealthiness, and persistence of GFM-BA.

Graph Transformers (GTs) have demonstrated great effectiveness across various graph analytical tasks. However, the existing GTs focus on training and testing graph data originated from the same distribution, but fail to generalize under distribution shifts. Graph invariant learning, aiming to capture generalizable graph structural patterns with labels under distribution shifts, is potentially a promising solution, but how to design attention mechanisms and positional and structural encodings (PSEs) based on graph invariant learning principles remains challenging. To solve these challenges, we introduce graph out-of-distribution generalized Transformer (GOODFormer), aiming to learn generalized graph representations by capturing invariant relationships between predictive graph structures and labels through jointly optimizing three modules. Specifically, we first develop a GT-based entropy-guided invariant subgraph disentangler to separate invariant and variant subgraphs while preserving the sharpness of the attention function. Next, we design an evolving subgraph positional and structural encoder to effectively and efficiently capture the encoding information of dynamically changing subgraphs during training. Finally, we propose an invariant learning module utilizing subgraph node representations and encodings to derive graph representations that can generalize to unseen test graphs. We also provide theoretical justifications for our method. Extensive experiments on benchmark datasets demonstrate the superiority of our method over state-of-the-art baselines under distribution shifts.

Graph representation learning encounters great difficulties under distribution shifts. This challenge has aroused considerable interest in graph out-of-distribution (OOD) generalization and detection, which can effectively handle covariate and semantic shifts, respectively. However, real-world graph tasks often involve complex unlabeled wild data with both covariate and semantic shifts, motivating a critical question: can we design a unified framework for joint graph OOD generalization and detection? Invariant graph learning, which extracts stable relationships between features and labels, offers a promising candidate for joint OOD generalization and detection, but faces three critical challenges (1) how to model invariant subgraphs with unlabeled data, (2) how to ensure graph representations benefit both tasks, and (3) how to integrate labeled and unlabeled data under proper invariance principles. To solve these challenges, we introduce Unified Graph Out-Of-Distribution generalization and detection framework (UniGOOD) with three tailored components. Specifically, to capture subgraphs without relying on labels, we first propose the distributional invariant subgraph generator to model subgraph conditional distributions. Next, to enable generalization and reliable detection, we propose the cross-invariant-subgraph spectral contrastive learning module to learn invariant representations from subgraph distributions. Finally, for accurate subgraph discovery across labeled and unlabeled graphs, we design the triple-population invariance regularizer to enforce the invariance principle through spectral graph theory. We prove that our method theoretically ensures accurate invariant subgraphs, enabling effective OOD generalization and detection. Experiments show that UniGOOD outperforms state-of-the-art baselines for both graph OOD generalization and detection tasks.

Graph Retrieval-Augmented Generation (GraphRAG) has shown great effectiveness in enhancing the reasoning abilities of Large Language Models (LLMs) by leveraging graph structures for knowledge representation and modeling complex real-world relationships. However, existing GraphRAG methods still face significant bottlenecks when handling complex problems that require multi-hop reasoning, as their query and retrieval phases are largely based on pre-defined heuristics and do not fully utilize the reasoning potentials of LLMs. To address this problem, we propose GraphRAG-R1, an adaptive GraphRAG framework by training LLMs with process-constrained outcome-based reinforcement learning (RL) to enhance the multi-hop reasoning ability. Our method can decompose complex problems, autonomously invoke retrieval tools to acquire necessary information, and perform effective reasoning. Specifically, we utilize a modified version of Group Relative Policy Optimization (GRPO) that supports rollout-with-thinking capability to train the model. Next, we design two process-constrained reward functions. To handle the shallow retrieval problem, we design a Progressive Retrieval Attenuation (PRA) reward to encourage essential retrievals. Then, to handle the over-thinking problem, we design a Cost-Aware F1 (CAF) reward to balance the model performance with computational costs. We further design a phase-dependent training strategy, containing three training stages corresponding to cold start and these two rewards. These stages empower GraphRAG with format following, behavior shaping, and smartness optimization abilities, respectively. Lastly, our method adopts a hybrid graph-textual retrieval to improve the reasoning capacity. Extensive experimental results demonstrate that GraphRAG-R1 significantly boosts LLM capabilities in solving complex reasoning problems compared to state-of-the-art GraphRAG methods on both in-domain and out-of-domain datasets. Furthermore, our framework can be flexibly integrated with various existing retrieval methods, consistently delivering performance improvements.

Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. Most existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. In this paper, we revisit why general neural networks cannot maintain transformation invariance. Our findings show that transformation-invariant and distance-preserving initial point representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNet), a straightforward and general plug-in for geometric data. Specifically, we realize transformation invariant and distance-preserving initial point representations by modifying multi-dimensional scaling and feed the representations into existing neural networks. We prove that TinvNet can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our method. We also extend our method into equivariance cases. Based on the results, we advocate that TinvNet should be considered as an essential baseline for further studies of transformation-invariant geometric deep learning.

Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To tackle the challenge, automated graph machine learning, which aims at discovering the best hyper-parameter and neural architecture configuration for different graph tasks/data without manual design, is gaining an increasing number of attentions from the research community. In this article, we extensively discuss automated graph machine learning approaches, covering hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We briefly overview existing libraries designed for either graph machine learning or automated machine learning, respectively, and further in-depth introduce AutoGL, our dedicated and the world’s first open source library for automated graph machine learning. Also, we describe a tailored benchmark that supports unified, reproducible, and efficient evaluations. Last but not least, we share our insights on future research directions for automated graph machine learning. To the best of our knowledge, this work presents systematic and comprehensive discussions of approaches, libraries, as well as research directions in automated graph machine learning.

Cross-domain recommendation (CDR) mitigates data sparsity and cold-start issues in recommendation systems. While recent CDR approaches using graph neural networks (GNNs) capture complex user-item interactions, they rely on manually designed architectures that are often suboptimal and labor-intensive. Additionally, extracting valuable behavioral information from source domains to improve target domain recommendations remains challenging. To address these challenges, we propose Behavior importance-aware Graph Neural Architecture Search (BiGNAS), a framework that jointly optimizes GNN architecture and data importance for CDR. BiGNAS introduces two key components: a Cross-Domain Customized Supernetwork and a Graph-Based Behavior Importance Perceptron. The supernetwork, as a one-shot, retrain-free module, automatically searches the optimal GNN architecture for each domain without the need for retraining. The perceptron uses auxiliary learning to dynamically assess the importance of source domain behaviors, thereby improving target domain recommendations. Extensive experiments on benchmark CDR datasets and a large-scale industry advertising dataset demonstrate that BiGNAS consistently outperforms state-of-the-art baselines. To the best of our knowledge, this is the first work to jointly optimize GNN architecture and behavior data importance for cross-domain recommendation.

