Conventional graph neural networks (GNNs) are often confronted with fairness issues that may stem from their input, including node attributes and neighbors surrounding a node. While several recent approaches have been proposed to eliminate the bias rooted in sensitive attributes, they ignore the other key input of GNNs, namely the neighbors of a node, which can introduce bias since GNNs hinge on neighborhood structures to generate node representations. In particular, the varying neighborhood structures across nodes, manifesting themselves in drastically different node degrees, give rise to the diverse behaviors of nodes and biased outcomes. In this paper, we first define and generalize the degree bias using a generalized definition of node degree as a manifestation and quantification of different multi-hop structures around different nodes. To address the bias in the context of node classification, we propose a novel GNN framework called Generalized Degree Fairness-centric Graph Neural Network (Deg-FairGNN). Specifically, in each GNN layer, we employ a learnable debiasing function to generate debiasing contexts, which modulate the layer-wise neighborhood aggregation to eliminate the degree bias originating from the diverse degrees among nodes. Extensive experiments on three benchmark datasets demonstrate the effectiveness of our model on both accuracy and fairness metrics.
Most graph neural networks follow the message passing mechanism. However, it faces the over-smoothing problem when multiple times of message passing is applied to a graph, causing indistinguishable node representations and prevents the model to effectively learn dependencies between farther-away nodes. On the other hand, features of neighboring nodes with different labels are likely to be falsely mixed, resulting in the heterophily problem. In this work, we propose to order the messages passing into the node representation, with specific blocks of neurons targeted for message passing within specific hops. This is achieved by aligning the hierarchy of the rooted-tree of a central node with the ordered neurons in its node representation. Experimental results on an extensive set of datasets show that our model can simultaneously achieve the state-of-the-art in both homophily and heterophily settings, without any targeted design. Moreover, its performance maintains pretty well while the model becomes really deep, effectively preventing the over-smoothing problem. Finally, visualizing the gating vectors shows that our model learns to behave differently between homophily and heterophily settings, providing an explainable graph neural model.
Hard negative mining has shown effective in enhancing self-supervised contrastive learning (CL) on diverse data types, including graph CL (GCL). The existing hardness-aware CL methods typically treat negative instances that are most similar to the anchor instance as hard negatives, which helps improve the CL performance, especially on image data. However, this approach often fails to identify the hard negatives but leads to many false negatives on graph data. This is mainly due to that the learned graph representations are not sufficiently discriminative due to oversmooth representations and/or non-independent and identically distributed (non-i.i.d.) issues in graph data. To tackle this problem, this article proposes a novel approach that builds a discriminative model on collective affinity information (i.e., two sets of pairwise affinities between the negative instances and the anchor instance) to mine hard negatives in GCL. In particular, the proposed approach evaluates how confident/uncertain the discriminative model is about the affinity of each negative instance to an anchor instance to determine its hardness weight relative to the anchor instance. This uncertainty information is then incorporated into the existing GCL loss functions via a weighting term to enhance their performance. The enhanced GCL is theoretically grounded that the resulting GCL loss is equivalent to a triplet loss with an adaptive margin being exponentially proportional to the learned uncertainty of each negative instance. Extensive experiments on ten graph datasets show that our approach does the following: 1) consistently enhances different state-of-the-art (SOTA) GCL methods in both graph and node classification tasks and 2) significantly improves their robustness against adversarial attacks. Code is available at https://github.com/mala-lab/AUGCL.
We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. The method is built of two main types of blocks: (i) We introduce unsupervised kernel machine layers propagating the node features in a one-hop neighborhood, using implicit node feature mappings. (ii) We specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. We derive an effective initialization scheme and efficient end-to-end training algorithm in the dual variables for the full architecture. The main idea underlying GCKM is that, because of the unsupervised core, the final model can achieve higher performance in semi-supervised node classification when few labels are available for training. Experimental results demonstrate the effectiveness of the proposed framework.
