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.
Large language models (LLMs) have presented significant opportunities to enhance various machine learning applications, including graph neural networks (GNNs). By leveraging the vast open-world knowledge within LLMs, we can more effectively interpret and utilize textual data to better characterize heterophilic graphs, where neighboring nodes often have different labels. However, existing approaches for heterophilic graphs overlook the rich textual data associated with nodes, which could unlock deeper insights into their heterophilic contexts. In this work, we explore the potential of LLMs for modeling heterophilic graphs and propose a novel two-stage framework: LLM-enhanced edge discriminator and LLM-guided edge reweighting. In the first stage, we fine-tune the LLM to better identify homophilic and heterophilic edges based on the textual content of their nodes. In the second stage, we adaptively manage message propagation in GNNs for different edge types based on node features, structures, and heterophilic or homophilic characteristics. To cope with the computational demands when deploying LLMs in practical scenarios, we further explore model distillation techniques to fine-tune smaller, more efficient models that maintain competitive performance. Extensive experiments validate the effectiveness of our framework, demonstrating the feasibility of using LLMs to enhance node classification on heterophilic graphs.
Graph Neural Networks (GNNs) have emerged as powerful tools for predicting outcomes in graph-structured data. However, a notable limitation of GNNs is their inability to provide robust uncertainty estimates, which undermines their reliability in contexts where errors are costly. One way to address this issue is by providing prediction sets that contain the true label with a predefined probability margin. Our approach builds upon conformal prediction (CP), a framework that promises to construct statistically robust prediction sets or intervals. There are two primary challenges: first, given dependent data like graphs, it is unclear whether the critical assumption in CP - exchangeability - still holds when applied to node classification. Second, even if the exchangeability assumption is valid for conformalized link prediction, we need to ensure high efficiency, i.e., the resulting prediction set or the interval length is small enough to provide useful information. In this article, we propose a novel approach termed Robust Conformal Prediction for GNNs (RoCP-GNN), which integrates conformal prediction (CP) directly into the GNN training process. This method generates prediction sets, instead of just point predictions, that are valid at a user-defined confidence level, assuming only exchangeability. Our approach robustly predicts outcomes with any predictive GNN model while quantifying the uncertainty in predictions within the realm of graph-based semi-supervised learning (SSL). Experimental results demonstrate that GNN models with size loss provide a statistically significant increase in performance. We validate our approach on standard graph benchmark datasets by coupling it with various state-of-the-art GNNs in node classification. The code will be made available after publication.
As graphs grow larger, full-batch GNN training becomes hard for single GPU memory. Therefore, to enhance the scalability of GNN training, some studies have proposed sampling-based mini-batch training and distributed graph learning. However, these methods still have drawbacks, such as performance degradation and heavy communication. This paper introduces SliceGCN, a feature-sliced distributed large-scale graph learning method. SliceGCN slices the node features, with each computing device, i.e., GPU, handling partial features. After each GPU processes its share, partial representations are obtained and concatenated to form complete representations, enabling a single GPU's memory to handle the entire graph structure. This aims to avoid the accuracy loss typically associated with mini-batch training (due to incomplete graph structures) and to reduce inter-GPU communication during message passing (the forward propagation process of GNNs). To study and mitigate potential accuracy reductions due to slicing features, this paper proposes feature fusion and slice encoding. Experiments were conducted on six node classification datasets, yielding some interesting analytical results. These results indicate that while SliceGCN does not enhance efficiency on smaller datasets, it does improve efficiency on larger datasets. Additionally, we found that SliceGCN and its variants have better convergence, feature fusion and slice encoding can make training more stable, reduce accuracy fluctuations, and this study also discovered that the design of SliceGCN has a potentially parameter-efficient nature.
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.
Graph neural networks (GNNs) have achieved impressive impressions for graph-related tasks. However, most GNNs are primarily studied under the cases of signal domain with supervised training, which requires abundant task-specific labels and is difficult to transfer to other domains. There are few works focused on domain adaptation for graph node classification. They mainly focused on aligning the feature space of the source and target domains, without considering the feature alignment between different categories, which may lead to confusion of classification in the target domain. However, due to the scarcity of labels of the target domain, we cannot directly perform effective alignment of categories from different domains, which makes the problem more challenging. In this paper, we present the \textit{Spectral Augmentation for Graph Domain Adaptation (\method{})} for graph node classification. First, we observe that nodes with the same category in different domains exhibit similar characteristics in the spectral domain, while different classes are quite different. Following the observation, we align the category feature space of different domains in the spectral domain instead of aligning the whole features space, and we theoretical proof the stability of proposed \method{}. Then, we develop a dual graph convolutional network to jointly exploits local and global consistency for feature aggregation. Last, we utilize a domain classifier with an adversarial learning submodule to facilitate knowledge transfer between different domain graphs. Experimental results on a variety of publicly available datasets reveal the effectiveness of our \method{}.