The ''Frontiers in Graph Machine Learning for the Large Model Era (GMLLM'25)'' workshop focuses on advancing graph machine learning (GML) techniques in the context of increasingly large and powerful models. Graphs offer a principled way to represent structured and relational data, making them essential for capturing complex dependencies in knowledge, systems, and behaviors. As the scale and influence of foundation models grow, graph learning stands at a unique vantage point to enhance model robustness, improve interpretability, and integrate domain-specific relational priors. This workshop explores how graph learning can support emerging needs in knowledge reasoning, temporal and multi-hop inference, and AI systems. It also investigates how advances in representation learning, structure-aware generalization, and efficient graph processing can contribute to trustworthy and scalable AI systems. By convening experts in graph learning, knowledge management, and LLMs, the workshop aims to identify core challenges and opportunities of GML in the large model era.

Graph neural architecture search (NAS) has emerged as a promising approach for autonomously designing graph neural network architectures by leveraging correlations between graphs and architectures. However, existing methods merely rely on correlations, which may be spurious and vary across distributions. This reliance, without considering causal graph-architecture relationships, limits their ability to generalize under distribution shifts that are ubiquitous in real-world graph scenarios. In this paper, we propose to handle the distribution shifts in NAS process by exploiting the causal graph-architecture relationship to search for optimal architectures that can generalize under distribution shifts. Key challenges remain unexplored: discovering causal graph-architecture relationships with stable cross-distribution predictive abilities, and leveraging them to handle distribution shifts. To address these challenges, we propose a novel approach, Causal-aware Graph Neural Architecture Search (CARNAS), which is capable of capturing causal graph-architecture relationship during NAS process and discovering optimal graph architecture under distribution shifts. We propose Disentangled Causal Subgraph Identification to extract causal subgraphs with stable predictive power across distributions, followed by Graph Embedding Intervention to intervene on these subgraphs in latent space by preserving essential features while filtering out non-causal elements, and Invariant Architecture Customization to enhance their causal invariance for optimizing graph architectures. Extensive experiments on synthetic and real-world datasets show that CARNAS enhances out-of-distribution generalization by uncovering causal graph-architecture relationships during NAS.

Graph incremental learning (GIL), which continuously updates graph models by sequential knowledge acquisition, has garnered significant interest recently. However, existing GIL approaches focus on task-incremental and class-incremental scenarios within a single domain. Graph domain-incremental learning (Domain-IL), aiming at updating models across multiple graph domains, has become critical with the development of graph foundation models (GFMs), but remains unexplored in the literature. In this paper, we propose **Graph** Domain-Incremental Learning via **K**nowledge Dis**e**ntangl**e**ment and **P**res**er**vation (**GraphKeeper**), to address catastrophic forgetting in Domain-IL scenario from the perspectives of embedding shifts and decision boundary deviations. Specifically, to prevent embedding shifts and confusion across incremental graph domains, we first propose the domain-specific parameter-efficient fine-tuning together with intra- and inter-domain disentanglement objectives. Consequently, to maintain a stable decision boundary, we introduce deviation-free knowledge preservation to continuously fit incremental domains. Additionally, for graphs with unobservable domains, we perform domain-aware distribution discrimination to obtain precise embeddings. Extensive experiments demonstrate the proposed GraphKeeper achieves state-of-the-art results with 6.5%\~16.6% improvement over the runner-up with negligible forgetting. Moreover, we show GraphKeeper can be seamlessly integrated with various representative GFMs, highlighting its broad applicative potential.

Graph machine learning has been extensively studied in both academia and industry. Although booming with a vast number of emerging methods and techniques, most of the literature is built on the in-distribution hypothesis, i.e., testing and training graph data are identically distributed. However, this in-distribution hypothesis can hardly be satisfied in many real-world graph scenarios where the model performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this critical problem, out-of-distribution (OOD) generalization on graphs, which goes beyond the in-distribution hypothesis, has made great progress and attracted ever-increasing attention from the research community. In this paper, we comprehensively survey OOD generalization on graphs and present a detailed review of recent advances in this area. First, we provide a formal problem definition of OOD generalization on graphs. Second, we categorize existing methods into three classes from conceptually different perspectives, i.e., data, model, and learning strategy, based on their positions in the graph machine learning pipeline, followed by detailed discussions for each category. We also review the theories related to OOD generalization on graphs and introduce the commonly used graph datasets for thorough evaluations. Finally, we share our insights on future research directions.

Multimodal graph neural architecture search (MGNAS) has shown great success for automatically designing the optimal multimodal graph neural network (MGNN) architecture by leveraging multimodal representation, crossmodal information and graph structure in one unified framework. However, existing MGNAS fails to handle distribution shifts that naturally exist in multimodal graph data, since the searched architectures inevitably capture spurious statistical correlations under distribution shifts. To solve this problem, we propose a novel Out-of-distribution Generalized Multimodal Graph Neural Architecture Search (OMG-NAS) method which optimizes the MGNN architecture with respect to its performance on decorrelated OOD data. Specifically, we propose a multimodal graph representation decorrelation strategy, which encourages the searched MGNN model to output representations that eliminate spurious correlations through iteratively optimizing the feature weights and controller. In addition, we propose a global sample weight estimator that facilitates the sharing of optimal sample weights learned from existing architectures. This design promotes the effective estimation of the sample weights for candidate MGNN architectures to generate decorrelated multimodal graph representations, concentrating more on the truly predictive relations between invariant features and ground-truth labels. Extensive experiments on real-world multimodal graph datasets demonstrate the superiority of our proposed method over SOTA baselines.

Graph neural architecture search (NAS) has achieved great success in designing architectures for graph data processing.However, distribution shifts pose great challenges for graph NAS, since the optimal searched architectures for the training graph data may fail to generalize to the unseen test graph data. The sole prior work tackles this problem by customizing architectures for each graph instance through learning graph structural information, but failed to consider data augmentation during training, which has been proven by existing works to be able to improve generalization.In this paper, we propose Data-augmented Curriculum Graph Neural Architecture Search (DCGAS), which learns an architecture customizer with good generalizability to data under distribution shifts. Specifically, we design an embedding-guided data generator, which can generate sufficient graphs for training to help the model better capture graph structural information. In addition, we design a two-factor uncertainty-based curriculum weighting strategy, which can evaluate the importance of data in enabling the model to learn key information in real-world distribution and reweight them during training. Experimental results on synthetic datasets and real datasets with distribution shifts demonstrate that our proposed method learns generalizable mappings and outperforms existing methods.

