Graph Neural Networks (GNNs) have emerged as a dominant approach in graph representation learning, yet they often struggle to capture consistent similarity relationships among graphs. While graph kernel methods such as the Weisfeiler-Lehman subtree (WL-subtree) and Weisfeiler-Lehman optimal assignment (WLOA) kernels are effective in capturing similarity relationships, they rely heavily on predefined kernels and lack sufficient non-linearity for more complex data patterns. Our work aims to bridge the gap between neural network methods and kernel approaches by enabling GNNs to consistently capture relational structures in their learned representations. Given the analogy between the message-passing process of GNNs and WL algorithms, we thoroughly compare and analyze the properties of WL-subtree and WLOA kernels. We find that the similarities captured by WLOA at different iterations are asymptotically consistent, ensuring that similar graphs remain similar in subsequent iterations, thereby leading to superior performance over the WL-subtree kernel. Inspired by these findings, we conjecture that the consistency in the similarities of graph representations across GNN layers is crucial in capturing relational structures and enhancing graph classification performance. Thus, we propose a loss to enforce the similarity of graph representations to be consistent across different layers. Our empirical analysis verifies our conjecture and shows that our proposed consistency loss can significantly enhance graph classification performance across several GNN backbones on various datasets.
Line graph transformation has been widely studied in graph theory, where each node in a line graph corresponds to an edge in the original graph. This has inspired a series of graph neural networks (GNNs) applied to transformed line graphs, which have proven effective in various graph representation learning tasks. However, there is limited theoretical study on how line graph transformation affects the expressivity of GNN models. In this study, we focus on two types of graphs known to be challenging to the Weisfeiler-Leman (WL) tests: Cai-F\"urer-Immerman (CFI) graphs and strongly regular graphs, and show that applying line graph transformation helps exclude these challenging graph properties, thus potentially assist WL tests in distinguishing these graphs. We empirically validate our findings by conducting a series of experiments that compare the accuracy and efficiency of graph isomorphism tests and GNNs on both line-transformed and original graphs across these graph structure types.
Graph representation learning (GRL), enhanced by graph augmentation methods, has emerged as an effective technique achieving performance improvements in wide tasks such as node classification and graph classification. In self-supervised GRL, paired graph augmentations are generated from each graph. Its objective is to infer similar representations for augmentations of the same graph, but maximally distinguishable representations for augmentations of different graphs. Analogous to image and language domains, the desiderata of an ideal augmentation method include both (1) semantics-preservation; and (2) data-perturbation; i.e., an augmented graph should preserve the semantics of its original graph while carrying sufficient variance. However, most existing (un-)/self-supervised GRL methods focus on data perturbation but largely neglect semantics preservation. To address this challenge, in this paper, we propose a novel method, Explanation-Preserving Augmentation (EPA), that leverages graph explanation techniques for generating augmented graphs that can bridge the gap between semantics-preservation and data-perturbation. EPA first uses a small number of labels to train a graph explainer to infer the sub-structures (explanations) that are most relevant to a graph's semantics. These explanations are then used to generate semantics-preserving augmentations for self-supervised GRL, namely EPA-GRL. We demonstrate theoretically, using an analytical example, and through extensive experiments on a variety of benchmark datasets that EPA-GRL outperforms the state-of-the-art (SOTA) GRL methods, which are built upon semantics-agnostic data augmentations.
Cells in multicellular organisms coordinate to form functional and structural niches. With spatial transcriptomics enabling gene expression profiling in spatial contexts, it has been revealed that spatial niches serve as cohesive and recurrent units in physiological and pathological processes. These observations suggest universal tissue organization principles encoded by conserved niche patterns, and call for a query-based niche analytical paradigm beyond current computational tools. In this work, we defined the Niche Query Task, which is to identify similar niches across ST samples given a niche of interest (NOI). We further developed QueST, a specialized method for solving this task. QueST models each niche as a subgraph, uses contrastive learning to learn discriminative niche embeddings, and incorporates adversarial training to mitigate batch effects. In simulations and benchmark datasets, QueST outperformed existing methods repurposed for niche querying, accurately capturing niche structures in heterogeneous environments and demonstrating strong generalizability across diverse sequencing platforms. Applied to tertiary lymphoid structures in renal and lung cancers, QueST revealed functionally distinct niches associated with patient prognosis and uncovered conserved and divergent spatial architectures across cancer types. These results demonstrate that QueST enables systematic, quantitative profiling of spatial niches across samples, providing a powerful tool to dissect spatial tissue architecture in health and disease.
