Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through pairwise regularization, where each pair of views is encouraged to have similar structures. However, this approach cannot infer the shared structure across views. In this work, we propose an alternative method based on consensus regularization, where views are ensured to be similar through a learned consensus graph representing the common structure of the views. In particular, we propose an optimization problem, where graph data is assumed to be smooth over the multiview graph and the topology of the individual views and that of the consensus graph are learned, simultaneously. Our optimization problem is designed to be general in the sense that different regularization functions can be used depending on what the shared structure across views is. Moreover, we propose two regularization functions that extend fused and group graphical lasso to consensus based regularization. Proposed multiview graph learning is evaluated on simulated data and shown to have better performance than existing methods. It is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings. The proposed method reveals the structure shared by subjects as well as the characteristics unique to each subject.
In this study, we explore the synergy of deep learning and financial market applications, focusing on pair trading. This market-neutral strategy is integral to quantitative finance and is apt for advanced deep-learning techniques. A pivotal challenge in pair trading is discerning temporal correlations among entities, necessitating the integration of diverse data modalities. Addressing this, we introduce a novel framework, Multi-modal Temporal Relation Graph Learning (MTRGL). MTRGL combines time series data and discrete features into a temporal graph and employs a memory-based temporal graph neural network. This approach reframes temporal correlation identification as a temporal graph link prediction task, which has shown empirical success. Our experiments on real-world datasets confirm the superior performance of MTRGL, emphasizing its promise in refining automated pair trading strategies.
Exploring the application of large language models (LLMs) to graph learning is a emerging endeavor. However, the vast amount of information inherent in large graphs poses significant challenges to this process. This work focuses on the link prediction task and introduces $\textbf{LPNL}$ (Link Prediction via Natural Language), a framework based on large language models designed for scalable link prediction on large-scale heterogeneous graphs. We design novel prompts for link prediction that articulate graph details in natural language. We propose a two-stage sampling pipeline to extract crucial information from the graphs, and a divide-and-conquer strategy to control the input tokens within predefined limits, addressing the challenge of overwhelming information. We fine-tune a T5 model based on our self-supervised learning designed for link prediction. Extensive experimental results demonstrate that LPNL outperforms multiple advanced baselines in link prediction tasks on large-scale graphs.
Despite remarkable success in diverse web-based applications, Graph Neural Networks(GNNs) inherit and further exacerbate historical discrimination and social stereotypes, which critically hinder their deployments in high-stake domains such as online clinical diagnosis, financial crediting, etc. However, current fairness research that primarily craft on i.i.d data, cannot be trivially replicated to non-i.i.d. graph structures with topological dependence among samples. Existing fair graph learning typically favors pairwise constraints to achieve fairness but fails to cast off dimensional limitations and generalize them into multiple sensitive attributes; besides, most studies focus on in-processing techniques to enforce and calibrate fairness, constructing a model-agnostic debiasing GNN framework at the pre-processing stage to prevent downstream misuses and improve training reliability is still largely under-explored. Furthermore, previous work on GNNs tend to enhance either fairness or privacy individually but few probe into their interplays. In this paper, we propose a novel model-agnostic debiasing framework named MAPPING (\underline{M}asking \underline{A}nd \underline{P}runing and Message-\underline{P}assing train\underline{ING}) for fair node classification, in which we adopt the distance covariance($dCov$)-based fairness constraints to simultaneously reduce feature and topology biases in arbitrary dimensions, and combine them with adversarial debiasing to confine the risks of attribute inference attacks. Experiments on real-world datasets with different GNN variants demonstrate the effectiveness and flexibility of MAPPING. Our results show that MAPPING can achieve better trade-offs between utility and fairness, and mitigate privacy risks of sensitive information leakage.