Graph neural networks (GNNs) have achieved impressive performance when testing and training graph data come from identical distribution. However, existing GNNs lack out-of-distribution generalization abilities so that their performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this problem, we propose an out-of-distribution generalized graph neural network (OOD-GNN) for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. OOD-GNN employs a novel nonlinear graph representation decorrelation method utilizing random Fourier features, which encourages the model to eliminate the statistical dependence between relevant and irrelevant graph representations through iteratively optimizing the sample graph weights and graph encoder. The learned weights help the graph encoder to get rid of spurious correlations and, in turn, concentrate more on the true connection between learned discriminative graph representations and their ground-truth labels. We conduct extensive experiments to validate the out-of-distribution generalization abilities on two synthetic and 12 real-world datasets with distribution shifts. The results demonstrate that our proposed OOD-GNN significantly outperforms state-of-the-art baselines.

Cross-device scenarios have become increasingly common, where non-independently and identically distributed (non-IID) data is generated and stored in different devices. However, the existing cross-device NAS methods only search for a fixed architecture for different devices, neglecting that different devices have varying hardware characteristics and data distributions. In this paper, we propose a novel NAS framework that can customize the most suitable architecture for each device and its associated dataset. Specifically, we propose a decoupled data feature extractor and a device feature extractor to characterize the complex distributions of the different datasets and diverse hardware features. Then, we propose a prototype matcher to customize the operators and shape selection parameters of architectures. Experiments on ImageNet and CIFAR-10 show that our method can discover more efficient and effective architectures in cross-device scenarios than the existing approaches. To the best of our knowledge, this is the first exploration on customized cross-device NAS problem.

Graph out-of-distribution (OOD) generalization, aiming to generalize graph neural networks (GNNs) under distribution shifts between training and testing environments, has attracted ever-increasing attention recently. However, existing literature heavily relies on sufficient task-dependent graph labels, which are often scarce or even unavailable, limiting their applications in real-world scenarios. In this paper, we study the self-supervised graph OOD generalization problem, i.e., learning GNNs capable of achieving relatively stable performances under distribution shifts without graph labels. However, the problem remains largely unexplored, with the critical challenge that the invariant and variant information are highly entangled in graphs. To solve this problem, we propose an OOD generalized disentangled graph contrastive learning model (OOD-GCL), which is capable of learning disentangled graph-level representations with self-supervision that can handle distribution shifts between training and testing graph data. Specifically, we first introduce a disentangled graph encoder to map each input graph into the factorized graph representation. Then we propose a tailored disentangled invariant self-supervised learning module to maximize predictive ability of the representations and make sure the representations other than from one specific channel are invariant to the environments partitioned by this latent factor for excluding the information corresponding to this latent factor for disentanglement. Finally, the disentangled graph representations are fed into a linear predictor and finetuned for the downstream tasks. We provide comprehensive theoretical analyses to show that our model can learn disentangled graph representations and achieve OOD generalization. Extensive experiments on real-world datasets demonstrate the superiority of our model against state-of-the-art baselines under distribution shifts for graph classification tasks.

The existing graph neural architecture search (GNAS) methods assume that the graph tasks are static during the search process, ignoring the ubiquitous scenarios where sequential graph tasks come in a continual fashion. Moreover, existing GNAS works resort to entangled graph factors during the architecture search process, resulting in the catastrophic forgetting problems. In this paper, we study the problem of continual graph neural architecture search that is expected to continually search the architecture to learn new graph tasks without forgetting the past, which remains largely unexplored in the literature. However, this problem poses the challenge of architecture conflicts, i.e., the optimal architecture for the new graph task may have performance deterioration and thus sub-optimal for past tasks. To address the challenge, we propose a novel Disentangled Continual Graph Neural Architecture Search with Invariant Modularization (GASIM) method, which is able to continually search the optimal architectures without forgetting past knowledge. Specifically, we first design a modular graph architecture super-network incorporating multiple modules to enable searching architecture with factor expertise. Second, we propose a factor-based task-module router that discovers the latent graph factors and routes the incoming task to the best suitable architecture module to alleviate the forgetting problem induced by architecture conflicts. Finally, we propose an invariant architecture search mechanism to capture the shared knowledge among tasks. Extensive experiments on real-world datasets demonstrate that the proposed method achieves state-of-the-art performance against baselines in continual graph neural architecture search.

Graph Neural Architecture Search (GNAS) has achieved superior performance on various graph-structured tasks. However, existing GNAS studies overlook the applications of GNAS in resource-constraint scenarios. This paper proposes to design a joint graph data and architecture mechanism, which identifies important sub-architectures via the valuable graph data. To search for optimal lightweight Graph Neural Networks (GNNs), we propose a Lightweight Graph Neural Architecture Search with Graph SparsIfication and Network Pruning (GASSIP) method. In particular, GASSIP comprises an operation-pruned architecture search module to enable efficient lightweight GNN search. Meanwhile, we design a novel curriculum graph data sparsification module with an architecture-aware edge-removing difficulty measurement to help select optimal sub-architectures. With the aid of two differentiable masks, we iteratively optimize these two modules to efficiently search for the optimal lightweight architecture. Extensive experiments on five benchmarks demonstrate the effectiveness of GASSIP. Particularly, our method achieves on-par or even higher node classification performance with half or fewer model parameters of searched GNNs and a sparser graph.

In an era marked by the increasing adoption of Large Language Models (LLMs) for various tasks, there is a growing focus on exploring LLMs' capabilities in handling web data, particularly graph data. Dynamic graphs, which capture temporal network evolution patterns, are ubiquitous in real-world web data. Evaluating LLMs' competence in understanding spatial-temporal information on dynamic graphs is essential for their adoption in web applications, which remains unexplored in the literature. In this paper, we bridge the gap via proposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic graphs, to the best of our knowledge, for the first time. Specifically, we propose the LLM4DyG benchmark, which includes nine specially designed tasks considering the capability evaluation of LLMs from both temporal and spatial dimensions. Then, we conduct extensive experiments to analyze the impacts of different data generators, data statistics, prompting techniques, and LLMs on the model performance. Finally, we propose Disentangled Spatial-Temporal Thoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal understanding abilities. Our main observations are: 1) LLMs have preliminary spatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph tasks show increasing difficulties for LLMs as the graph size and density increase, while not sensitive to the time span and data generation mechanism, 3) the proposed DST2 prompting method can help to improve LLMs' spatial-temporal understanding abilities on dynamic graphs for most tasks. The data and codes are publicly available at Github.