Heterophilic Graph Neural Networks (HGNNs) have shown promising results for semi-supervised learning tasks on graphs. Notably, most real-world heterophilic graphs are composed of a mixture of nodes with different neighbor patterns, exhibiting local node-level homophilic and heterophilic structures. However, existing works are only devoted to designing better HGNN backbones or architectures for node classification tasks on heterophilic and homophilic graph benchmarks simultaneously, and their analyses of HGNN performance with respect to nodes are only based on the determined data distribution without exploring the effect caused by this structural difference between training and testing nodes. How to learn invariant node representations on heterophilic graphs to handle this structure difference or distribution shifts remains unexplored. In this paper, we first discuss the limitations of previous graph-based invariant learning methods from the perspective of data augmentation. Then, we propose \textbf{HEI}, a framework capable of generating invariant node representations through incorporating heterophily information to infer latent environments without augmentation, which are then used for invariant prediction, under heterophilic graph structure distribution shifts. We theoretically show that our proposed method can achieve guaranteed performance under heterophilic graph structure distribution shifts. Extensive experiments on various benchmarks and backbones can also demonstrate the effectiveness of our method compared with existing state-of-the-art baselines.
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
Textual graphs are ubiquitous in real-world applications, featuring rich text information with complex relationships, which enables advanced research across various fields. Textual graph representation learning aims to generate low-dimensional feature embeddings from textual graphs that can improve the performance of downstream tasks. A high-quality feature embedding should effectively capture both the structural and the textual information in a textual graph. However, most textual graph dataset benchmarks rely on word2vec techniques to generate feature embeddings, which inherently limits their capabilities. Recent works on textual graph representation learning can be categorized into two folds: supervised and unsupervised methods. Supervised methods finetune a language model on labeled nodes, which have limited capabilities when labeled data is scarce. Unsupervised methods, on the other hand, extract feature embeddings by developing complex training pipelines. To address these limitations, we propose a novel unified unsupervised learning autoencoder framework, named Node Level Graph AutoEncoder (NodeGAE). We employ language models as the backbone of the autoencoder, with pretraining on text reconstruction. Additionally, we add an auxiliary loss term to make the feature embeddings aware of the local graph structure. Our method maintains simplicity in the training process and demonstrates generalizability across diverse textual graphs and downstream tasks. We evaluate our method on two core graph representation learning downstream tasks: node classification and link prediction. Comprehensive experiments demonstrate that our approach substantially enhances the performance of diverse graph neural networks (GNNs) across multiple textual graph datasets.
Dynamic graph learning aims to uncover evolutionary laws in real-world systems, enabling accurate social recommendation (link prediction) or early detection of cancer cells (classification). Inspired by the success of state space models, e.g., Mamba, for efficiently capturing long-term dependencies in language modeling, we propose DyG-Mamba, a new continuous state space model (SSM) for dynamic graph learning. Specifically, we first found that using inputs as control signals for SSM is not suitable for continuous-time dynamic network data with irregular sampling intervals, resulting in models being insensitive to time information and lacking generalization properties. Drawing inspiration from the Ebbinghaus forgetting curve, which suggests that memory of past events is strongly correlated with time intervals rather than specific details of the events themselves, we directly utilize irregular time spans as control signals for SSM to achieve significant robustness and generalization. Through exhaustive experiments on 12 datasets for dynamic link prediction and dynamic node classification tasks, we found that DyG-Mamba achieves state-of-the-art performance on most of the datasets, while also demonstrating significantly improved computation and memory efficiency.
Node classification using Graph Neural Networks (GNNs) has been widely applied in various practical scenarios, such as predicting user interests and detecting communities in social networks. However, recent studies have shown that graph-structured networks often contain potential noise and attacks, in the form of topological perturbations and weight disturbances, which can lead to decreased classification performance in GNNs. To improve the robustness of the model, we propose a novel method: Random Walk Negative Sampling Graph Convolutional Network (RW-NSGCN). Specifically, RW-NSGCN integrates the Random Walk with Restart (RWR) and PageRank (PGR) algorithms for negative sampling and employs a Determinantal Point Process (DPP)-based GCN for convolution operations. RWR leverages both global and local information to manage noise and local variations, while PGR assesses node importance to stabilize the topological structure. The DPP-based GCN ensures diversity among negative samples and aggregates their features to produce robust node embeddings, thereby improving classification performance. Experimental results demonstrate that the RW-NSGCN model effectively addresses network topology attacks and weight instability, increasing the accuracy of anomaly detection and overall stability. In terms of classification accuracy, RW-NSGCN significantly outperforms existing methods, showing greater resilience across various scenarios and effectively mitigating the impact of such vulnerabilities.