Graph Transformer (GT) recently has emerged as a new paradigm of graph learning algorithms, outperforming the previously popular Message Passing Neural Network (MPNN) on multiple benchmarks. Previous work (Kim et al., 2022) shows that with proper position embedding, GT can approximate MPNN arbitrarily well, implying that GT is at least as powerful as MPNN. In this paper, we study the inverse connection and show that MPNN with virtual node (VN), a commonly used heuristic with little theoretical understanding, is powerful enough to arbitrarily approximate the self-attention layer of GT. In particular, we first show that if we consider one type of linear transformer, the so-called Performer/Linear Transformer (Choromanski et al., 2020; Katharopoulos et al., 2020), then MPNN + VN with only O(1) depth and O(1) width can approximate a self-attention layer in Performer/Linear Transformer. Next, via a connection between MPNN + VN and DeepSets, we prove the MPNN + VN with O(n^d) width and O(1) depth can approximate the self-attention layer arbitrarily well, where d is the input feature dimension. Lastly, under some assumptions, we provide an explicit construction of MPNN + VN with O(1) width and O(n) depth approximating the self-attention layer in GT arbitrarily well. On the empirical side, we demonstrate that 1) MPNN + VN is a surprisingly strong baseline, outperforming GT on the recently proposed Long Range Graph Benchmark (LRGB) dataset, 2) our MPNN + VN improves over early implementation on a wide range of OGB datasets and 3) MPNN + VN outperforms Linear Transformer and MPNN on the climate modeling task.
Graph neural networks (GNNs) have been proved powerful in graph-oriented tasks. However, many real-world graphs are heterophilous, challenging the homophily assumption of classical GNNs. To solve the universality problem, many studies deepen networks or concatenate intermediate representations, which does not inherently change neighbor aggregation and introduces noise. Recent studies propose new metrics to characterize the homophily, but rarely consider the correlation of the proposed metrics and models. In this paper, we first design a new metric, Neighborhood Homophily (\textit{NH}), to measure the label complexity or purity in node neighborhoods. Furthermore, we incorporate the metric into the classical graph convolutional network (GCN) architecture and propose \textbf{N}eighborhood \textbf{H}omophily-based \textbf{G}raph \textbf{C}onvolutional \textbf{N}etwork (\textbf{NHGCN}). In this framework, neighbors are grouped by estimated \textit{NH} values and aggregated from different channels, and the resulting node predictions are then used in turn to estimate and update \textit{NH} values. The two processes of metric estimation and model inference are alternately optimized to achieve better node classification. NHGCN achieves top overall performance on both homophilous and heterophilous benchmarks, with an improvement of up to 7.4\% compared to the current SOTA methods.
Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired instance representations. To this end, we introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states that progressively incorporate other instances' information by their interactions. The diffusion process is constrained by descent criteria w.r.t.~a principled energy function that characterizes the global consistency of instance representations over latent structures. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs, which gives rise to a new class of neural encoders, dubbed as DIFFormer (diffusion-based Transformers), with two instantiations: a simple version with linear complexity for prohibitive instance numbers, and an advanced version for learning complex structures. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks, such as node classification on large graphs, semi-supervised image/text classification, and spatial-temporal dynamics prediction.
Graph neural networks (GNNs) have been widely used in graph-structured data computation, showing promising performance in various applications such as node classification, link prediction, and network recommendation. Existing works mainly focus on node-wise correlation when doing weighted aggregation of neighboring nodes based on attention, such as dot product by the dense vectors of two nodes. This may cause conflicting noise in nodes to be propagated when doing information propagation. To solve this problem, we propose a General Information Propagation Algorithm (GIPA in short), which exploits more fine-grained information fusion including bit-wise and feature-wise correlations based on edge features in their propagation. Specifically, the bit-wise correlation calculates the element-wise attention weight through a multi-layer perceptron (MLP) based on the dense representations of two nodes and their edge; The feature-wise correlation is based on the one-hot representations of node attribute features for feature selection. We evaluate the performance of GIPA on the Open Graph Benchmark proteins (OGBN-proteins for short) dataset and the Alipay dataset of Alibaba. Experimental results reveal that GIPA outperforms the state-of-the-art models in terms of prediction accuracy, e.g., GIPA achieves an average ROC-AUC of $0.8901\pm 0.0011$, which is better than that of all the existing methods listed in the OGBN-proteins leaderboard.