Node representation learning methods, such as graph neural networks, show promising results when testing and training graph data come from the same distribution. However, the existing approaches fail to generalize under distribution shifts when the nodes reside in multiple latent environments. How to learn invariant node representations to handle distribution shifts with multiple latent environments remains unexplored. In this article, we propose a novel I nvariant N ode representation L earning (INL) approach capable of generating invariant node representations based on the invariant patterns under distribution shifts with multiple latent environments by leveraging the invariance principle. Specifically, we define invariant and variant patterns as ego-subgraphs of each node and identify the invariant ego-subgraphs through jointly accounting for node features and graph structures. To infer the latent environments of nodes, we propose a contrastive modularity-based graph clustering method based on the variant patterns. We further propose an invariant learning module to learn node representations that can generalize to distribution shifts. We theoretically show that our proposed method can achieve guaranteed performance under distribution shifts. Extensive experiments on both synthetic and real-world node classification benchmarks demonstrate that our method greatly outperforms state-of-the-art baselines under distribution shifts.

Dynamic heterogeneous graph neural networks (DHGNNs) have been shown to be effective in handling the ubiquitous dynamic heterogeneous graphs. However, the existing DHGNNs are hand-designed, requiring extensive human efforts and failing to adapt to diverse dynamic heterogeneous graph scenarios. In this paper, we propose to automate the design of DHGNN, which faces two major challenges: 1) how to design the search space to jointly consider the spatial-temporal dependencies and heterogeneous interactions in graphs; 2) how to design an efficient search algorithm in the potentially large and complex search space. To tackle these challenges, we propose a novel Dynamic Heterogeneous Graph Attention Search (DHGAS) method. Our proposed method can automatically discover the optimal DHGNN architecture and adapt to various dynamic heterogeneous graph scenarios without human guidance. In particular, we first propose a unified dynamic heterogeneous graph attention (DHGA) framework, which enables each node to jointly attend its heterogeneous and dynamic neighbors. Based on the framework, we design a localization space to determine where the attention should be applied and a parameterization space to determine how the attention should be parameterized. Lastly, we design a multi-stage differentiable search algorithm to efficiently explore the search space. Extensive experiments on real-world dynamic heterogeneous graph datasets demonstrate that our proposed method significantly outperforms state-of-the-art baselines for tasks including link prediction, node classification and node regression. To the best of our knowledge, DHGAS is the first dynamic heterogeneous graph neural architecture search method.

Graph Neural Networks (GNNs) obtain tremendous success in modeling relational data. Still, they are prone to adversarial attacks, which are massive threats to applying GNNs to risk-sensitive domains. Existing defensive methods neither guarantee performance facing new data/tasks or adversarial attacks nor provide insights to understand GNN robustness from an architectural perspective. Neural Architecture Search (NAS) has the potential to solve this problem by automating GNN architecture designs. Nevertheless, current graph NAS approaches lack robust design and are vulnerable to adversarial attacks. To tackle these challenges, we propose a novel Robust Neural Architecture search framework for GNNs (G-RNA). Specifically, we design a robust search space for the message-passing mechanism by adding graph structure mask operations into the search space, which comprises various defensive operation candidates and allows us to search for defensive GNNs. Furthermore, we define a robustness metric to guide the search procedure, which helps to filter robust architectures. In this way, G-RNA helps understand GNN robustness from an architectural perspective and effectively searches for optimal adversarial robust GNNs. Extensive experimental results on benchmark datasets show that G-RNA significantly outperforms manually designed robust GNNs and vanilla graph NAS baselines by 12.1% to 23.4% under adversarial attacks.

Human behaviors in recommendation systems are driven by many high-level, complex, and evolving intentions behind their decision making processes. In order to achieve better performance, it is important for recommendation systems to be aware of user intentions besides considering the historical interaction behaviors. However, user intentions are seldom fully or easily observed in practice, so that the existing works are incapable of fully tracking and modeling user intentions, not to mention using them effectively into recommendation. In this paper, we present the Intention-Aware Sequential Recommendation (ISRec) method, for capturing the underlying intentions of each user that may lead to her next consumption behavior and improving recommendation performance. Specifically, we first extract the intentions of the target user from sequential contexts, then take complex intent transition into account through the message-passing mechanism on an intention graph, and finally obtain the future intentions of this target user from inference on the intention graph. The sequential recommendation for a user will be made based on the predicted user intentions, offering more transparent and explainable intermediate results for each recommendation. Extensive experiments on various real-world datasets demonstrate the superiority of our method against several state-of-the-art baselines in sequential recommendation in terms of different metrics.

Graph neural architecture search (GraphNAS) has shown great potential for automatically designing graph neural architectures for graph related tasks. However, multi-task GraphNAS capable of handling multiple tasks simultaneously has been largely unexplored in literature, posing great challenges to capture the complex relations and influences among different tasks. To tackle this problem, we propose a novel multi-task graph neural architecture search with task-aware collaboration and curriculum (MTGC3), which is able to simultaneously discover optimal architectures for different tasks and learn the collaborative relationships among different tasks in a joint manner. Specifically, we design the layer-wise disentangled supernet capable of managing multiple architectures in a unified framework, which combines with our proposed soft task-collaborative module to learn the transferability relationships between tasks. We further develop the task-wise curriculum training strategy to improve the architecture search procedure via reweighing the influence of different tasks based on task difficulties. Extensive experiments show that our proposed MTGC3 model achieves state-of-the-art performance against several baselines in multi-task scenarios, demonstrating its ability to discover effective architectures and capture the collaborative relationships for multiple tasks.

