Federated graph learning is an emerging field with significant practical challenges. While algorithms have been proposed to improve the accuracy of training graph neural networks, such as node classification on federated graphs, the system performance is often overlooked, despite it is crucial for real-world deployment. To bridge this gap, we introduce FedGraph, a research library designed for practical distributed training and comprehensive benchmarking of FGL algorithms. FedGraph supports a range of state-of-the-art graph learning methods and includes a monitoring class that evaluates system performance, with a particular focus on communication and computation costs during training. Unlike existing federated learning platforms, FedGraph natively integrates homomorphic encryption to enhance privacy preservation and supports scalable deployment across multiple physical machines with system-level performance evaluation to guide the system design of future algorithms. To enhance efficiency and privacy, we propose a low-rank communication scheme for algorithms like FedGCN that require pre-training communication, accelerating both the pre-training and training phases. Extensive experiments benchmark different FGL algorithms on three major graph learning tasks and demonstrate FedGraph as the first efficient FGL framework to support encrypted low-rank communication and scale to graphs with 100 million nodes.
Attention mechanisms have made significant strides in graph learning, yet they still exhibit notable limitations: local attention faces challenges in capturing long-range information due to the inherent problems of the message-passing scheme, while global attention cannot reflect the hierarchical neighborhood structure and fails to capture fine-grained local information. In this paper, we propose a novel multi-hop graph attention mechanism, named Subtree Attention (STA), to address the aforementioned issues. STA seamlessly bridges the fully-attentional structure and the rooted subtree, with theoretical proof that STA approximates the global attention under extreme settings. By allowing direct computation of attention weights among multi-hop neighbors, STA mitigates the inherent problems in existing graph attention mechanisms. Further we devise an efficient form for STA by employing kernelized softmax, which yields a linear time complexity. Our resulting GNN architecture, the STAGNN, presents a simple yet performant STA-based graph neural network leveraging a hop-aware attention strategy. Comprehensive evaluations on ten node classification datasets demonstrate that STA-based models outperform existing graph transformers and mainstream GNNs. The code is available at https://github.com/LUMIA-Group/SubTree-Attention.
The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the Local Euler Characteristic Transform ($\ell$-ECT), a novel extension of the ECT particularly designed to enhance expressivity and interpretability in graph representation learning. Unlike traditional Graph Neural Networks (GNNs), which may lose critical local details through aggregation, the $\ell$-ECT provides a lossless representation of local neighborhoods. This approach addresses key limitations in GNNs by preserving nuanced local structures while maintaining global interpretability. Moreover, we construct a rotation-invariant metric based on $\ell$-ECTs for spatial alignment of data spaces. Our method exhibits superior performance compared to standard GNNs on a variety of node-classification tasks, while also offering theoretical guarantees that demonstrate its effectiveness.
Graph Neural Networks (GNNs) have proven effective in various medical imaging applications, such as automated disease diagnosis. However, due to the local neighborhood aggregation paradigm in message passing which characterizes these models, they inherently suffer from two fundamental limitations: first, indistinguishable node embeddings due to heterophilic node aggregation (known as over-smoothing), and second, impaired message passing due to aggregation through graph bottlenecks (known as over-squashing). These challenges hinder the model expressiveness and prevent us from using deeper models to capture long-range node dependencies within the graph. Popular solutions in the literature are either too expensive to process large graphs due to high time complexity or do not generalize across all graph topologies. To address these limitations, we propose DuoGNN, a scalable and generalizable architecture which leverages topology to decouple homophilic and heterophilic edges and capture both short-range and long-range interactions. Our three core contributions introduce (i) a topological edge-filtering algorithm which extracts homophilic interactions and enables the model to generalize well for any graph topology, (ii) a heterophilic graph condensation technique which extracts heterophilic interactions and ensures scalability, and (iii) a dual homophilic and heterophilic aggregation pipeline which prevents over-smoothing and over-squashing during the message passing. We benchmark our model on medical and non-medical node classification datasets and compare it with its variants, showing consistent improvements across all tasks. Our DuoGNN code is available at https://github.com/basiralab/DuoGNN.
