Training on large-scale graphs has achieved remarkable results in graph representation learning, but its cost and storage have raised growing concerns. As one of the most promising directions, graph condensation methods address these issues by employing gradient matching, aiming to condense the full graph into a more concise yet information-rich synthetic set. Though encouraging, these strategies primarily emphasize matching directions of the gradients, which leads to deviations in the training trajectories. Such deviations are further magnified by the differences between the condensation and evaluation phases, culminating in accumulated errors, which detrimentally affect the performance of the condensed graphs. In light of this, we propose a novel graph condensation method named \textbf{C}raf\textbf{T}ing \textbf{R}ationa\textbf{L} trajectory (\textbf{CTRL}), which offers an optimized starting point closer to the original dataset's feature distribution and a more refined strategy for gradient matching. Theoretically, CTRL can effectively neutralize the impact of accumulated errors on the performance of condensed graphs. We provide extensive experiments on various graph datasets and downstream tasks to support the effectiveness of CTRL. Code is released at https://github.com/NUS-HPC-AI-Lab/CTRL.
Graph representation learning (GRL) is critical for extracting insights from complex network structures, but it also raises security concerns due to potential privacy vulnerabilities in these representations. This paper investigates the structural vulnerabilities in graph neural models where sensitive topological information can be inferred through edge reconstruction attacks. Our research primarily addresses the theoretical underpinnings of similarity-based edge reconstruction attacks (SERA), furnishing a non-asymptotic analysis of their reconstruction capacities. Moreover, we present empirical corroboration indicating that such attacks can perfectly reconstruct sparse graphs as graph size increases. Conversely, we establish that sparsity is a critical factor for SERA's effectiveness, as demonstrated through analysis and experiments on (dense) stochastic block models. Finally, we explore the resilience of private graph representations produced via noisy aggregation (NAG) mechanism against SERA. Through theoretical analysis and empirical assessments, we affirm the mitigation of SERA using NAG . In parallel, we also empirically delineate instances wherein SERA demonstrates both efficacy and deficiency in its capacity to function as an instrument for elucidating the trade-off between privacy and utility.
Temporal graph representation learning (TGRL) is essential for modeling dynamic systems in real-world networks. However, traditional TGRL methods, despite their effectiveness, often face significant computational challenges and inference delays due to the inefficient sampling of temporal neighbors. Conventional sampling methods typically involve backtracking through the interaction history of each node. In this paper, we propose a novel TGRL framework, No-Looking-Back (NLB), which overcomes these challenges by introducing a forward recent sampling strategy. This strategy eliminates the need to backtrack through historical interactions by utilizing a GPU-executable, size-constrained hash table for each node. The hash table records a down-sampled set of recent interactions, enabling rapid query responses with minimal inference latency. The maintenance of this hash table is highly efficient, operating with $O(1)$ complexity. Fully compatible with GPU processing, NLB maximizes programmability, parallelism, and power efficiency. Empirical evaluations demonstrate that NLB not only matches or surpasses state-of-the-art methods in accuracy for tasks like link prediction and node classification across six real-world datasets but also achieves 1.32-4.40x faster training, 1.2-7.94x greater energy efficiency, and 1.63-12.95x lower inference latency compared to competitive baselines. The link to the code: https://github.com/Graph-COM/NLB.
Can we model Non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The Non-Euclidean property have posed a long term challenge in graph modeling. Despite recent graph neural networks and graph transformers efforts encoding graphs as Euclidean vectors, recovering the original graph from vectors remains a challenge. In this paper, we introduce GraphsGPT, featuring an Graph2Seq encoder that transforms Non-Euclidean graphs into learnable Graph Words in the Euclidean space, along with a GraphGPT decoder that reconstructs the original graph from Graph Words to ensure information equivalence. We pretrain GraphsGPT on $100$M molecules and yield some interesting findings: (1) The pretrained Graph2Seq excels in graph representation learning, achieving state-of-the-art results on $8/9$ graph classification and regression tasks. (2) The pretrained GraphGPT serves as a strong graph generator, demonstrated by its strong ability to perform both few-shot and conditional graph generation. (3) Graph2Seq+GraphGPT enables effective graph mixup in the Euclidean space, overcoming previously known Non-Euclidean challenges. (4) The edge-centric pretraining framework GraphsGPT demonstrates its efficacy in graph domain tasks, excelling in both representation and generation. Code is available at \href{https://github.com/A4Bio/GraphsGPT}{GitHub}.