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As the generation of dynamic graphs is heavily influenced by latent environments, investigating their impacts on the out-of-distribution (OOD) generalization is critical. However, it remains unexplored with the following two major challenges: **(1)** How to properly model and infer the complex environments on dynamic graphs with distribution shifts? **(2)** How to discover invariant patterns given inferred spatio-temporal environments? To solve these challenges, we propose a novel **E**nvironment-**A**ware dynamic **G**raph **LE**arning (**EAGLE**) framework for OOD generalization by modeling complex coupled environments and exploiting spatio-temporal invariant patterns. Specifically, we first design the environment-aware EA-DGNN to model environments by multi-channel environments disentangling. Then, we propose an environment instantiation mechanism for environment diversification with inferred distributions. Finally, we discriminate spatio-temporal invariant patterns for out-of-distribution prediction by the invariant pattern recognition mechanism and perform fine-grained causal interventions node-wisely with a mixture of instantiated environment samples. Experiments on real-world and synthetic dynamic graph datasets demonstrate the superiority of our method against state-of-the-art baselines under distribution shifts. To the best of our knowledge, we are the first to study OOD generalization on dynamic graphs from the environment learning perspective.

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts.

The existing graph neural architecture search (GNAS) methods heavily rely on supervised labels during the search process, failing to handle ubiquitous scenarios where supervisions are not available. In this paper, we study the problem of unsupervised graph neural architecture search, which remains unexplored in the literature. The key problem is to discover the latent graph factors that drive the formation of graph data as well as the underlying relations between the factors and the optimal neural architectures. Handling this problem is challenging given that the latent graph factors together with architectures are highly entangled due to the nature of the graph and the complexity of the neural architecture search process. To address the challenge, we propose a novel Disentangled Self-supervised Graph Neural Architecture Search (DSGAS) model, which is able to discover the optimal architectures capturing various latent graph factors in a self-supervised fashion based on unlabeled graph data. Specifically, we first design a disentangled graph super-network capable of incorporating multiple architectures with factor-wise disentanglement, which are optimized simultaneously. Then, we estimate the performance of architectures under different factors by our proposed self-supervised training with joint architecture-graph disentanglement. Finally, we propose a contrastive search with architecture augmentations to discover architectures with factor-specific expertise. Extensive experiments on 11 real-world datasets demonstrate that the proposed model is able to achieve state-of-the-art performance against several baseline methods in an unsupervised manner.

Graph neural networks (GNNs) have achieved impressive performance when testing and training graph data come from identical distribution. However, existing GNNs lack out-of-distribution generalization abilities so that their performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this problem, in this work, we propose an out-of-distribution generalized graph neural network (OOD-GNN) for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. Our proposedOOD-GNNemploys a novel nonlinear graph representation decorrelation method utilizing random Fourier features, which encourages the model to eliminate the statistical dependence between relevant and irrelevant graph representations through iteratively optimizing the sample graph weights and graph encoder. We further present a global weight estimator to learn weights for training graphs such that variables in graph representations are forced to be independent. The learned weights help the graph encoder to get rid of spurious correlations and, in turn, concentrate more on the true connection between learned discriminative graph representations and their ground-truth labels. We conduct extensive experiments to validate the out-of-distribution generalization abilities on two synthetic and 12 real-world datasets with distribution shifts. The results demonstrate that our proposedOOD-GNNsignificantly outperforms state-of-the-art baselines.

Self-supervised learning for graph neural networks has attracted considerable attention and shows notable successes in graph representation learning. However, the formation of a real-world graph typically arises from highly complex interactions of many latent factors. The existing self-supervised learning methods for GNNs are inherently holistic and neglect the entanglement of the latent factors, resulting in suboptimal learned representations for downstream tasks and difficult to be interpreted. Learning disentangled graph representations with self-supervised learning poses great challenges and remains largely ignored by the existing literature. In this paper, we introduce Independence Promoted Disentangled Graph Contrastive Learning (IDGCL) method, which can learn disentangled graph-level representations with self-supervision. In particular, we first identify the latent factors of the input graph and derive its factorized representations. Then we propose a factor-wise discrimination objective in a contrastive learning manner, which can force the factorized representations to independently reflect the expressive information from different latent factors. To further promote the independence between the representations, we employ the Hilbert-Schmidt Independence Criterion to eliminate the dependence among different representations, which is effectively integrated into the self-supervised framework as a regularizer. Extensive experiments on synthetic and real-world datasets demonstrate the superiority of our method against several state-of-the-art baselines.

Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Although sufficiently deep GNNs are shown theoretically capable of fully preserving graph structures, most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. To overcome this fundamental challenge, we propose Eigen-GNN, a simple yet effective and general plug-in module to boost GNNs ability in preserving graph structures. Specifically, we integrate the eigenspace of graph structures with GNNs by treating GNNs as a type of dimensionality reduction and expanding the initial dimensionality reduction bases. Without needing to increase depths, Eigen-GNN possesses more flexibilities in handling both feature-driven and structure-driven tasks since the initial bases contain both node features and graph structures. We present extensive experimental results to demonstrate the effectiveness of Eigen-GNN for tasks including node classification, link prediction, and graph isomorphism tests.

Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. Both properties are needed to tackle some challenging graph problems, such as finding communities and leaders. In this paper, we first analytically show that the existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. Then, we propose Stochastic Message Passing (SMP) model, a general and simple GNN to maintain both proximity-awareness and permutation-equivariance. In order to preserve node proximities, we augment the existing GNNs with stochastic node representations. We theoretically prove that the mechanism can enable GNNs to preserve node proximities, and at the same time, maintain permutation-equivariance with certain parametrization. We report extensive experimental results on ten datasets and demonstrate the effectiveness and efficiency of SMP for various typical graph mining tasks, including graph reconstruction, node classification, and link prediction.

Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are independent and identically distributed. However, the existing literature fails to solve TSP instances when training and testing data have different distributions. Concretely, we find that different training and testing distribution will result in more difficult TSP instances, i.e., the solution obtained by the model has a large gap from the optimal solution. To tackle this problem, in this work, we study learning-based TSP methods when training and testing data have different distributions using adaptive-hardness, i.e., how difficult a TSP instance can be for a solver. This problem is challenging because it is non-trivial to (1) define hardness measurement quantitatively; (2) efficiently and continuously generate sufficiently hard TSP instances upon model training; (3) fully utilize instances with different levels of hardness to learn a more powerful TSP solver. To solve these challenges, we first propose a principled hardness measurement to quantify the hardness of TSP instances. Then, we propose a hardness-adaptive generator to generate instances with different hardness. We further propose a curriculum learner fully utilizing these instances to train the TSP solver. Experiments show that our hardness-adaptive generator can generate instances ten times harder than the existing methods, and our proposed method achieves significant improvement over state-of-the-art models in terms of the optimality gap. The codes are publicly available.

