Federated Graph Learning (FGL) is a distributed machine learning paradigm that enables collaborative training on large-scale subgraphs across multiple local systems. Existing FGL studies fall into two categories: (i) FGL Optimization, which improves multi-client training in existing machine learning models; (ii) FGL Model, which enhances performance with complex local models and multi-client interactions. However, most FGL optimization strategies are designed specifically for the computer vision domain and ignore graph structure, presenting dissatisfied performance and slow convergence. Meanwhile, complex local model architectures in FGL Models studies lack scalability for handling large-scale subgraphs and have deployment limitations. To address these issues, we propose Federated Graph Topology-aware Aggregation (FedGTA), a personalized optimization strategy that optimizes through topology-aware local smoothing confidence and mixed neighbor features. During experiments, we deploy FedGTA in 12 multi-scale real-world datasets with the Louvain and Metis split. This allows us to evaluate the performance and robustness of FedGTA across a range of scenarios. Extensive experiments demonstrate that FedGTA achieves state-of-the-art performance while exhibiting high scalability and efficiency. The experiment includes ogbn-papers100M, the most representative large-scale graph database so that we can verify the applicability of our method to large-scale graph learning. To the best of our knowledge, our study is the first to bridge large-scale graph learning with FGL using this optimization strategy, contributing to the development of efficient and scalable FGL methods.
Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems. Despite their state-of-the-art performances, existing GNNs only use local information from a very limited neighborhood around each node, suffering from loss of multi-modal information and overheads of excessive computation. To address these issues, we propose a novel Tensor-view Topological Graph Neural Network (TTG-NN), a class of simple yet effective topological deep learning built upon persistent homology, graph convolution, and tensor operations. This new method incorporates tensor learning to simultaneously capture Tensor-view Topological (TT), as well as Tensor-view Graph (TG) structural information on both local and global levels. Computationally, to fully exploit graph topology and structure, we propose two flexible TT and TG representation learning modules that disentangle feature tensor aggregation and transformation and learn to preserve multi-modal structure with less computation. Theoretically, we derive high probability bounds on both the out-of-sample and in-sample mean squared approximation errors for our proposed Tensor Transformation Layer (TTL). Real data experiments show that the proposed TTG-NN outperforms 20 state-of-the-art methods on various graph benchmarks.
Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines.
Graph learning architectures based on the k-dimensional Weisfeiler-Leman (k-WL) hierarchy offer a theoretically well-understood expressive power. However, such architectures often fail to deliver solid predictive performance on real-world tasks, limiting their practical impact. In contrast, global attention-based models such as graph transformers demonstrate strong performance in practice, but comparing their expressive power with the k-WL hierarchy remains challenging, particularly since these architectures rely on positional or structural encodings for their expressivity and predictive performance. To address this, we show that the recently proposed Edge Transformer, a global attention model operating on node pairs instead of nodes, has at least 3-WL expressive power. Empirically, we demonstrate that the Edge Transformer surpasses other theoretically aligned architectures regarding predictive performance while not relying on positional or structural encodings. Our code is available at https://github.com/luis-mueller/towards-principled-gts
Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and found many real-world applications. Meanwhile, increasing efforts have been made to advance learning from graphs with heterophily. Various graph heterophily measures, benchmark datasets, and learning paradigms are emerging rapidly. In this survey, we comprehensively review existing works on learning from graphs with heterophily. First, we overview over 500 publications, of which more than 340 are directly related to heterophilic graphs. After that, we survey existing metrics of graph heterophily and list recent benchmark datasets. Further, we systematically categorize existing methods based on a hierarchical taxonomy including GNN models, learning paradigms and practical applications. In addition, broader topics related to graph heterophily are also included. Finally, we discuss the primary challenges of existing studies and highlight promising avenues for future research.