Graph Neural Networks (GNNs) are proficient in graph representation learning and achieve promising performance on versatile tasks such as node classification and link prediction. Usually, a comprehensive hyperparameter tuning is essential for fully unlocking GNN's top performance, especially for complicated tasks such as node classification on large graphs and long-range graphs. This is usually associated with high computational and time costs and careful design of appropriate search spaces. This work introduces a graph-conditioned latent diffusion framework (GNN-Diff) to generate high-performing GNNs based on the model checkpoints of sub-optimal hyperparameters selected by a light-tuning coarse search. We validate our method through 166 experiments across four graph tasks: node classification on small, large, and long-range graphs, as well as link prediction. Our experiments involve 10 classic and state-of-the-art target models and 20 publicly available datasets. The results consistently demonstrate that GNN-Diff: (1) boosts the performance of GNNs with efficient hyperparameter tuning; and (2) presents high stability and generalizability on unseen data across multiple generation runs. The code is available at https://github.com/lequanlin/GNN-Diff.
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.
Over the past decade, Graph Neural Networks (GNNs) have transformed graph representation learning. In the widely adopted message-passing GNN framework, nodes refine their representations by aggregating information from neighboring nodes iteratively. While GNNs excel in various domains, recent theoretical studies have raised concerns about their capabilities. GNNs aim to address various graph-related tasks by utilizing such node representations, however, this one-size-fits-all approach proves suboptimal for diverse tasks. Motivated by these observations, we conduct empirical tests to compare the performance of current GNN models with more conventional and direct methods in link prediction tasks. Introducing our model, PROXI, which leverages proximity information of node pairs in both graph and attribute spaces, we find that standard machine learning (ML) models perform competitively, even outperforming cutting-edge GNN models when applied to these proximity metrics derived from node neighborhoods and attributes. This holds true across both homophilic and heterophilic networks, as well as small and large benchmark datasets, including those from the Open Graph Benchmark (OGB). Moreover, we show that augmenting traditional GNNs with PROXI significantly boosts their link prediction performance. Our empirical findings corroborate the previously mentioned theoretical observations and imply that there exists ample room for enhancement in current GNN models to reach their potential.
Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in recent years. The overwhelming majority of existing methods handle unsigned graphs. However, signed graphs appear in an increasing number of application domains to model systems involving two types of opposed relationships. Several authors took an interest in signed graphs and proposed methods for providing vertex-level representations, but only one exists for whole-graph representations, and it can handle only fully connected graphs. In this article, we tackle this issue by proposing two approaches to learning whole-graph representations of general signed graphs. The first is a SG2V, a signed generalization of the whole-graph embedding method Graph2vec that relies on a modification of the Weisfeiler--Lehman relabelling procedure. The second one is WSGCN, a whole-graph generalization of the signed vertex embedding method SGCN that relies on the introduction of master nodes into the GCN. We propose several variants of both these approaches. A bottleneck in the development of whole-graph-oriented methods is the lack of data. We constitute a benchmark composed of three collections of signed graphs with corresponding ground truths. We assess our methods on this benchmark, and our results show that the signed whole-graph methods learn better representations for this task. Overall, the baseline obtains an F-measure score of 58.57, when SG2V and WSGCN reach 73.01 and 81.20, respectively. Our source code and benchmark dataset are both publicly available online.
Although modern imaging technologies allow us to study connectivity between two distinct brain regions in-vivo, an in-depth understanding of how anatomical structure supports brain function and how spontaneous functional fluctuations emerge remarkable cognition is still elusive. Meanwhile, tremendous efforts have been made in the realm of machine learning to establish the nonlinear mapping between neuroimaging data and phenotypic traits. However, the absence of neuroscience insight in the current approaches poses significant challenges in understanding cognitive behavior from transient neural activities. To address this challenge, we put the spotlight on the coupling mechanism of structural connectivity (SC) and functional connectivity (FC) by formulating such network neuroscience question into an expressive graph representation learning problem for high-order topology. Specifically, we introduce the concept of topological detour to characterize how a ubiquitous instance of FC (direct link) is supported by neural pathways (detour) physically wired by SC, which forms a cyclic loop interacted by brain structure and function. In the clich\'e of machine learning, the multi-hop detour pathway underlying SC-FC coupling allows us to devise a novel multi-head self-attention mechanism within Transformer to capture multi-modal feature representation from paired graphs of SC and FC. Taken together, we propose a biological-inspired deep model, coined as NeuroPath, to find putative connectomic feature representations from the unprecedented amount of neuroimages, which can be plugged into various downstream applications such as task recognition and disease diagnosis. We have evaluated NeuroPath on large-scale public datasets including HCP and UK Biobank under supervised and zero-shot learning, where the state-of-the-art performance by our NeuroPath indicates great potential in network neuroscience.