Generating programs to describe visual observations has gained much research attention recently. However, most of the existing approaches are based on non-parametric primitive functions, making them unable to handle complex visual scenes involving many attributes and details. In this paper, we propose the concept of parametric visual program induction. Learning to generate parametric programs for visual scenes is challenging due to the huge number of function variants and the complex function correlations. To solve these challenges, we propose the method of function modularization, capable of dealing with numerous function variants and complex correlations. Specifically, we model each parametric function as a multi-head self-contained neural module to cover different function variants. Moreover, to eliminate the complex correlations between functions, we propose the hierarchical heterogeneous Monto-Carlo tree search (H2MCTS) algorithm which can provide high-quality uncorrelated supervision during training, and serve as an efficient searching technique during testing. We demonstrate the superiority of the proposed method on three visual program induction datasets involving parametric primitive functions. Experimental results show that our proposed model is able to significantly outperform the state-of-the-art baseline methods in terms of generating accurate programs.

Graph Neural Architecture Search (GNAS) has become a powerful method in automatically discovering suitable Graph Neural Network (GNN) architectures for different tasks. However, existing approaches fail to handle large-scale graphs because current performance estimation strategies in GNAS are computationally expensive for large-scale graphs and suffer from consistency collapse issues. To tackle these problems, we propose the Graph ArchitectUre Search at Scale (GAUSS) method that can handle large-scale graphs by designing an efficient light-weight supernet and the joint architecture-graph sampling. In particular, a graph sampling-based single-path one-shot supernet is proposed to reduce the computation burden. To address the consistency collapse issues, we further explicitly consider the joint architecture-graph sampling through a novel architecture peer learning mechanism on the sampled sub-graphs and an architecture importance sampling algorithm. Our proposed framework is able to smooth the highly non-convex optimization objective and stabilize the architecture sampling process. We provide theoretical analyses on GAUSS and empirically evaluate it on five datasets whose vertex sizes range from 10^4 to 10^8. The experimental results demonstrate substantial improvements of GAUSS over other GNAS baselines on all datasets. To the best of our knowledge, the proposed GAUSS method is the first graph neural architecture search framework that can handle graphs with billions of edges within 1 GPU day.

Graph neural architecture search has shown great potentials for automatically designing graph neural network (GNN) architectures for graph classification tasks. However, when there is a distribution shift between training and testing graphs, the existing approaches fail to deal with the problem of adapting to unknown test graph structures since they only search for a fixed architecture for all graphs. To solve this problem, we propose a novel GRACES model which is able to generalize under distribution shifts through tailoring a customized GNN architecture suitable for each graph instance with unknown distribution. Specifically, we design a self-supervised disentangled graph encoder to characterize invariant factors hidden in diverse graph structures. Then, we propose a prototype-based architecture customization strategy to generate the most suitable GNN architecture weights in a continuous space for each graph instance. We further propose a customized super-network to share weights among different architectures for the sake of efficient training. Extensive experiments on both synthetic and real-world datasets demonstrate that our proposed GRACES model can adapt to diverse graph structures and achieve state-of-the-art performance for graph classification tasks under distribution shifts.

Graph representation learning has shown effectiveness when testing and training graph data come from the same distribution, but most existing approaches fail to generalize under distribution shifts. Invariant learning, backed by the invariance principle from causality, can achieve guaranteed generalization under distribution shifts in theory and has shown great successes in practice. However, invariant learning for graphs under distribution shifts remains unexplored and challenging. To solve this problem, we propose Graph Invariant Learning (GIL) model capable of learning generalized graph representations under distribution shifts. Our proposed method can capture the invariant relationships between predictive graph structural information and labels in a mixture of latent environments through jointly optimizing three tailored modules. Specifically, we first design a GNN-based subgraph generator to identify invariant subgraphs. Then we use the variant subgraphs, i.e., complements of invariant subgraphs, to infer the latent environment labels. We further propose an invariant learning module to learn graph representations that can generalize to unknown test graphs. Theoretical justifications for our proposed method are also provided. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of our method against state-of-the-art baselines under distribution shifts for the graph classification task.

Graph neural architecture search (GraphNAS) has recently aroused considerable attention in both academia and industry. However, two key challenges seriously hinder the further research of GraphNAS. First, since there is no consensus for the experimental setting, the empirical results in different research papers are often not comparable and even not reproducible, leading to unfair comparisons. Secondly, GraphNAS often needs extensive computations, which makes it highly inefficient and inaccessible to researchers without access to large-scale computation. To solve these challenges, we propose NAS-Bench-Graph, a tailored benchmark that supports unified, reproducible, and efficient evaluations for GraphNAS. Specifically, we construct a unified, expressive yet compact search space, covering 26,206 unique graph neural network (GNN) architectures and propose a principled evaluation protocol. To avoid unnecessary repetitive training, we have trained and evaluated all of these architectures on nine representative graph datasets, recording detailed metrics including train, validation, and test performance in each epoch, the latency, the number of parameters, etc. Based on our proposed benchmark, the performance of GNN architectures can be directly obtained by a look-up table without any further computation, which enables fair, fully reproducible, and efficient comparisons. To demonstrate its usage, we make in-depth analyses of our proposed NAS-Bench-Graph, revealing several interesting findings for GraphNAS. We also showcase how the benchmark can be easily compatible with GraphNAS open libraries such as AutoGL and NNI. To the best of our knowledge, our work is the first benchmark for graph neural architecture search.

Dynamic graph neural networks (DyGNNs) have demonstrated powerful predictive abilities by exploiting graph structural and temporal dynamics. However, the existing DyGNNs fail to handle distribution shifts, which naturally exist in dynamic graphs, mainly because the patterns exploited by DyGNNs may be variant with respect to labels under distribution shifts. In this paper, we propose to handle spatio-temporal distribution shifts in dynamic graphs by discovering and utilizing {\it invariant patterns}, i.e., structures and features whose predictive abilities are stable across distribution shifts, which faces two key challenges: 1) How to discover the complex variant and invariant spatio-temporal patterns in dynamic graphs, which involve both time-varying graph structures and node features. 2) How to handle spatio-temporal distribution shifts with the discovered variant and invariant patterns. To tackle these challenges, we propose the Disentangled Intervention-based Dynamic graph Attention networks (DIDA). Our proposed method can effectively handle spatio-temporal distribution shifts in dynamic graphs by discovering and fully utilizing invariant spatio-temporal patterns. Specifically, we first propose a disentangled spatio-temporal attention network to capture the variant and invariant patterns. Then, we design a spatio-temporal intervention mechanism to create multiple interventional distributions by sampling and reassembling variant patterns across neighborhoods and time stamps to eliminate the spurious impacts of variant patterns. Lastly, we propose an invariance regularization term to minimize the variance of predictions in intervened distributions so that our model can make predictions based on invariant patterns with stable predictive abilities and therefore handle distribution shifts. Experiments on three real-world datasets and one synthetic dataset demonstrate the superiority of our method over state-of-the-art baselines under distribution shifts. Our work is the first study of spatio-temporal distribution shifts in dynamic graphs, to the best of our knowledge.