Restricted access window (RAW) in Wi-Fi 802.11ah networks manages contention and interference by grouping users and allocating periodic time slots for each group's transmissions. We will find the optimal user grouping decisions in RAW to maximize the network's worst-case user throughput. We review existing user grouping approaches and highlight their performance limitations in the above problem. We propose formulating user grouping as a graph construction problem where vertices represent users and edge weights indicate the contention and interference. This formulation leverages the graph's max cut to group users and optimizes edge weights to construct the optimal graph whose max cut yields the optimal grouping decisions. To achieve this optimal graph construction, we design an actor-critic graph representation learning (AC-GRL) algorithm. Specifically, the actor neural network (NN) is trained to estimate the optimal graph's edge weights using path losses between users and access points. A graph cut procedure uses semidefinite programming to solve the max cut efficiently and return the grouping decisions for the given weights. The critic NN approximates user throughput achieved by the above-returned decisions and is used to improve the actor. Additionally, we present an architecture that uses the online-measured throughput and path losses to fine-tune the decisions in response to changes in user populations and their locations. Simulations show that our methods achieve $30\%\sim80\%$ higher worst-case user throughput than the existing approaches and that the proposed architecture can further improve the worst-case user throughput by $5\%\sim30\%$ while ensuring timely updates of grouping decisions.
As graph representation learning often suffers from label scarcity problems in real-world applications, researchers have proposed graph domain adaptation (GDA) as an effective knowledge-transfer paradigm across graphs. In particular, to enhance model performance on target graphs with specific tasks, GDA introduces a bunch of task-related graphs as source graphs and adapts the knowledge learnt from source graphs to the target graphs. Since GDA combines the advantages of graph representation learning and domain adaptation, it has become a promising direction of transfer learning on graphs and has attracted an increasing amount of research interest in recent years. In this paper, we comprehensively overview the studies of GDA and present a detailed survey of recent advances. Specifically, we outline the research status and challenges, propose a taxonomy, introduce the details of representative works, and discuss the prospects. To the best of our knowledge, this paper is the first survey for graph domain adaptation. A detailed paper list is available at https://github.com/Skyorca/Awesome-Graph-Domain-Adaptation-Papers.
For analysing real-world networks, graph representation learning is a popular tool. These methods, such as a graph autoencoder (GAE), typically rely on low-dimensional representations, also called embeddings, which are obtained through minimising a loss function; these embeddings are used with a decoder for downstream tasks such as node classification and edge prediction. While GAEs tend to be fairly accurate, they suffer from scalability issues. For improved speed, a Local2Global approach, which combines graph patch embeddings based on eigenvector synchronisation, was shown to be fast and achieve good accuracy. Here we propose L2G2G, a Local2Global method which improves GAE accuracy without sacrificing scalability. This improvement is achieved by dynamically synchronising the latent node representations, while training the GAEs. It also benefits from the decoder computing an only local patch loss. Hence, aligning the local embeddings in each epoch utilises more information from the graph than a single post-training alignment does, while maintaining scalability. We illustrate on synthetic benchmarks, as well as real-world examples, that L2G2G achieves higher accuracy than the standard Local2Global approach and scales efficiently on the larger data sets. We find that for large and dense networks, it even outperforms the slow, but assumed more accurate, GAEs.
Graph representation learning, a critical step in graph-centric tasks, has seen significant advancements. Earlier techniques often operate in an end-to-end setting, which heavily rely on the availability of ample labeled data. This constraint has spurred the emergence of few-shot learning on graphs, where only a few labels are available for each task. Given the extensive literature in this field, this survey endeavors to synthesize recent developments, provide comparative insights, and identify future directions. We systematically categorize existing studies based on two major taxonomies: (1) Problem taxonomy, which explores different types of data scarcity problems and their applications, and (2) Technique taxonomy, which details key strategies for addressing these data-scarce few-shot problems. The techniques can be broadly categorized into meta-learning, pre-training, and hybrid approaches, with a finer-grained classification in each category to aid readers in their method selection process. Within each category, we analyze the relationships among these methods and compare their strengths and limitations. Finally, we outline prospective directions for few-shot learning on graphs to catalyze continued innovation in this field. The website for this survey can be accessed by \url{https://github.com/smufang/fewshotgraph}.