Conformal prediction has become increasingly popular for quantifying the uncertainty associated with machine learning models. Recent work in graph uncertainty quantification has built upon this approach for conformal graph prediction. The nascent nature of these explorations has led to conflicting choices for implementations, baselines, and method evaluation. In this work, we analyze the design choices made in the literature and discuss the tradeoffs associated with existing methods. Building on the existing implementations, we introduce techniques to scale existing methods to large-scale graph datasets without sacrificing performance. Our theoretical and empirical results justify our recommendations for future scholarship in graph conformal prediction.
With the prosperity of contrastive learning for visual representation learning (VCL), it is also adapted to the graph domain and yields promising performance. However, through a systematic study of various graph contrastive learning (GCL) methods, we observe that some common phenomena among existing GCL methods that are quite different from the original VCL methods, including 1) positive samples are not a must for GCL; 2) negative samples are not necessary for graph classification, neither for node classification when adopting specific normalization modules; 3) data augmentations have much less influence on GCL, as simple domain-agnostic augmentations (e.g., Gaussian noise) can also attain fairly good performance. By uncovering how the implicit inductive bias of GNNs works in contrastive learning, we theoretically provide insights into the above intriguing properties of GCL. Rather than directly porting existing VCL methods to GCL, we advocate for more attention toward the unique architecture of graph learning and consider its implicit influence when designing GCL methods. Code is available at https: //github.com/PKU-ML/ArchitectureMattersGCL.
The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing as a special case. Most approaches to mitigate over-smoothing extend common message-passing schemes, e.g., the graph convolutional network, by utilizing residual connections, gating mechanisms, normalization, or regularization techniques. Our work contrarily proposes to directly tackle the cause of this issue by modifying the message-passing scheme and exchanging different types of messages using multi-relational graphs. We identify a sufficient condition to ensure linearly independent node representations. As one instantion, we show that operating on multiple directed acyclic graphs always satisfies our condition and propose to obtain these by defining a strict partial ordering of the nodes. We conduct comprehensive experiments that confirm the benefits of operating on multi-relational graphs to achieve more informative node representations.
Heterophilous graphs, where dissimilar nodes tend to connect, pose a challenge for graph neural networks (GNNs). Increasing the GNN depth can expand the scope (i.e., receptive field), potentially finding homophily from the higher-order neighborhoods. However, GNNs suffer from performance degradation as depth increases. Despite having better expressivity, state-of-the-art deeper GNNs achieve only marginal improvements compared to their shallow variants. Through theoretical and empirical analysis, we systematically demonstrate a shift in GNN generalization preferences across nodes with different homophily levels as depth increases. This creates a disparity in generalization patterns between GNN models with varying depth. Based on these findings, we propose to improve deeper GNN generalization while maintaining high expressivity by Mixture of scope experts at test (Moscat). Experimental results show that Moscat works flexibly with various GNNs across a wide range of datasets while significantly improving accuracy. Our code is available at (https://github.com/Hydrapse/moscat).
In this study, we undertake a reproducibility analysis of 'Learning Fair Graph Representations Via Automated Data Augmentations' by Ling et al. (2022). We assess the validity of the original claims focused on node classification tasks and explore the performance of the Graphair framework in link prediction tasks. Our investigation reveals that we can partially reproduce one of the original three claims and fully substantiate the other two. Additionally, we broaden the application of Graphair from node classification to link prediction across various datasets. Our findings indicate that, while Graphair demonstrates a comparable fairness-accuracy trade-off to baseline models for mixed dyadic-level fairness, it has a superior trade-off for subgroup dyadic-level fairness. These findings underscore Graphair's potential for wider adoption in graph-based learning. Our code base can be found on GitHub at https://github.com/juellsprott/graphair-reproducibility.
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order information, i.e., information that goes \emph{beyond} pairwise interactions. Recent work has shown that persistent homology, a tool from topological data analysis, can enrich graph neural networks with topological information that they otherwise could not capture. Calculating such features is efficient for dimension 0 (connected components) and dimension 1 (cycles). However, when it comes to higher-order structures, it does not scale well, with a complexity of $O(n^d)$, where $n$ is the number of nodes and $d$ is the order of the structures. In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm. On standard benchmark datasets, we show that our method can lead to up to $31\%$ improvements in test accuracy.