Real-world recommendation systems need to deal with millions of item candidates. Therefore, most practical large-scale recommendation systems usually contain two modules. The matching module aims to efficiently retrieve hundreds of high-quality items from large corpora, while the ranking module aims to generate specific ranks for these items. Recommendation diversity is an essential factor that strongly impacts user experience. There are lots of efforts that have explored recommendation diversity in ranking, while the matching module should take more responsibility for diversity. In this article, we propose a novel Heterogeneous graph neural network framework for diversified recommendation (GraphDR) in matching to improve both recommendation accuracy and diversity. Specifically, GraphDR builds a huge heterogeneous preference network to record different types of user preferences, and conducts a field-level heterogeneous graph attention network for node aggregation. We conduct a neighbor-similarity based loss with a multi-channel matching to improve both accuracy and diversity. In experiments, we conduct extensive online and offline evaluations on a real-world recommendation system with various accuracy and diversity metrics and achieve significant improvements. GraphDR has been deployed on a well-known recommendation system named WeChat Top Stories, which affects millions of users. The source code will be released inhttps://github.com/lqfarmer/GraphDR.

Human behaviors in recommendation systems are driven by many high-level, complex, and evolving intentions behind their decision making processes. In order to achieve better performance, it is important for recommendation systems to be aware of user intentions besides considering the historical interaction behaviors. However, user intentions are seldom fully or easily observed in practice, so that the existing works are incapable of fully tracking and modeling user intentions, not to mention using them effectively into recommendation. In this paper, we present theIntention-AwareSequentialRecommendation (ISRec) method, for capturing the underlying intentions of each user that may lead to her next consumption behavior and improving recommendation performance. Specifically, we first extract the intentions of the target user from sequential contexts, then take complex intent transition into account through the message-passing mechanism on an intention graph, and finally obtain the future intentions of this target user from inference on the intention graph. The sequential recommendation for a user will be made based on the predicted user intentions, offering more transparent and explainable intermediate results for each recommendation. Extensive experiments on various real-world datasets demonstrate the superiority of our method against several state-of-the-art baselines in sequential recommendation in terms of different metrics.

Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique characteristics of graphs. Recently, substantial research efforts have been devoted to applying deep learning methods to graphs, resulting in beneficial advances in graph analysis techniques. In this survey, we comprehensively review the different types of deep learning methods on graphs. We divide the existing methods into five categories based on their model architectures and training strategies: graph recurrent neural networks, graph convolutional networks, graph autoencoders, graph reinforcement learning, and graph adversarial methods. We then provide a comprehensive overview of these methods in a systematic manner mainly by following their development history. We also analyze the differences and compositions of different methods. Finally, we briefly outline the applications in which they have been used and discuss potential future research directions.

Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.

Signed graph representation learning is an effective approach to analyze the complex patterns in real-world signed graphs with the co-existence of positive and negative links. Most previous signed graph representation learning methods resort to balance theory, a classic social theory that originated from psychology as the core assumption. However, since balance theory is shown equivalent to a simple assumption that nodes can be divided into two conflicting groups, it fails to model the structure of real signed graphs. To solve this problem, we propose Group Signed Graph Neural Network (GS-GNN) model for signed graph representation learning beyond the balance theory assumption. GS-GNN has a dual GNN architecture that consists of the global and the local module. In the global module, we adopt a more generalized assumption that nodes can be divided into multiple latent groups and that the groups can have arbitrary relations and propose a novel prototype-based GNN to learn node representations based on the assumption. In the local module, to give the model enough flexibility in modeling other factors, we do not make any prior assumptions, treat positive links and negative links as two independent relations, and adopt a relational GNN to learn node representations. Both modules can complement each other, and the concatenation of two modules is fed into downstream tasks. Extensive experimental results demonstrate the effectiveness of our GS-GNN model on both synthetic and real-world signed graphs by greatly and consistently outperforming all the baselines and achieving new state-of-the-art results. Our implementation is available in PyTorch.

Recently, self-supervised learning for graph neural networks (GNNs) has attracted considerable attention because of their notable successes in learning the representation of graph-structure data. However, the formation of a real-world graph typically arises from the highly complex interaction of many latent factors. The existing self-supervised learning methods for GNNs are inherently holistic and neglect the entanglement of the latent factors, resulting in the learned representations suboptimal for downstream tasks and difficult to be interpreted. Learning disentangled graph representations with self-supervised learning poses great challenges and remains largely ignored by the existing literature. In this paper, we introduce the Disentangled Graph Contrastive Learning (DGCL) method, which is able to learn disentangled graph-level representations with self-supervision. In particular, we first identify the latent factors of the input graph and derive its factorized representations. Each of the factorized representations describes a latent and disentangled aspect pertinent to a specific latent factor of the graph. Then we propose a novel factor-wise discrimination objective in a contrastive learning manner, which can force the factorized representations to independently reflect the expressive information from different latent factors. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of our method against several state-of-the-art baselines.

Graph Convolutional Networks (GCNs) are an emerging type of neural network model on graphs which have achieved state-of-the-art performance in the task of node classification. However, recent studies show that GCNs are vulnerable to adversarial attacks, i.e. small deliberate perturbations in graph structures and node attributes, which poses great challenges for applying GCNs to real world applications. How to enhance the robustness of GCNs remains a critical open problem. To address this problem, we propose Robust GCN (RGCN), a novel model that "fortifies'' GCNs against adversarial attacks. Specifically, instead of representing nodes as vectors, our method adopts Gaussian distributions as the hidden representations of nodes in each convolutional layer. In this way, when the graph is attacked, our model can automatically absorb the effects of adversarial changes in the variances of the Gaussian distributions. Moreover, to remedy the propagation of adversarial attacks in GCNs, we propose a variance-based attention mechanism, i.e. assigning different weights to node neighborhoods according to their variances when performing convolutions. Extensive experimental results demonstrate that our proposed method can effectively improve the robustness of GCNs. On three benchmark graphs, our RGCN consistently shows a substantial gain in node classification accuracy compared with state-of-the-art GCNs against various adversarial attack strategies.