Graph contrastive learning (GCL) has emerged as a state-of-the-art strategy for learning representations of diverse graphs including social and biomedical networks. GCL widely uses stochastic graph topology augmentation, such as uniform node dropping, to generate augmented graphs. However, such stochastic augmentations may severely damage the intrinsic properties of a graph and deteriorate the following representation learning process. We argue that incorporating an awareness of cohesive subgraphs during the graph augmentation and learning processes has the potential to enhance GCL performance. To this end, we propose a novel unified framework called CTAug, to seamlessly integrate cohesion awareness into various existing GCL mechanisms. In particular, CTAug comprises two specialized modules: topology augmentation enhancement and graph learning enhancement. The former module generates augmented graphs that carefully preserve cohesion properties, while the latter module bolsters the graph encoder's ability to discern subgraph patterns. Theoretical analysis shows that CTAug can strictly improve existing GCL mechanisms. Empirical experiments verify that CTAug can achieve state-of-the-art performance for graph representation learning, especially for graphs with high degrees. The code is available at https://doi.org/10.5281/zenodo.10594093, or https://github.com/wuyucheng2002/CTAug.
Recently, Transformers for graph representation learning have become increasingly popular, achieving state-of-the-art performance on a wide-variety of graph datasets, either alone or in combination with message-passing graph neural networks (MP-GNNs). Infusing graph inductive-biases in the innately structure-agnostic transformer architecture in the form of structural or positional encodings (PEs) is key to achieving these impressive results. However, designing such encodings is tricky and disparate attempts have been made to engineer such encodings including Laplacian eigenvectors, relative random-walk probabilities (RRWP), spatial encodings, centrality encodings, edge encodings etc. In this work, we argue that such encodings may not be required at all, provided the attention mechanism itself incorporates information about the graph structure. We introduce Eigenformer, a Graph Transformer employing a novel spectrum-aware attention mechanism cognizant of the Laplacian spectrum of the graph, and empirically show that it achieves performance competetive with SOTA Graph Transformers on a number of standard GNN benchmarks. Additionally, we theoretically prove that Eigenformer can express various graph structural connectivity matrices, which is particularly essential when learning over smaller graphs.
Machine learning models that embed graphs in non-Euclidean spaces have shown substantial benefits in a variety of contexts, but their application has not been studied extensively in the biological domain, particularly with respect to biological pathway graphs. Such graphs exhibit a variety of complex network structures, presenting challenges to existing embedding approaches. Learning high-quality embeddings for biological pathway graphs is important for researchers looking to understand the underpinnings of disease and train high-quality predictive models on these networks. In this work, we investigate the effects of embedding pathway graphs in non-Euclidean mixed-curvature spaces and compare against traditional Euclidean graph representation learning models. We then train a supervised model using the learned node embeddings to predict missing protein-protein interactions in pathway graphs. We find large reductions in distortion and boosts on in-distribution edge prediction performance as a result of using mixed-curvature embeddings and their corresponding graph neural network models. However, we find that mixed-curvature representations underperform existing baselines on out-of-distribution edge prediction performance suggesting that these representations may overfit to the training graph topology. We provide our Mixed-Curvature Product Graph Convolutional Network code at https://github.com/mcneela/Mixed-Curvature-GCN and our pathway analysis code at https://github.com/mcneela/Mixed-Curvature-Pathways.
Self-supervised graph representation learning has recently shown considerable promise in a range of fields, including bioinformatics and social networks. A large number of graph contrastive learning approaches have shown promising performance for representation learning on graphs, which train models by maximizing agreement between original graphs and their augmented views (i.e., positive views). Unfortunately, these methods usually involve pre-defined augmentation strategies based on the knowledge of human experts. Moreover, these strategies may fail to generate challenging positive views to provide sufficient supervision signals. In this paper, we present a novel approach named Graph Pooling ContraSt (GPS) to address these issues. Motivated by the fact that graph pooling can adaptively coarsen the graph with the removal of redundancy, we rethink graph pooling and leverage it to automatically generate multi-scale positive views with varying emphasis on providing challenging positives and preserving semantics, i.e., strongly-augmented view and weakly-augmented view. Then, we incorporate both views into a joint contrastive learning framework with similarity learning and consistency learning, where our pooling module is adversarially trained with respect to the encoder for adversarial robustness. Experiments on twelve datasets on both graph classification and transfer learning tasks verify the superiority of the proposed method over its counterparts.
Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an exclusive topological imprint of data by tracing the evolution of latent structures as a scale parameter changes. Present PH tools are confined to analyzing data through a single filter parameter. However, many scenarios necessitate the consideration of multiple relevant parameters to attain finer insights into the data. We address this issue by introducing the Effective Multidimensional Persistence (EMP) framework. This framework empowers the exploration of data by simultaneously varying multiple scale parameters. The framework integrates descriptor functions into the analysis process, yielding a highly expressive data summary. It seamlessly integrates established single PH summaries into multidimensional counterparts like EMP Landscapes, Silhouettes, Images, and Surfaces. These summaries represent data's multidimensional aspects as matrices and arrays, aligning effectively with diverse ML models. We provide theoretical guarantees and stability proofs for EMP summaries. We demonstrate EMP's utility in graph classification tasks, showing its effectiveness. Results reveal that EMP enhances various single PH descriptors, outperforming cutting-edge methods on multiple benchmark datasets.
Entity alignment (EA), a pivotal process in integrating multi-source Knowledge Graphs (KGs), seeks to identify equivalent entity pairs across these graphs. Most existing approaches regard EA as a graph representation learning task, concentrating on enhancing graph encoders. However, the decoding process in EA - essential for effective operation and alignment accuracy - has received limited attention and remains tailored to specific datasets and model architectures, necessitating both entity and additional explicit relation embeddings. This specificity limits its applicability, particularly in GNN-based models. To address this gap, we introduce a novel, generalized, and efficient decoding approach for EA, relying solely on entity embeddings. Our method optimizes the decoding process by minimizing Dirichlet energy, leading to the gradient flow within the graph, to maximize graph homophily. The discretization of the gradient flow produces a fast and scalable approach, termed Triple Feature Propagation (TFP). TFP innovatively generalizes adjacency matrices to multi-views matrices:entity-to-entity, entity-to-relation, relation-to-entity, and relation-to-triple. The gradient flow through generalized matrices enables TFP to harness the multi-view structural information of KGs. Rigorous experimentation on diverse public datasets demonstrates that our approach significantly enhances various EA methods. Notably, the approach achieves these advancements with less than 6 seconds of additional computational time, establishing a new benchmark in efficiency and adaptability for future EA methods.
We present a novel graph Transformer generative adversarial network (GTGAN) to learn effective graph node relations in an end-to-end fashion for challenging graph-constrained architectural layout generation tasks. The proposed graph-Transformer-based generator includes a novel graph Transformer encoder that combines graph convolutions and self-attentions in a Transformer to model both local and global interactions across connected and non-connected graph nodes. Specifically, the proposed connected node attention (CNA) and non-connected node attention (NNA) aim to capture the global relations across connected nodes and non-connected nodes in the input graph, respectively. The proposed graph modeling block (GMB) aims to exploit local vertex interactions based on a house layout topology. Moreover, we propose a new node classification-based discriminator to preserve the high-level semantic and discriminative node features for different house components. To maintain the relative spatial relationships between ground truth and predicted graphs, we also propose a novel graph-based cycle-consistency loss. Finally, we propose a novel self-guided pre-training method for graph representation learning. This approach involves simultaneous masking of nodes and edges at an elevated mask ratio (i.e., 40%) and their subsequent reconstruction using an asymmetric graph-centric autoencoder architecture. This method markedly improves the model's learning proficiency and expediency. Experiments on three challenging graph-constrained architectural layout generation tasks (i.e., house layout generation, house roof generation, and building layout generation) with three public datasets demonstrate the effectiveness of the proposed method in terms of objective quantitative scores and subjective visual realism. New state-of-the-art results are established by large margins on these three tasks.
Dynamic graphs (DG) describe dynamic interactions between entities in many practical scenarios. Most existing DG representation learning models combine graph convolutional network and sequence neural network, which model spatial-temporal dependencies through two different types of neural networks. However, this hybrid design cannot well capture the spatial-temporal continuity of a DG. In this paper, we propose a tensor graph convolutional network to learn DG representations in one convolution framework based on the tensor product with the following two-fold ideas: a) representing the information of DG by tensor form; b) adopting tensor product to design a tensor graph convolutional network modeling spatial-temporal feature simultaneously. Experiments on real-world DG datasets demonstrate that our model obtains state-of-the-art performance.