Few-shot node classification aims at classifying nodes with limited labeled nodes as references. Recent few-shot node classification methods typically learn from classes with abundant labeled nodes (i.e., meta-training classes) and then generalize to classes with limited labeled nodes (i.e., meta-test classes). Nevertheless, on real-world graphs, it is usually difficult to obtain abundant labeled nodes for many classes. In practice, each meta-training class can only consist of several labeled nodes, known as the extremely weak supervision problem. In few-shot node classification, with extremely limited labeled nodes for meta-training, the generalization gap between meta-training and meta-test will become larger and thus lead to suboptimal performance. To tackle this issue, we study a novel problem of few-shot node classification with extremely weak supervision and propose a principled framework X-FNC under the prevalent meta-learning framework. Specifically, our goal is to accumulate meta-knowledge across different meta-training tasks with extremely weak supervision and generalize such knowledge to meta-test tasks. To address the challenges resulting from extremely scarce labeled nodes, we propose two essential modules to obtain pseudo-labeled nodes as extra references and effectively learn from extremely limited supervision information. We further conduct extensive experiments on four node classification datasets with extremely weak supervision to validate the superiority of our framework compared to the state-of-the-art baselines.
Understanding traffic scenes requires considering heterogeneous information about dynamic agents and the static infrastructure. In this work we propose SCENE, a methodology to encode diverse traffic scenes in heterogeneous graphs and to reason about these graphs using a heterogeneous Graph Neural Network encoder and task-specific decoders. The heterogeneous graphs, whose structures are defined by an ontology, consist of different nodes with type-specific node features and different relations with type-specific edge features. In order to exploit all the information given by these graphs, we propose to use cascaded layers of graph convolution. The result is an encoding of the scene. Task-specific decoders can be applied to predict desired attributes of the scene. Extensive evaluation on two diverse binary node classification tasks show the main strength of this methodology: despite being generic, it even manages to outperform task-specific baselines. The further application of our methodology to the task of node classification in various knowledge graphs shows its transferability to other domains.
The development of social media user stance detection and bot detection methods rely heavily on large-scale and high-quality benchmarks. However, in addition to low annotation quality, existing benchmarks generally have incomplete user relationships, suppressing graph-based account detection research. To address these issues, we propose a Multi-Relational Graph-Based Twitter Account Detection Benchmark (MGTAB), the first standardized graph-based benchmark for account detection. To our knowledge, MGTAB was built based on the largest original data in the field, with over 1.55 million users and 130 million tweets. MGTAB contains 10,199 expert-annotated users and 7 types of relationships, ensuring high-quality annotation and diversified relations. In MGTAB, we extracted the 20 user property features with the greatest information gain and user tweet features as the user features. In addition, we performed a thorough evaluation of MGTAB and other public datasets. Our experiments found that graph-based approaches are generally more effective than feature-based approaches and perform better when introducing multiple relations. By analyzing experiment results, we identify effective approaches for account detection and provide potential future research directions in this field. Our benchmark and standardized evaluation procedures are freely available at: https://github.com/GraphDetec/MGTAB.
Given a large graph with few node labels, how can we (a) identify whether there is generalized network-effects (GNE) or not, (b) estimate GNE to explain the interrelations among node classes, and (c) exploit GNE efficiently to improve the performance on downstream tasks? The knowledge of GNE is valuable for various tasks like node classification, and targeted advertising. However, identifying GNE such as homophily, heterophily or their combination is challenging in real-world graphs due to limited availability of node labels and noisy edges. We propose NetEffect, a graph mining approach to address the above issues, enjoying the following properties: (i) Principled: a statistical test to determine the presence of GNE in a graph with few node labels; (ii) General and Explainable: a closed-form solution to estimate the specific type of GNE observed; and (iii) Accurate and Scalable: the integration of GNE for accurate and fast node classification. Applied on real-world graphs, NetEffect discovers the unexpected absence of GNE in numerous graphs, which were recognized to exhibit heterophily. Further, we show that incorporating GNE is effective on node classification. On a million-scale real-world graph, NetEffect achieves over 7 times speedup (14 minutes vs. 2 hours) compared to most competitors.