Designing expressive Graph Neural Networks (GNNs) is a fundamental topic in the graph learning community. So far, GNN expressiveness has been primarily assessed via the Weisfeiler-Lehman (WL) hierarchy. However, such an expressivity measure has notable limitations: it is inherently coarse, qualitative, and may not well reflect practical requirements (e.g., the ability to encode substructures). In this paper, we introduce a unified framework for quantitatively studying the expressiveness of GNN architectures, addressing all the above limitations. Specifically, we identify a fundamental expressivity measure termed homomorphism expressivity, which quantifies the ability of GNN models to count graphs under homomorphism. Homomorphism expressivity offers a complete and practical assessment tool: the completeness enables direct expressivity comparisons between GNN models, while the practicality allows for understanding concrete GNN abilities such as subgraph counting. By examining four classes of prominent GNNs as case studies, we derive simple, unified, and elegant descriptions of their homomorphism expressivity for both invariant and equivariant settings. Our results provide novel insights into a series of previous work, unify the landscape of different subareas in the community, and settle several open questions. Empirically, extensive experiments on both synthetic and real-world tasks verify our theory, showing that the practical performance of GNN models aligns well with the proposed metric.
Graphs are a powerful representation tool in machine learning applications, with link prediction being a key task in graph learning. Temporal link prediction in dynamic networks is of particular interest due to its potential for solving complex scientific and real-world problems. Traditional approaches to temporal link prediction have focused on finding the aggregation of dynamics of the network as a unified output. In this study, we propose a novel perspective on temporal link prediction by defining nodes as Newtonian objects and incorporating the concept of velocity to predict network dynamics. By computing more specific dynamics of each node, rather than overall dynamics, we improve both accuracy and explainability in predicting future connections. We demonstrate the effectiveness of our approach using two datasets, including 17 years of co-authorship data from PubMed. Experimental results show that our temporal graph embedding dynamics approach improves downstream classification models' ability to predict future collaboration efficacy in co-authorship networks by 17.34% (AUROC improvement relative to the baseline model). Furthermore, our approach offers an interpretable layer over traditional approaches to address the temporal link prediction problem.
Traffic forecasting is the foundation for intelligent transportation systems. Spatiotemporal graph neural networks have demonstrated state-of-the-art performance in traffic forecasting. However, these methods do not explicitly model some of the natural characteristics in traffic data, such as the multiscale structure that encompasses spatial and temporal variations at different levels of granularity or scale. To that end, we propose a Wavelet-Inspired Graph Convolutional Recurrent Network (WavGCRN) which combines multiscale analysis (MSA)-based method with Deep Learning (DL)-based method. In WavGCRN, the traffic data is decomposed into time-frequency components with Discrete Wavelet Transformation (DWT), constructing a multi-stream input structure; then Graph Convolutional Recurrent networks (GCRNs) are employed as encoders for each stream, extracting spatiotemporal features in different scales; and finally the learnable Inversed DWT and GCRN are combined as the decoder, fusing the information from all streams for traffic metrics reconstruction and prediction. Furthermore, road-network-informed graphs and data-driven graph learning are combined to accurately capture spatial correlation. The proposed method can offer well-defined interpretability, powerful learning capability, and competitive forecasting performance on real-world traffic data sets.
Forecasting future stock trends remains challenging for academia and industry due to stochastic inter-stock dynamics and hierarchical intra-stock dynamics influencing stock prices. In recent years, graph neural networks have achieved remarkable performance in this problem by formulating multiple stocks as graph-structured data. However, most of these approaches rely on artificially defined factors to construct static stock graphs, which fail to capture the intrinsic interdependencies between stocks that rapidly evolve. In addition, these methods often ignore the hierarchical features of the stocks and lose distinctive information within. In this work, we propose a novel graph learning approach implemented without expert knowledge to address these issues. First, our approach automatically constructs dynamic stock graphs by entropy-driven edge generation from a signal processing perspective. Then, we further learn task-optimal dependencies between stocks via a generalized graph diffusion process on constructed stock graphs. Last, a decoupled representation learning scheme is adopted to capture distinctive hierarchical intra-stock features. Experimental results demonstrate substantial improvements over state-of-the-art baselines on real-world datasets. Moreover, the ablation study and sensitivity study further illustrate the effectiveness of the proposed method in modeling the time-evolving inter-stock and intra-stock dynamics.