Spectral Graph Convolutional Networks (GCNs) have gained popularity in graph machine learning applications due, in part, to their flexibility in specification of network propagation rules. These propagation rules are often constructed as polynomial filters whose coefficients are learned using label information during training. In contrast to learned polynomial filters, explicit filter functions are useful in capturing relationships between network topology and distribution of labels across the network. A number of algorithms incorporating either approach have been proposed; however the relationship between filter functions and polynomial approximations is not fully resolved. This is largely due to the ill-conditioned nature of the linear systems that must be solved to derive polynomial approximations of filter functions. To address this challenge, we propose a novel Arnoldi orthonormalization-based algorithm, along with a unifying approach, called G-Arnoldi-GCN that can efficiently and effectively approximate a given filter function with a polynomial. We evaluate G-Arnoldi-GCN in the context of multi-class node classification across ten datasets with diverse topological characteristics. Our experiments show that G-Arnoldi-GCN consistently outperforms state-of-the-art methods when suitable filter functions are employed. Overall, G-Arnoldi-GCN opens important new directions in graph machine learning by enabling the explicit design and application of diverse filter functions. Code link: https://github.com/mustafaCoskunAgu/GArnoldi-GCN
In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.
Graph distillation has emerged as a solution for reducing large graph datasets to smaller, more manageable, and informative ones. Existing methods primarily target node classification, involve computationally intensive processes, and fail to capture the true distribution of the full graph dataset. To address these issues, we introduce Graph Distillation with Structural Attention Matching (GSTAM), a novel method for condensing graph classification datasets. GSTAM leverages the attention maps of GNNs to distill structural information from the original dataset into synthetic graphs. The structural attention-matching mechanism exploits the areas of the input graph that GNNs prioritize for classification, effectively distilling such information into the synthetic graphs and improving overall distillation performance. Comprehensive experiments demonstrate GSTAM's superiority over existing methods, achieving 0.45% to 6.5% better performance in extreme condensation ratios, highlighting its potential use in advancing distillation for graph classification tasks (Code available at https://github.com/arashrasti96/GSTAM).
Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combines symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: i) G-SympGNN and ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. We also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.
Zero-shot graph machine learning, especially with graph neural networks (GNNs), has garnered significant interest due to the challenge of scarce labeled data. While methods like self-supervised learning and graph prompt learning have been extensively explored, they often rely on fine-tuning with task-specific labels, limiting their effectiveness in zero-shot scenarios. Inspired by the zero-shot capabilities of instruction-fine-tuned large language models (LLMs), we introduce a novel framework named Token Embedding-Aligned Graph Language Model (TEA-GLM) that leverages LLMs as cross-dataset and cross-task zero-shot learners for graph machine learning. Concretely, we pretrain a GNN, aligning its representations with token embeddings of an LLM. We then train a linear projector that transforms the GNN's representations into a fixed number of graph token embeddings without tuning the LLM. A unified instruction is designed for various graph tasks at different levels, such as node classification (node-level) and link prediction (edge-level). These design choices collectively enhance our method's effectiveness in zero-shot learning, setting it apart from existing methods. Experiments show that our graph token embeddings help the LLM predictor achieve state-of-the-art performance on unseen datasets and tasks compared to other methods using LLMs as predictors.
Federated Graph Learning (FGL) aims to learn graph learning models over graph data distributed in multiple data owners, which has been applied in various applications such as social recommendation and financial fraud detection. Inherited from generic Federated Learning (FL), FGL similarly has the data heterogeneity issue where the label distribution may vary significantly for distributed graph data across clients. For instance, a client can have the majority of nodes from a class, while another client may have only a few nodes from the same class. This issue results in divergent local objectives and impairs FGL convergence for node-level tasks, especially for node classification. Moreover, FGL also encounters a unique challenge for the node classification task: the nodes from a minority class in a client are more likely to have biased neighboring information, which prevents FGL from learning expressive node embeddings with Graph Neural Networks (GNNs). To grapple with the challenge, we propose FedSpray, a novel FGL framework that learns local class-wise structure proxies in the latent space and aligns them to obtain global structure proxies in the server. Our goal is to obtain the aligned structure proxies that can serve as reliable, unbiased neighboring information for node classification. To achieve this, FedSpray trains a global feature-structure encoder and generates unbiased soft targets with structure proxies to regularize local training of GNN models in a personalized way. We conduct extensive experiments over four datasets, and experiment results validate the superiority of FedSpray compared with other baselines. Our code is available at https://github.com/xbfu/FedSpray.