Graph condensation has emerged as an intriguing technique to save the expensive training costs of Graph Neural Networks (GNNs) by substituting a condensed small graph with the original graph. Despite the promising results achieved, previous methods usually employ an entangled paradigm of redundant parameters (nodes, edges, GNNs), which incurs complex joint optimization during condensation. This paradigm has considerably impeded the scalability of graph condensation, making it challenging to condense extremely large-scale graphs and generate high-fidelity condensed graphs. Therefore, we propose to disentangle the condensation process into a two-stage GNN-free paradigm, independently condensing nodes and generating edges while eliminating the need to optimize GNNs at the same time. The node condensation module avoids the complexity of GNNs by focusing on node feature alignment with anchors of the original graph, while the edge translation module constructs the edges of the condensed nodes by transferring the original structure knowledge with neighborhood anchors. This simple yet effective approach achieves at least 10 times faster than state-of-the-art methods with comparable accuracy on medium-scale graphs. Moreover, the proposed DisCo can successfully scale up to the Ogbn-papers100M graph containing over 100 million nodes with flexible reduction rates and improves performance on the second-largest Ogbn-products dataset by over 5%. Extensive downstream tasks and ablation study on five common datasets further demonstrate the effectiveness of the proposed DisCo framework. Our code is available at https://github.com/BangHonor/DisCo.
Property prediction is a fundamental task in crystal material research. To model atoms and structures, structures represented as graphs are widely used and graph learning-based methods have achieved significant progress. Bond angles and bond distances are two key structural information that greatly influence crystal properties. However, most of the existing works only consider bond distances and overlook bond angles. The main challenge lies in the time cost of handling bond angles, which leads to a significant increase in inference time. To solve this issue, we first propose a crystal structure modeling based on dual scale neighbor partitioning mechanism, which uses a larger scale cutoff for edge neighbors and a smaller scale cutoff for angle neighbors. Then, we propose a novel Atom-Distance-Angle Graph Neural Network (ADA-GNN) for property prediction tasks, which can process node information and structural information separately. The accuracy of predictions and inference time are improved with the dual scale modeling and the specially designed architecture of ADA-GNN. The experimental results validate that our approach achieves state-of-the-art results in two large-scale material benchmark datasets on property prediction tasks.
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.
Recently, Federated Graph Learning (FGL) has attracted significant attention as a distributed framework based on graph neural networks, primarily due to its capability to break data silos. Existing FGL studies employ community split on the homophilous global graph by default to simulate federated semi-supervised node classification settings. Such a strategy assumes the consistency of topology between the multi-client subgraphs and the global graph, where connected nodes are highly likely to possess similar feature distributions and the same label. However, in real-world implementations, the varying perspectives of local data engineering result in various subgraph topologies, posing unique heterogeneity challenges in FGL. Unlike the well-known label Non-independent identical distribution (Non-iid) problems in federated learning, FGL heterogeneity essentially reveals the topological divergence among multiple clients, namely homophily or heterophily. To simulate and handle this unique challenge, we introduce the concept of structure Non-iid split and then present a new paradigm called \underline{Ada}ptive \underline{F}ederated \underline{G}raph \underline{L}earning (AdaFGL), a decoupled two-step personalized approach. To begin with, AdaFGL employs standard multi-client federated collaborative training to acquire the federated knowledge extractor by aggregating uploaded models in the final round at the server. Then, each client conducts personalized training based on the local subgraph and the federated knowledge extractor. Extensive experiments on the 12 graph benchmark datasets validate the superior performance of AdaFGL over state-of-the-art baselines. Specifically, in terms of test accuracy, our proposed AdaFGL outperforms baselines by significant margins of 3.24\% and 5.57\% on community split and structure Non-iid split, respectively.
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.
Boolean algebraic manipulation is at the core of logic synthesis in Electronic Design Automation (EDA) design flow. Existing methods struggle to fully exploit optimization opportunities, and often suffer from an explosive search space and limited scalability efficiency. This work presents BoolGebra, a novel attributed graph-learning approach for Boolean algebraic manipulation that aims to improve fundamental logic synthesis. BoolGebra incorporates Graph Neural Networks (GNNs) and takes initial feature embeddings from both structural and functional information as inputs. A fully connected neural network is employed as the predictor for direct optimization result predictions, significantly reducing the search space and efficiently locating the optimization space. The experiments involve training the BoolGebra model w.r.t design-specific and cross-design inferences using the trained model, where BoolGebra demonstrates generalizability for cross-design inference and its potential to scale from small, simple training datasets to large, complex inference datasets. Finally, BoolGebra is integrated with existing synthesis tool ABC to perform end-to-end logic minimization evaluation w.r.t SOTA baselines.