We introduce \textit{GraphGPT}, a novel model for Graph learning by self-supervised Generative Pre-training Transformers. Our model transforms each graph or sampled subgraph into a sequence of tokens representing the node, edge and attributes reversibly using the Eulerian path first. Then we feed the tokens into a standard transformer decoder and pre-train it with the next-token-prediction (NTP) task. Lastly, we fine-tune the GraphGPT model with the supervised tasks. This intuitive, yet effective model achieves superior or close results to the state-of-the-art methods for the graph-, edge- and node-level tasks on the large scale molecular dataset PCQM4Mv2, the protein-protein association dataset ogbl-ppa and the ogbn-proteins dataset from the Open Graph Benchmark (OGB). Furthermore, the generative pre-training enables us to train GraphGPT up to 400M+ parameters with consistently increasing performance, which is beyond the capability of GNNs and previous graph transformers. The source code and pre-trained checkpoints will be released soon\footnote{\url{https://github.com/alibaba/graph-gpt}} to pave the way for the graph foundation model research, and also to assist the scientific discovery in pharmaceutical, chemistry, material and bio-informatics domains, etc.
We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed to handle digraphs with weights of arbitrary sign). In addition to its generality, our Quaternionic Laplacian is the only Laplacian to completely preserve the topology of a digraph, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weights without reducing them to a single (directed or undirected) edge as done with other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.
The multimodal recommendation has gradually become the infrastructure of online media platforms, enabling them to provide personalized service to users through a joint modeling of user historical behaviors (e.g., purchases, clicks) and item various modalities (e.g., visual and textual). The majority of existing studies typically focus on utilizing modal features or modal-related graph structure to learn user local interests. Nevertheless, these approaches encounter two limitations: (1) Shared updates of user ID embeddings result in the consequential coupling between collaboration and multimodal signals; (2) Lack of exploration into robust global user interests to alleviate the sparse interaction problems faced by local interest modeling. To address these issues, we propose a novel Local and Global Graph Learning-guided Multimodal Recommender (LGMRec), which jointly models local and global user interests. Specifically, we present a local graph embedding module to independently learn collaborative-related and modality-related embeddings of users and items with local topological relations. Moreover, a global hypergraph embedding module is designed to capture global user and item embeddings by modeling insightful global dependency relations. The global embeddings acquired within the hypergraph embedding space can then be combined with two decoupled local embeddings to improve the accuracy and robustness of recommendations. Extensive experiments conducted on three benchmark datasets demonstrate the superiority of our LGMRec over various state-of-the-art recommendation baselines, showcasing its effectiveness in modeling both local and global user interests.
While machine learning has witnessed significant advancements, the emphasis has largely been on data acquisition and model creation. However, achieving a comprehensive assessment of machine learning solutions in real-world settings necessitates standardization throughout the entire pipeline. This need is particularly acute in time series forecasting, where diverse settings impede meaningful comparisons between various methods. To bridge this gap, we propose a unified benchmarking framework that exposes the crucial modelling and machine learning decisions involved in developing time series forecasting models. This framework fosters seamless integration of models and datasets, aiding both practitioners and researchers in their development efforts. We benchmark recently proposed models within this framework, demonstrating that carefully implemented deep learning models with minimal effort can rival gradient-boosting decision trees requiring extensive feature engineering and expert knowledge.