When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to jointly denoise the features and rewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.
Graph Transformers (GTs) have recently achieved significant success in the graph domain by effectively capturing both long-range dependencies and graph inductive biases. However, these methods face two primary challenges: (1) multi-view chaos, which results from coupling multi-view information (positional, structural, attribute), thereby impeding flexible usage and the interpretability of the propagation process. (2) local-global chaos, which arises from coupling local message passing with global attention, leading to issues of overfitting and over-globalizing. To address these challenges, we propose a high-level decoupled perspective of GTs, breaking them down into three components and two interaction levels: positional attention, structural attention, and attribute attention, alongside local and global interaction. Based on this decoupled perspective, we design a decoupled graph triple attention network named DeGTA, which separately computes multi-view attentions and adaptively integrates multi-view local and global information. This approach offers three key advantages: enhanced interpretability, flexible design, and adaptive integration of local and global information. Through extensive experiments, DeGTA achieves state-of-the-art performance across various datasets and tasks, including node classification and graph classification. Comprehensive ablation studies demonstrate that decoupling is essential for improving performance and enhancing interpretability. Our code is available at: https://github.com/wangxiaotang0906/DeGTA
Contrastive learning is a significant paradigm in graph self-supervised learning. However, it requires negative samples to prevent model collapse and learn discriminative representations. These negative samples inevitably lead to heavy computation, memory overhead and class collision, compromising the representation learning. Recent studies present that methods obviating negative samples can attain competitive performance and scalability enhancements, exemplified by bootstrapped graph latents (BGRL). However, BGRL neglects the inherent graph homophily, which provides valuable insights into underlying positive pairs. Our motivation arises from the observation that subtly introducing a few ground-truth positive pairs significantly improves BGRL. Although we can't obtain ground-truth positive pairs without labels under the self-supervised setting, edges in the graph can reflect noisy positive pairs, i.e., neighboring nodes often share the same label. Therefore, we propose to expand the positive pair set with node-neighbor pairs. Subsequently, we introduce a cross-attention module to predict the supportiveness score of a neighbor with respect to the anchor node. This score quantifies the positive support from each neighboring node, and is encoded into the training objective. Consequently, our method mitigates class collision from negative and noisy positive samples, concurrently enhancing intra-class compactness. Extensive experiments are conducted on five benchmark datasets and three downstream task node classification, node clustering, and node similarity search. The results demonstrate that our method generates node representations with enhanced intra-class compactness and achieves state-of-the-art performance.
Graph Neural Networks (GNNs) are important across different domains, such as social network analysis and recommendation systems, due to their ability to model complex relational data. This paper introduces subgraph queries as a new task for deep graph learning. Unlike traditional graph prediction tasks that focus on individual components like link prediction or node classification, subgraph queries jointly predict the components of a target subgraph based on evidence that is represented by an observed subgraph. For instance, a subgraph query can predict a set of target links and/or node labels. To answer subgraph queries, we utilize a probabilistic deep Graph Generative Model. Specifically, we inductively train a Variational Graph Auto-Encoder (VGAE) model, augmented to represent a joint distribution over links, node features and labels. Bayesian optimization is used to tune a weighting for the relative importance of links, node features and labels in a specific domain. We describe a deterministic and a sampling-based inference method for estimating subgraph probabilities from the VGAE generative graph distribution, without retraining, in zero-shot fashion. For evaluation, we apply the inference methods on a range of subgraph queries on six benchmark datasets. We find that inference from a model achieves superior predictive performance, surpassing independent prediction baselines with improvements in AUC scores ranging from 0.06 to 0.2 points, depending on the dataset.