Gaussian graphical models emerge in a wide range of fields. They model the statistical relationships between variables as a graph, where an edge between two variables indicates conditional dependence. Unfortunately, well-established estimators, such as the graphical lasso or neighborhood selection, are known to be susceptible to a high prevalence of false edge detections. False detections may encourage inaccurate or even incorrect scientific interpretations, with major implications in applications, such as biomedicine or healthcare. In this paper, we introduce a nodewise variable selection approach to graph learning and provably control the false discovery rate of the selected edge set at a self-estimated level. A novel fusion method of the individual neighborhoods outputs an undirected graph estimate. The proposed method is parameter-free and does not require tuning by the user. Benchmarks against competing false discovery rate controlling methods in numerical experiments considering different graph topologies show a significant gain in performance.
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.
Real-time and precise traffic flow prediction is vital for the efficiency of intelligent transportation systems. Traditional methods often employ graph neural networks (GNNs) with predefined graphs to describe spatial correlations among traffic nodes in urban road networks. However, these pre-defined graphs are limited by existing knowledge and graph generation methodologies, offering an incomplete picture of spatial correlations. While time-varying graphs based on data-driven learning have attempted to address these limitations, they still struggle with adequately capturing the inherent spatial correlations in traffic data. Moreover, most current methods for capturing dynamic temporal correlations rely on a unified calculation scheme using a temporal multi-head self-attention mechanism, which at some level might leads to inaccuracies. In order to overcome these challenges, we have proposed a novel hybrid time-varying graph neural network (HTVGNN) for traffic flow prediction. Firstly, a novel enhanced temporal perception multi-head self-attention mechanism based on time-varying mask enhancement was reported to more accurately model the dynamic temporal dependencies among distinct traffic nodes in the traffic network. Secondly, we have proposed a novel graph learning strategy to concurrently learn both static and dynamic spatial associations between different traffic nodes in road networks. Meanwhile, in order to enhance the learning ability of time-varying graphs, a coupled graph learning mechanism was designed to couple the graphs learned at each time step. Finally, the effectiveness of the proposed method HTVGNN was demonstrated with four real data sets. Simulation results revealed that HTVGNN achieves superior prediction accuracy compared to the state of the art spatio-temporal graph neural network models. Additionally, the ablation experiment verifies that the coupled graph learning mechanism can effectively improve the long-term prediction performance of HTVGNN.
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.
In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal processing. The parameter $k$ represents the number of neighbors that are connected to the target node; however, its appropriate selection is still a challenging problem. Therefore, most $k$NNGs use ad hoc selection methods for $k$. In the proposed method, we assume that a different $k$ can be chosen for each node. We formulate a discrete optimization problem to seek the best $k$ with a constraint on the sum of distances of the connected nodes. The optimal $k$ values are efficiently obtained without solving a complex optimization. Furthermore, we reveal that the proposed method is closely related to existing graph learning methods. In experiments on real datasets, we demonstrate that the $k$NNGs obtained with our method are sparse and can determine an appropriate variable number of edges per node. We validate the effectiveness of the proposed method for point cloud denoising, comparing our denoising performance with achievable graph construction methods that can be scaled to typical point cloud sizes (e.g., thousands of nodes).
Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for diverse networks such as transportation, brain, social, and internet networks. Furthermore, the rapid advancements in machine learning have expanded the scope of dynamic graph applications beyond the aforementioned domains. In this paper, we present a review of lesser-explored applications of dynamic graph learning. This study revealed the potential of machine learning on dynamic graphs in addressing challenges across diverse domains, including those with limited levels of association with the field.
Dynamic graph learning is crucial for modeling real-world systems with evolving relationships and temporal dynamics. However, the lack of a unified benchmark framework in current research has led to inaccurate evaluations of dynamic graph models. This paper highlights the significance of dynamic graph learning and its applications in various domains. It emphasizes the need for a standardized benchmark framework that captures temporal dynamics, evolving graph structures, and downstream task requirements. Establishing a unified benchmark will help researchers understand the strengths and limitations of existing models, foster innovation, and advance dynamic graph learning. In conclusion, this paper identifies the lack of a standardized benchmark framework as a current limitation in dynamic graph learning research . Such a framework will facilitate accurate model evaluation, drive advancements in dynamic graph learning techniques, and enable the development of more effective models for real-world applications.