Graph Neural Networks (GNNs) have been widely employed for feature representation learning in molecular graphs. Therefore, it is crucial to enhance the expressiveness of feature representation to ensure the effectiveness of GNNs. However, a significant portion of current research primarily focuses on the structural features within individual molecules, often overlooking the structural similarity between molecules, which is a crucial aspect encapsulating rich information on the relationship between molecular properties and structural characteristics. Thus, these approaches fail to capture the rich semantic information at the molecular structure level. To bridge this gap, we introduce the \textbf{Molecular Structural Similarity Motif GNN (MSSM-GNN)}, a novel molecular graph representation learning method that can capture structural similarity information among molecules from a global perspective. In particular, we propose a specially designed graph that leverages graph kernel algorithms to represent the similarity between molecules quantitatively. Subsequently, we employ GNNs to learn feature representations from molecular graphs, aiming to enhance the accuracy of property prediction by incorporating additional molecular representation information. Finally, through a series of experiments conducted on both small-scale and large-scale molecular datasets, we demonstrate that our model consistently outperforms eleven state-of-the-art baselines. The codes are available at https://github.com/yaoyao-yaoyao-cell/MSSM-GNN.
Unsupervised heterogeneous graph representation learning (UHGRL) has gained increasing attention due to its significance in handling practical graphs without labels. However, heterophily has been largely ignored, despite its ubiquitous presence in real-world heterogeneous graphs. In this paper, we define semantic heterophily and propose an innovative framework called Latent Graphs Guided Unsupervised Representation Learning (LatGRL) to handle this problem. First, we develop a similarity mining method that couples global structures and attributes, enabling the construction of fine-grained homophilic and heterophilic latent graphs to guide the representation learning. Moreover, we propose an adaptive dual-frequency semantic fusion mechanism to address the problem of node-level semantic heterophily. To cope with the massive scale of real-world data, we further design a scalable implementation. Extensive experiments on benchmark datasets validate the effectiveness and efficiency of our proposed framework. The source code and datasets have been made available at https://github.com/zxlearningdeep/LatGRL.
Graph Neural Networks (GNNs) have become essential tools for graph representation learning in various domains, such as social media and healthcare. However, they often suffer from fairness issues due to inherent biases in node attributes and graph structure, leading to unfair predictions. To address these challenges, we propose a novel GNN framework, DAB-GNN, that Disentangles, Amplifies, and deBiases attribute, structure, and potential biases in the GNN mechanism. DAB-GNN employs a disentanglement and amplification module that isolates and amplifies each type of bias through specialized disentanglers, followed by a debiasing module that minimizes the distance between subgroup distributions. Extensive experiments on five datasets demonstrate that DAB-GNN significantly outperforms ten state-of-the-art competitors in terms of achieving an optimal balance between accuracy and fairness. The codebase of DAB-GNN is available at https://github.com/Bigdasgit/DAB-GNN
Molecular property prediction is a crucial foundation for drug discovery. In recent years, pre-trained deep learning models have been widely applied to this task. Some approaches that incorporate prior biological domain knowledge into the pre-training framework have achieved impressive results. However, these methods heavily rely on biochemical experts, and retrieving and summarizing vast amounts of domain knowledge literature is both time-consuming and expensive. Large Language Models (LLMs) have demonstrated remarkable performance in understanding and efficiently providing general knowledge. Nevertheless, they occasionally exhibit hallucinations and lack precision in generating domain-specific knowledge. Conversely, Domain-specific Small Models (DSMs) possess rich domain knowledge and can accurately calculate molecular domain-related metrics. However, due to their limited model size and singular functionality, they lack the breadth of knowledge necessary for comprehensive representation learning. To leverage the advantages of both approaches in molecular property prediction, we propose a novel Molecular Graph representation learning framework that integrates Large language models and Domain-specific small models (MolGraph-LarDo). Technically, we design a two-stage prompt strategy where DSMs are introduced to calibrate the knowledge provided by LLMs, enhancing the accuracy of domain-specific information and thus enabling LLMs to generate more precise textual descriptions for molecular samples. Subsequently, we employ a multi-modal alignment method to coordinate various modalities, including molecular graphs and their corresponding descriptive texts, to guide the pre-training of molecular representations. Extensive experiments demonstrate the effectiveness of the proposed method.