Singular Value Decomposition (SVD) is a popular approach in various network applications, such as link prediction and network parameter characterization. Incremental SVD approaches are proposed to process newly changed nodes and edges in dynamic networks. However, incremental SVD approaches suffer from serious error accumulation inevitably due to approximation on incremental updates. SVD restart is an effective approach to reset the aggregated error, but when to restart SVD for dynamic networks is not addressed in literature. In this paper, we propose TIMERS, Theoretically Instructed Maximum-Error-bounded Restart of SVD, a novel approach which optimally sets the restart time in order to reduce error accumulation in time. Specifically, we monitor the margin between reconstruction loss of incremental updates and the minimum loss in SVD model. To reduce the complexity of monitoring, we theoretically develop a lower bound of SVD minimum loss for dynamic networks and use the bound to replace the minimum loss in monitoring. By setting a maximum tolerated error as a threshold, we can trigger SVD restart automatically when the margin exceeds this threshold. We prove that the time complexity of our method is linear with respect to the number of local dynamic changes, and our method is general across different types of dynamic networks. We conduct extensive experiments on several synthetic and real dynamic networks. The experimental results demonstrate that our proposed method significantly outperforms the existing methods by reducing 27% to 42% in terms of the maximum error for dynamic network reconstruction when fixing the number of restarts. Our method reduces the number of restarts by 25% to 50% when fixing the maximum error tolerated.

Network embedding, which learns low-dimensional vector representation for nodes in the network, has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accelerated by distributed computing schemes. To address these problems, we propose RandNE (Iterative Random Projection Network Embedding), a novel and simple billion-scale network embedding method. Specifically, we propose a Gaussian random projection approach to map the network into a low-dimensional embedding space while preserving the high-order proximities between nodes. To reduce the time complexity, we design an iterative projection procedure to avoid the explicit calculation of the high-order proximities. Theoretical analysis shows that our method is extremely efficient, and friendly to distributed computing schemes without any communication cost in the calculation. We also design a dynamic updating procedure which can efficiently incorporate the dynamic changes of the networks without error aggregation. Extensive experimental results demonstrate the efficiency and efficacy of RandNE over state-of-the-art methods in several tasks including network reconstruction, link prediction and node classification on multiple datasets with different scales, ranging from thousands to billions of nodes and edges.

Trust prediction, aiming to predict the trust relations between users in a social network, is a key to helping users discover the reliable information. Many trust prediction methods are proposed based on the low-rank assumption of a trust network. However, one typical property of the trust network is that the trust relations follow the power-law distribution, i.e., few users are trusted by many other users, while most tail users have few trustors. Due to these tail users, the fundamental low-rank assumption made by existing methods is seriously violated and becomes unrealistic. In this paper, we propose a simple yet effective method to address the problem of the violated low-rank assumption. Instead of discovering the low-rank component of the trust network alone, we learn a sparse component of the trust network to describe the tail users simultaneously. With both of the learned low-rank and sparse components, the trust relations in the whole network can be better captured. Moreover, the transitive closure structure of the trust relations is also integrated into our model. We then derive an effective iterative algorithm to infer the parameters of our model, along with the proof of correctness. Extensive experimental results on real-world trust networks demonstrate the superior performance of our proposed method over the state-of-the-arts.

Network embedding has received increasing research attention in recent years. The existing methods show that the high-order proximity plays a key role in capturing the underlying structure of the network. However, two fundamental problems in preserving the high-order proximity remain unsolved. First, all the existing methods can only preserve fixed-order proximities, despite that proximities of different orders are often desired for distinct networks and target applications. Second, given a certain order proximity, the existing methods cannot guarantee accuracy and efficiency simultaneously. To address these challenges, we propose AROPE (arbitrary-order proximity preserved embedding), a novel network embedding method based on SVD framework. We theoretically prove the eigen-decomposition reweighting theorem, revealing the intrinsic relationship between proximities of different orders. With this theorem, we propose a scalable eigen-decomposition solution to derive the embedding vectors and shift them between proximities of arbitrary orders. Theoretical analysis is provided to guarantee that i) our method has a low marginal cost in shifting the embedding vectors across different orders, ii) given a certain order, our method can get the global optimal solutions, and iii) the overall time complexity of our method is linear with respect to network size. Extensive experimental results on several large-scale networks demonstrate that our proposed method greatly and consistently outperforms the baselines in various tasks including network reconstruction, link prediction and node classification.

Network embedding, aiming to embed a network into a low dimensional vector space while preserving the inherent structural properties of the network, has attracted considerable attention. However, most existing embedding methods focus on the static network while neglecting the evolving characteristic of real-world networks. Meanwhile, most of previous methods cannot well preserve the high-order proximity, which is a critical structural property of networks. These problems motivate us to seek an effective and efficient way to preserve the high-order proximity in embedding vectors when the networks evolve over time. In this paper, we propose a novel method of Dynamic High-order Proximity preserved Embedding (DHPE). Specifically, we adopt the generalized SVD (GSVD) to preserve the high-order proximity. Then, by transforming the GSVD problem to a generalized eigenvalue problem, we propose a generalized eigen perturbation to incrementally update the results of GSVD to incorporate the changes of dynamic networks. Further, we propose an accelerated solution to the DHPE model so that it achieves a linear time complexity with respect to the number of nodes and number of changed edges in the network. Our empirical experiments on one synthetic network and several real-world networks demonstrate the effectiveness and efficiency of the proposed method.

Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved. The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs. Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v. Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs. To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high-order proximity which are based on asymmetric transitivity. In particular, we develop a novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity. More specifically, we first derive a general formulation that cover multiple popular high-order proximity measurements, then propose a scalable embedding algorithm to approximate the high-order proximity measurements based on their general formulation. Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation. Our empirical experiments on a synthetic dataset and three real-world datasets demonstrate that HOPE can approximate the high-order proximities significantly better than the state-of-art algorithms and outperform the state-of-art algorithms in tasks of reconstruction, link prediction and vertex recommendation.