Unified graph representation learning aims to produce node embeddings, which can be applied to multiple downstream applications. However, existing studies based on graph neural networks and language models either suffer from the limitations of numerous training needed toward specific downstream predictions or have shallow semantic features. In this work, we propose a novel Path-LLM model to learn unified graph representation, which leverages a powerful large language model (LLM) to incorporate our proposed path features. Our Path-LLM framework consists of several well-designed techniques. First, we develop a new mechanism of long-to-short shortest path (L2SP) selection, which covers essential connections between different dense groups. An in-depth comparison of different path selection plans is offered to illustrate the strength of our designed L2SP. Then, we design path textualization to obtain L2SP-based training texts. Next, we feed the texts into a self-supervised LLM training process to learn embeddings. Extensive experiments on benchmarks validate the superiority of Path-LLM against the state-of-the-art WalkLM method on two classical graph learning tasks (node classification and link prediction) and one NP-hard graph query processing task (keyword search), meanwhile saving more than 90% of training paths.
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.
Knowledge graphs (KGs) enhance the performance of large language models (LLMs) and search engines by providing structured, interconnected data that improves reasoning and context-awareness. However, KGs only focus on text data, thereby neglecting other modalities such as speech. In this work, we introduce wav2graph, the first framework for supervised learning knowledge graph from speech data. Our pipeline are straightforward: (1) constructing a KG based on transcribed spoken utterances and a named entity database, (2) converting KG into embedding vectors, and (3) training graph neural networks (GNNs) for node classification and link prediction tasks. Through extensive experiments conducted in inductive and transductive learning contexts using state-of-the-art GNN models, we provide baseline results and error analysis for node classification and link prediction tasks on human transcripts and automatic speech recognition (ASR) transcripts, including evaluations using both encoder-based and decoder-based node embeddings, as well as monolingual and multilingual acoustic pre-trained models. All related code, data, and models are published online.
Graph learning methods have been extensively applied in diverse application areas. However, what kind of inherent graph properties e.g. graph proximity, graph structural information has been encoded into graph representation learning for downstream tasks is still under-explored. In this paper, we propose a novel graph probing framework (GraphProbe) to investigate and interpret whether the family of graph learning methods has encoded different levels of knowledge in graph representation learning. Based on the intrinsic properties of graphs, we design three probes to systematically investigate the graph representation learning process from different perspectives, respectively the node-wise level, the path-wise level, and the structural level. We construct a thorough evaluation benchmark with nine representative graph learning methods from random walk based approaches, basic graph neural networks and self-supervised graph methods, and probe them on six benchmark datasets for node classification, link prediction and graph classification. The experimental evaluation verify that GraphProbe can estimate the capability of graph representation learning. Remaking results have been concluded: GCN and WeightedGCN methods are relatively versatile methods achieving better results with respect to different tasks.
Graph Neural Networks (GNNs) have attracted substantial interest due to their exceptional performance on graph-based data. However, their robustness, especially on heterogeneous graphs, remains underexplored, particularly against adversarial attacks. This paper proposes HeteroKRLAttack, a targeted evasion black-box attack method for heterogeneous graphs. By integrating reinforcement learning with a Top-K algorithm to reduce the action space, our method efficiently identifies effective attack strategies to disrupt node classification tasks. We validate the effectiveness of HeteroKRLAttack through experiments on multiple heterogeneous graph datasets, showing significant reductions in classification accuracy compared to baseline methods. An ablation study underscores the critical role of the Top-K algorithm in enhancing attack performance. Our findings highlight potential vulnerabilities in current models and provide guidance for future defense strategies against adversarial attacks on heterogeneous graphs.
This paper provides a comprehensive and detailed derivation of the backpropagation algorithm for graph convolutional neural networks using matrix calculus. The derivation is extended to include arbitrary element-wise activation functions and an arbitrary number of layers. The study addresses two fundamental problems, namely node classification and link prediction. To validate our method, we compare it with reverse-mode automatic differentiation. The experimental results demonstrate that the median sum of squared errors of the updated weight matrices, when comparing our method to the approach using reverse-mode automatic differentiation, falls within the range of $10^{-18}$ to $10^{-14}$. These outcomes are obtained from conducting experiments on a five-layer graph convolutional network, applied to a node classification problem on Zachary's karate club social network and a link prediction problem on a drug-drug interaction network. Finally, we show how the derived closed-form solution can facilitate the development of explainable AI and sensitivity analysis.