The advent of the "pre-train, prompt" paradigm has recently extended its generalization ability and data efficiency to graph representation learning, following its achievements in Natural Language Processing (NLP). Initial graph prompt tuning approaches tailored specialized prompting functions for Graph Neural Network (GNN) models pre-trained with specific strategies, such as edge prediction, thus limiting their applicability. In contrast, another pioneering line of research has explored universal prompting via adding prompts to the input graph's feature space, thereby removing the reliance on specific pre-training strategies. However, the necessity to add feature prompts to all nodes remains an open question. Motivated by findings from prompt tuning research in the NLP domain, which suggest that highly capable pre-trained models need less conditioning signal to achieve desired behaviors, we advocate for strategically incorporating necessary and lightweight feature prompts to certain graph nodes to enhance downstream task performance. This introduces a combinatorial optimization problem, requiring a policy to decide 1) which nodes to prompt and 2) what specific feature prompts to attach. We then address the problem by framing the prompt incorporation process as a sequential decision-making problem and propose our method, RELIEF, which employs Reinforcement Learning (RL) to optimize it. At each step, the RL agent selects a node (discrete action) and determines the prompt content (continuous action), aiming to maximize cumulative performance gain. Extensive experiments on graph and node-level tasks with various pre-training strategies in few-shot scenarios demonstrate that our RELIEF outperforms fine-tuning and other prompt-based approaches in classification performance and data efficiency. The code is available at https://github.com/JasonZhujp/RELIEF.
Graph Neural Networks (GNNs)-based recommendation algorithms typically assume that training and testing data are drawn from independent and identically distributed (IID) spaces. However, this assumption often fails in the presence of out-of-distribution (OOD) data, resulting in significant performance degradation. In this study, we construct a Structural Causal Model (SCM) to analyze interaction data, revealing that environmental confounders (e.g., the COVID-19 pandemic) lead to unstable correlations in GNN-based models, thus impairing their generalization to OOD data. To address this issue, we propose a novel approach, graph representation learning via causal diffusion (CausalDiffRec) for OOD recommendation. This method enhances the model's generalization on OOD data by eliminating environmental confounding factors and learning invariant graph representations. Specifically, we use backdoor adjustment and variational inference to infer the real environmental distribution, thereby eliminating the impact of environmental confounders. This inferred distribution is then used as prior knowledge to guide the representation learning in the reverse phase of the diffusion process to learn the invariant representation. In addition, we provide a theoretical derivation that proves optimizing the objective function of CausalDiffRec can encourage the model to learn environment-invariant graph representations, thereby achieving excellent generalization performance in recommendations under distribution shifts. Our extensive experiments validate the effectiveness of CausalDiffRec in improving the generalization of OOD data, and the average improvement is up to 10.69% on Food, 18.83% on KuaiRec, 22.41% on Yelp2018, and 11.65% on Douban datasets.
Designing effective graph neural networks (GNNs) with message passing has two fundamental challenges, i.e., determining optimal message-passing pathways and designing local aggregators. Previous methods of designing optimal pathways are limited with information loss on the input features. On the other hand, existing local aggregators generally fail to extract multi-scale features and approximate diverse operators under limited parameter scales. In contrast to these methods, Euclidean convolution has been proven as an expressive aggregator, making it a perfect candidate for GNN construction. However, the challenges of generalizing Euclidean convolution to graphs arise from the irregular structure of graphs. To bridge the gap between Euclidean space and graph topology, we propose a differentiable method that applies permutations to calibrate input graphs for Euclidean convolution. The permutations constrain all nodes in a row regardless of their input order and therefore enable the flexible generalization of Euclidean convolution to graphs. Based on the graph calibration, we propose the Compressed Convolution Network (CoCN) for hierarchical graph representation learning. CoCN follows local feature-learning and global parameter-sharing mechanisms of convolution neural networks. The whole model can be trained end-to-end, with compressed convolution applied to learn individual node features and their corresponding structure features. CoCN can further borrow successful practices from Euclidean convolution, including residual connection and inception mechanism. We validate CoCN on both node-level and graph-level benchmarks. CoCN achieves superior performance over competitive GNN baselines. Codes are available at https://github.com/sunjss/CoCN.