When handling streaming graphs, existing graph representation learning models encounter a catastrophic forgetting problem, where previously learned knowledge of these models is easily overwritten when learning with newly incoming graphs. In response, Continual Graph Learning (CGL) emerges as a novel paradigm enabling graph representation learning from streaming graphs. Our prior work, Condense and Train (CaT) is a replay-based CGL framework with a balanced continual learning procedure, which designs a small yet effective memory bankn for replaying. Although the CaT alleviates the catastrophic forgetting problem, there exist three issues: (1) The graph condensation only focuses on labelled nodes while neglecting abundant information carried by unlabelled nodes; (2) The continual training scheme of the CaT overemphasises on the previously learned knowledge, limiting the model capacity to learn from newly added memories; (3) Both the condensation process and replaying process of the CaT are time-consuming. In this paper, we propose a PsUdo-label guided Memory bAnk (PUMA) CGL framework, extending from the CaT to enhance its efficiency and effectiveness by overcoming the above-mentioned weaknesses and limits. To fully exploit the information in a graph, PUMA expands the coverage of nodes during graph condensation with both labelled and unlabelled nodes. Furthermore, a training-from-scratch strategy is proposed to upgrade the previous continual learning scheme for a balanced training between the historical and the new graphs. Besides, PUMA uses a one-time prorogation and wide graph encoders to accelerate the graph condensation and the graph encoding process in the training stage to improve the efficiency of the whole framework. Extensive experiments on six datasets for the node classification task demonstrate the state-of-the-art performance and efficiency over existing methods.
Recently, the paradigm of pre-training and fine-tuning graph neural networks has been intensively studied and applied in a wide range of graph mining tasks. Its success is generally attributed to the structural consistency between pre-training and downstream datasets, which, however, does not hold in many real-world scenarios. Existing works have shown that the structural divergence between pre-training and downstream graphs significantly limits the transferability when using the vanilla fine-tuning strategy. This divergence leads to model overfitting on pre-training graphs and causes difficulties in capturing the structural properties of the downstream graphs. In this paper, we identify the fundamental cause of structural divergence as the discrepancy of generative patterns between the pre-training and downstream graphs. Furthermore, we propose G-Tuning to preserve the generative patterns of downstream graphs. Given a downstream graph G, the core idea is to tune the pre-trained GNN so that it can reconstruct the generative patterns of G, the graphon W. However, the exact reconstruction of a graphon is known to be computationally expensive. To overcome this challenge, we provide a theoretical analysis that establishes the existence of a set of alternative graphons called graphon bases for any given graphon. By utilizing a linear combination of these graphon bases, we can efficiently approximate W. This theoretical finding forms the basis of our proposed model, as it enables effective learning of the graphon bases and their associated coefficients. Compared with existing algorithms, G-Tuning demonstrates an average improvement of 0.5% and 2.6% on in-domain and out-of-domain transfer learning experiments, respectively.
Complex spatial dependencies in transportation networks make traffic prediction extremely challenging. Much existing work is devoted to learning dynamic graph structures among sensors, and the strategy of mining spatial dependencies from traffic data, known as data-driven, tends to be an intuitive and effective approach. However, Time-Shift of traffic patterns and noise induced by random factors hinder data-driven spatial dependence modeling. In this paper, we propose a novel dynamic frequency domain graph convolution network (DFDGCN) to capture spatial dependencies. Specifically, we mitigate the effects of time-shift by Fourier transform, and introduce the identity embedding of sensors and time embedding when capturing data for graph learning since traffic data with noise is not entirely reliable. The graph is combined with static predefined and self-adaptive graphs during graph convolution to predict future traffic data through classical causal convolutions. Extensive experiments on four real-world datasets demonstrate that our model is effective and outperforms the baselines.
Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the computational feasibility of the global attention mechanism is possible. The next goal is to scale up these architectures to handle very large graphs on the scale of millions or even billions of nodes. With large-scale graphs, global attention learning is proven impractical due to its quadratic complexity w.r.t. the number of nodes. On the other hand, neighborhood sampling techniques become essential to manage large graph sizes, yet finding the optimal trade-off between speed and accuracy with sampling techniques remains challenging. This work advances representation learning on single large-scale graphs with a focus on identifying model characteristics and critical design constraints for developing scalable graph transformer (GT) architectures. We argue such GT requires layers that can adeptly learn both local and global graph representations while swiftly sampling the graph topology. As such, a key innovation of this work lies in the creation of a fast neighborhood sampling technique coupled with a local attention mechanism that encompasses a 4-hop reception field, but achieved through just 2-hop operations. This local node embedding is then integrated with a global node embedding, acquired via another self-attention layer with an approximate global codebook, before finally sent through a downstream layer for node predictions. The proposed GT framework, named LargeGT, overcomes previous computational bottlenecks and is validated on three large-scale node classification benchmarks. We report a 3x speedup and 16.8% performance gain on ogbn-products and snap-patents, while we also scale LargeGT on ogbn-papers100M with a 5.9% performance improvement.
Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to errors stemming from observational noise, graph-learning limitations, or adversarial attacks. If ignored, these perturbations may drastically hinder the performance of GNNs. To address this limitation, this work proposes a robust implementation of GNNs that explicitly accounts for the presence of perturbations in the observed topology. For any task involving GNNs, our core idea is to i) solve an optimization problem not only over the learnable parameters of the GNN but also over the true graph, and ii) augment the fitting cost with a term accounting for discrepancies on the graph. Specifically, we consider a convolutional GNN based on graph filters and follow an alternating optimization approach to handle the (non-differentiable and constrained) optimization problem by combining gradient descent and projected proximal updates. The resulting algorithm is not limited to a particular type of graph and is amenable to incorporating prior information about the perturbations. Finally, we assess the performance of the proposed method through several numerical experiments.
Graph Neural Networks (GNNs) play a crucial role in various fields. However, most existing deep graph learning frameworks assume pre-stored static graphs and do not support training on graph streams. In contrast, many real-world graphs are dynamic and contain time domain information. We introduce GNNFlow, a distributed framework that enables efficient continuous temporal graph representation learning on dynamic graphs on multi-GPU machines. GNNFlow introduces an adaptive time-indexed block-based data structure that effectively balances memory usage with graph update and sampling operation efficiency. It features a hybrid GPU-CPU graph data placement for rapid GPU-based temporal neighborhood sampling and kernel optimizations for enhanced sampling processes. A dynamic GPU cache for node and edge features is developed to maximize cache hit rates through reuse and restoration strategies. GNNFlow supports distributed training across multiple machines with static scheduling to ensure load balance. We implement GNNFlow based on DGL and PyTorch. Our experimental results show that GNNFlow provides up to 21.1x faster continuous learning than existing systems.
Graph condensation, which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has immediate benefits for various graph learning tasks. However, existing graph condensation methods rely on the joint optimization of nodes and structures in the condensed graph, and overlook critical issues in effectiveness and generalization ability. In this paper, we advocate a new Structure-Free Graph Condensation paradigm, named SFGC, to distill a large-scale graph into a small-scale graph node set without explicit graph structures, i.e., graph-free data. Our idea is to implicitly encode topology structure information into the node attributes in the synthesized graph-free data, whose topology is reduced to an identity matrix. Specifically, SFGC contains two collaborative components: (1) a training trajectory meta-matching scheme for effectively synthesizing small-scale graph-free data; (2) a graph neural feature score metric for dynamically evaluating the quality of the condensed data. Through training trajectory meta-matching, SFGC aligns the long-term GNN learning behaviors between the large-scale graph and the condensed small-scale graph-free data, ensuring comprehensive and compact transfer of informative knowledge to the graph-free data. Afterward, the underlying condensed graph-free data would be dynamically evaluated with the graph neural feature score, which is a closed-form metric for ensuring the excellent expressiveness of the condensed graph-free data. Extensive experiments verify the superiority of SFGC across different condensation ratios.