Transfer learning refers to the transfer of knowledge or information from a relevant source domain to a target domain. However, most existing transfer learning theories and algorithms focus on IID tasks, where the source/target samples are assumed to be independent and identically distributed. Very little effort is devoted to theoretically studying the knowledge transferability on non-IID tasks, e.g., cross-network mining. To bridge the gap, in this paper, we propose rigorous generalization bounds and algorithms for cross-network transfer learning from a source graph to a target graph. The crucial idea is to characterize the cross-network knowledge transferability from the perspective of the Weisfeiler-Lehman graph isomorphism test. To this end, we propose a novel Graph Subtree Discrepancy to measure the graph distribution shift between source and target graphs. Then the generalization error bounds on cross-network transfer learning, including both cross-network node classification and link prediction tasks, can be derived in terms of the source knowledge and the Graph Subtree Discrepancy across domains. This thereby motivates us to propose a generic graph adaptive network (GRADE) to minimize the distribution shift between source and target graphs for cross-network transfer learning. Experimental results verify the effectiveness and efficiency of our GRADE framework on both cross-network node classification and cross-domain recommendation tasks.
Contrastive learning (CL), which can extract the information shared between different contrastive views, has become a popular paradigm for vision representation learning. Inspired by the success in computer vision, recent work introduces CL into graph modeling, dubbed as graph contrastive learning (GCL). However, generating contrastive views in graphs is more challenging than that in images, since we have little prior knowledge on how to significantly augment a graph without changing its labels. We argue that typical data augmentation techniques (e.g., edge dropping) in GCL cannot generate diverse enough contrastive views to filter out noises. Moreover, previous GCL methods employ two view encoders with exactly the same neural architecture and tied parameters, which further harms the diversity of augmented views. To address this limitation, we propose a novel paradigm named model augmented GCL (MA-GCL), which will focus on manipulating the architectures of view encoders instead of perturbing graph inputs. Specifically, we present three easy-to-implement model augmentation tricks for GCL, namely asymmetric, random and shuffling, which can respectively help alleviate high- frequency noises, enrich training instances and bring safer augmentations. All three tricks are compatible with typical data augmentations. Experimental results show that MA-GCL can achieve state-of-the-art performance on node classification benchmarks by applying the three tricks on a simple base model. Extensive studies also validate our motivation and the effectiveness of each trick. (Code, data and appendix are available at https://github.com/GXM1141/MA-GCL. )
Few-shot node classification is tasked to provide accurate predictions for nodes from novel classes with only few representative labeled nodes. This problem has drawn tremendous attention for its projection to prevailing real-world applications, such as product categorization for newly added commodity categories on an E-commerce platform with scarce records or diagnoses for rare diseases on a patient similarity graph. To tackle such challenging label scarcity issues in the non-Euclidean graph domain, meta-learning has become a successful and predominant paradigm. More recently, inspired by the development of graph self-supervised learning, transferring pretrained node embeddings for few-shot node classification could be a promising alternative to meta-learning but remains unexposed. In this work, we empirically demonstrate the potential of an alternative framework, \textit{Transductive Linear Probing}, that transfers pretrained node embeddings, which are learned from graph contrastive learning methods. We further extend the setting of few-shot node classification from standard fully supervised to a more realistic self-supervised setting, where meta-learning methods cannot be easily deployed due to the shortage of supervision from training classes. Surprisingly, even without any ground-truth labels, transductive linear probing with self-supervised graph contrastive pretraining can outperform the state-of-the-art fully supervised meta-learning based methods under the same protocol. We hope this work can shed new light on few-shot node classification problems and foster future research on learning from scarcely labeled instances on graphs.
A lot of theoretical and empirical evidence shows that the flatter local minima tend to improve generalization. Adversarial Weight Perturbation (AWP) is an emerging technique to efficiently and effectively find such minima. In AWP we minimize the loss w.r.t. a bounded worst-case perturbation of the model parameters thereby favoring local minima with a small loss in a neighborhood around them. The benefits of AWP, and more generally the connections between flatness and generalization, have been extensively studied for i.i.d. data such as images. In this paper, we extensively study this phenomenon for graph data. Along the way, we first derive a generalization bound for non-i.i.d. node classification tasks. Then we identify a vanishing-gradient issue with all existing formulations of AWP and we propose a new Weighted Truncated AWP (WT-AWP) to alleviate this issue. We show that regularizing graph neural networks with WT-AWP consistently improves both natural and robust generalization across many different graph learning tasks and models.
Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since real-world graphs are often complex mixtures of diverse subgraph patterns, learning a universal spectral filter on the graph from the global perspective as in most current works may still suffer from great difficulty in adapting to the variation of local patterns. On the basis of the theoretical analysis of local patterns, we rethink the existing spectral filtering methods and propose the node-oriented spectral filtering for graph neural network (namely NFGNN). By estimating the node-oriented spectral filter for each node, NFGNN is provided with the capability of precise local node positioning via the generalized translated operator, thus discriminating the variations of local homophily patterns adaptively. Meanwhile, the utilization of re-parameterization brings a good trade-off between global consistency and local sensibility for learning the node-oriented spectral filters. Furthermore, we theoretically analyze the localization property of NFGNN, demonstrating that the signal after adaptive filtering is still positioned around the corresponding node. Extensive experimental results demonstrate that the proposed NFGNN achieves more favorable performance.
Graph convolutional networks (GCNs) have achieved great success in graph representation learning by extracting high-level features from nodes and their topology. Since GCNs generally follow a message-passing mechanism, each node aggregates information from its first-order neighbour to update its representation. As a result, the representations of nodes with edges between them should be positively correlated and thus can be considered positive samples. However, there are more non-neighbour nodes in the whole graph, which provide diverse and useful information for the representation update. Two non-adjacent nodes usually have different representations, which can be seen as negative samples. Besides the node representations, the structural information of the graph is also crucial for learning. In this paper, we used quality-diversity decomposition in determinant point processes (DPP) to obtain diverse negative samples. When defining a distribution on diverse subsets of all non-neighbouring nodes, we incorporate both graph structure information and node representations. Since the DPP sampling process requires matrix eigenvalue decomposition, we propose a new shortest-path-base method to improve computational efficiency. Finally, we incorporate the obtained negative samples into the graph convolution operation. The ideas are evaluated empirically in experiments on node classification tasks. These experiments show that the newly proposed methods not only improve the overall performance of standard representation learning but also significantly alleviate over-smoothing problems.
Training labels for graph embedding algorithms could be costly to obtain in many practical scenarios. Active learning (AL) algorithms are very helpful to obtain the most useful labels for training while keeping the total number of label queries under a certain budget. The existing Active Graph Embedding framework proposes to use centrality score, density score, and entropy score to evaluate the value of unlabeled nodes, and it has been shown to be capable of bringing some improvement to the node classification tasks of Graph Convolutional Networks. However, when evaluating the importance of unlabeled nodes, it fails to consider the influence of existing labeled nodes on the value of unlabeled nodes. In other words, given the same unlabeled node, the computed informative score is always the same and is agnostic to the labeled node set. With the aim to address this limitation, in this work, we introduce 3 dissimilarity-based information scores for active learning: feature dissimilarity score (FDS), structure dissimilarity score (SDS), and embedding dissimilarity score (EDS). We find out that those three scores are able to take the influence of the labeled set on the value of unlabeled candidates into consideration, boosting our AL performance. According to experiments, our newly proposed scores boost the classification accuracy by 2.1% on average and are capable of generalizing to different Graph Neural Network architectures.
The prevalence of tree-like structures, encompassing hierarchical structures and power law distributions, exists extensively in real-world applications, including recommendation systems, ecosystems, financial networks, social networks, etc. Recently, the exploitation of hyperbolic space for tree-likeness modeling has garnered considerable attention owing to its exponential growth volume. Compared to the flat Euclidean space, the curved hyperbolic space provides a more amenable and embeddable room, especially for datasets exhibiting implicit tree-like architectures. However, the intricate nature of real-world tree-like data presents a considerable challenge, as it frequently displays a heterogeneous composition of tree-like, flat, and circular regions. The direct embedding of such heterogeneous structures into a homogeneous embedding space (i.e., hyperbolic space) inevitably leads to heavy distortions. To mitigate the aforementioned shortage, this study endeavors to explore the curvature between discrete structure and continuous learning space, aiming at encoding the message conveyed by the network topology in the learning process, thereby improving tree-likeness modeling. To the end, a curvature-aware hyperbolic graph convolutional neural network, \{kappa}HGCN, is proposed, which utilizes the curvature to guide message passing and improve long-range propagation. Extensive experiments on node classification and link prediction tasks verify the superiority of the proposal as it consistently outperforms various competitive models by a large margin.