The integration of Spiking Neural Networks (SNNs) and Graph Neural Networks (GNNs) is gradually attracting attention due to the low power consumption and high efficiency in processing the non-Euclidean data represented by graphs. However, as a common problem, dynamic graph representation learning faces challenges such as high complexity and large memory overheads. Current work often uses SNNs instead of Recurrent Neural Networks (RNNs) by using binary features instead of continuous ones for efficient training, which would overlooks graph structure information and leads to the loss of details during propagation. Additionally, optimizing dynamic spiking models typically requires propagation of information across time steps, which increases memory requirements. To address these challenges, we present a framework named \underline{Dy}namic \underline{S}p\underline{i}king \underline{G}raph \underline{N}eural Networks (\method{}). To mitigate the information loss problem, \method{} propagates early-layer information directly to the last layer for information compensation. To accommodate the memory requirements, we apply the implicit differentiation on the equilibrium state, which does not rely on the exact reverse of the forward computation. While traditional implicit differentiation methods are usually used for static situations, \method{} extends it to the dynamic graph setting. Extensive experiments on three large-scale real-world dynamic graph datasets validate the effectiveness of \method{} on dynamic node classification tasks with lower computational costs.
While graph neural networks (GNNs) are widely used for node and graph representation learning tasks, the reliability of GNN uncertainty estimates under distribution shifts remains relatively under-explored. Indeed, while post-hoc calibration strategies can be used to improve in-distribution calibration, they need not also improve calibration under distribution shift. However, techniques which produce GNNs with better intrinsic uncertainty estimates are particularly valuable, as they can always be combined with post-hoc strategies later. Therefore, in this work, we propose G-$\Delta$UQ, a novel training framework designed to improve intrinsic GNN uncertainty estimates. Our framework adapts the principle of stochastic data centering to graph data through novel graph anchoring strategies, and is able to support partially stochastic GNNs. While, the prevalent wisdom is that fully stochastic networks are necessary to obtain reliable estimates, we find that the functional diversity induced by our anchoring strategies when sampling hypotheses renders this unnecessary and allows us to support G-$\Delta$UQ on pretrained models. Indeed, through extensive evaluation under covariate, concept and graph size shifts, we show that G-$\Delta$UQ leads to better calibrated GNNs for node and graph classification. Further, it also improves performance on the uncertainty-based tasks of out-of-distribution detection and generalization gap estimation. Overall, our work provides insights into uncertainty estimation for GNNs, and demonstrates the utility of G-$\Delta$UQ in obtaining reliable estimates.
Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most of them present a single curvature (radius) regardless of structural complexity, suffer from numerical instability due to the exponential/logarithmic map, and lack the ability to capture motif regularity. In light of the issues above, we propose the problem of \emph{Motif-aware Riemannian Graph Representation Learning}, seeking a numerically stable encoder to capture motif regularity in a diverse-curvature manifold without labels. To this end, we present a novel Motif-aware Riemannian model with Generative-Contrastive learning (MotifRGC), which conducts a minmax game in Riemannian manifold in a self-supervised manner. First, we propose a new type of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold by a product layer with the diversified factor, and replace the exponential/logarithmic map by a stable kernel layer. Second, we introduce a motif-aware Riemannian generative-contrastive learning to capture motif regularity in the constructed manifold and learn motif-aware node representation without external labels. Empirical results show the superiority of MofitRGC.
Knowledge Graphs (KGs) have emerged as invaluable resources for enriching recommendation systems by providing a wealth of factual information and capturing semantic relationships among items. Leveraging KGs can significantly enhance recommendation performance. However, not all relations within a KG are equally relevant or beneficial for the target recommendation task. In fact, certain item-entity connections may introduce noise or lack informative value, thus potentially misleading our understanding of user preferences. To bridge this research gap, we propose a novel knowledge graph diffusion model for recommendation, referred to as DiffKG. Our framework integrates a generative diffusion model with a data augmentation paradigm, enabling robust knowledge graph representation learning. This integration facilitates a better alignment between knowledge-aware item semantics and collaborative relation modeling. Moreover, we introduce a collaborative knowledge graph convolution mechanism that incorporates collaborative signals reflecting user-item interaction patterns, guiding the knowledge graph diffusion process. We conduct extensive experiments on three publicly available datasets, consistently demonstrating the superiority of our DiffKG compared to various competitive baselines. We provide the source code repository of our proposed DiffKG model at the following link: https://github.com/HKUDS/DiffKG.