Spectral Graph Neural Networks have demonstrated superior performance in graph representation learning. However, many current methods focus on employing shared polynomial coefficients for all nodes, i.e., learning node-unified filters, which limits the filters' flexibility for node-level tasks. The recent DSF attempts to overcome this limitation by learning node-wise coefficients based on positional encoding. However, the initialization and updating process of the positional encoding are burdensome, hindering scalability on large-scale graphs. In this work, we propose a scalable node-wise filter, PolyAttn. Leveraging the attention mechanism, PolyAttn can directly learn node-wise filters in an efficient manner, offering powerful representation capabilities. Building on PolyAttn, we introduce the whole model, named PolyFormer. In the lens of Graph Transformer models, PolyFormer, which calculates attention scores within nodes, shows great scalability. Moreover, the model captures spectral information, enhancing expressiveness while maintaining efficiency. With these advantages, PolyFormer offers a desirable balance between scalability and expressiveness for node-level tasks. Extensive experiments demonstrate that our proposed methods excel at learning arbitrary node-wise filters, showing superior performance on both homophilic and heterophilic graphs, and handling graphs containing up to 100 million nodes. The code is available at https://github.com/air029/PolyFormer.
One-class learning (OCL) comprises a set of techniques applied when real-world problems have a single class of interest. The usual procedure for OCL is learning a hypersphere that comprises instances of this class and, ideally, repels unseen instances from any other classes. Besides, several OCL algorithms for graphs have been proposed since graph representation learning has succeeded in various fields. These methods may use a two-step strategy, initially representing the graph and, in a second step, classifying its nodes. On the other hand, end-to-end methods learn the node representations while classifying the nodes in one learning process. We highlight three main gaps in the literature on OCL for graphs: (i) non-customized representations for OCL; (ii) the lack of constraints on hypersphere parameters learning; and (iii) the methods' lack of interpretability and visualization. We propose One-cLass Graph Autoencoder (OLGA). OLGA is end-to-end and learns the representations for the graph nodes while encapsulating the interest instances by combining two loss functions. We propose a new hypersphere loss function to encapsulate the interest instances. OLGA combines this new hypersphere loss with the graph autoencoder reconstruction loss to improve model learning. OLGA achieved state-of-the-art results and outperformed six other methods with a statistically significant difference from five methods. Moreover, OLGA learns low-dimensional representations maintaining the classification performance with an interpretable model representation learning and results.
Graph anomaly detection (GAD) is increasingly crucial in various applications, ranging from financial fraud detection to fake news detection. However, current GAD methods largely overlook the fairness problem, which might result in discriminatory decisions skewed toward certain demographic groups defined on sensitive attributes (e.g., gender, religion, ethnicity, etc.). This greatly limits the applicability of these methods in real-world scenarios in light of societal and ethical restrictions. To address this critical gap, we make the first attempt to integrate fairness with utility in GAD decision-making. Specifically, we devise a novel DisEntangle-based FairnEss-aware aNomaly Detection framework on the attributed graph, named DEFEND. DEFEND first introduces disentanglement in GNNs to capture informative yet sensitive-irrelevant node representations, effectively reducing societal bias inherent in graph representation learning. Besides, to alleviate discriminatory bias in evaluating anomalous nodes, DEFEND adopts a reconstruction-based anomaly detection, which concentrates solely on node attributes without incorporating any graph structure. Additionally, given the inherent association between input and sensitive attributes, DEFEND constrains the correlation between the reconstruction error and the predicted sensitive attributes. Our empirical evaluations on real-world datasets reveal that DEFEND performs effectively in GAD and significantly enhances fairness compared to state-of-the-art baselines. To foster reproducibility, our code is available at https://github.com/AhaChang/DEFEND.
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable. We use a link-cut tree data structure and parallelism to lower the complexity of computing extended persistence, obtaining a speedup of more than 60x over the state-of-the-art for extended persistence computation. This makes extended persistence feasible for machine learning. We show that, under certain conditions, extended persistence surpasses both the WL[1] graph isomorphism test and 0-dimensional barcodes in terms of expressivity because it adds more global (topological) information. In particular, arbitrarily long cycles can be represented, which is difficult for finite receptive field message passing graph neural networks. Furthermore, we show the effectiveness of our method on real world datasets compared to many existing recent graph representation learning methods.