We present a novel edge-level ego-network encoding for learning on graphs that can boost Message Passing Graph Neural Networks (MP-GNNs) by providing additional node and edge features or extending message-passing formats. The proposed encoding is sufficient to distinguish Strongly Regular Graphs, a family of challenging 3-WL equivalent graphs. We show theoretically that such encoding is more expressive than node-based sub-graph MP-GNNs. In an empirical evaluation on four benchmarks with 10 graph datasets, our results match or improve previous baselines on expressivity, graph classification, graph regression, and proximity tasks -- while reducing memory usage by 18.1x in certain real-world settings.
Graph Neural Networks (GNNs) have displayed considerable promise in graph representation learning across various applications. The core learning process requires the initialization of model weight matrices within each GNN layer, which is typically accomplished via classic initialization methods such as Xavier initialization. However, these methods were originally motivated to stabilize the variance of hidden embeddings and gradients across layers of Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to avoid vanishing gradients and maintain steady information flow. In contrast, within the GNN context classical initializations disregard the impact of the input graph structure and message passing on variance. In this paper, we analyze the variance of forward and backward propagation across GNN layers and show that the variance instability of GNN initializations comes from the combined effect of the activation function, hidden dimension, graph structure and message passing. To better account for these influence factors, we propose a new initialization method for Variance Instability Reduction within GNN Optimization (Virgo), which naturally tends to equate forward and backward variances across successive layers. We conduct comprehensive experiments on 15 datasets to show that Virgo can lead to superior model performance and more stable variance at initialization on node classification, link prediction and graph classification tasks. Codes are in https://github.com/LspongebobJH/virgo_icml2023.
Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing the information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly, but lack graph inductive bias and have to rely on ad-hoc positional encoding. In this paper, we propose a new architecture to reconcile these challenges. Our approach stems from the recent breakthroughs in long-range modeling provided by deep state-space models: for a given target node, our model aggregates other nodes by their shortest distances to the target and uses a linear RNN to encode the sequence of hop representations. The linear RNN is parameterized in a particular diagonal form for stable long-range signal propagation and is theoretically expressive enough to encode the neighborhood hierarchy. With no need for positional encoding, we empirically show that the performance of our model is comparable to or better than that of state-of-the-art graph transformers on various benchmarks, with a significantly reduced computational cost. Our code is open-source at https://github.com/skeletondyh/GRED.
We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and symmetrize it to be equivariant to the given group by employing a small equivariant network that parameterizes the probabilistic distribution underlying the symmetrization. The distribution is end-to-end trained with the base model which can maximize performance while reducing sample complexity of symmetrization. We show that this approach ensures not only equivariance to given group but also universal approximation capability in expectation. We implement our method on various base models, including patch-based transformers that can be initialized from pretrained vision transformers, and test them for a wide range of symmetry groups including permutation and Euclidean groups and their combinations. Empirical tests show competitive results against tailored equivariant architectures, suggesting the potential for learning equivariant functions for diverse groups using a non-equivariant universal base architecture. We further show evidence of enhanced learning in symmetric modalities, like graphs, when pretrained from non-symmetric modalities, like vision. Code is available at https://github.com/jw9730/lps.
Contrastive learning (CL) has emerged as a powerful framework for learning representations of images and text in a self-supervised manner while enhancing model robustness against adversarial attacks. More recently, researchers have extended the principles of contrastive learning to graph-structured data, giving birth to the field of graph contrastive learning (GCL). However, whether GCL methods can deliver the same advantages in adversarial robustness as their counterparts in the image and text domains remains an open question. In this paper, we introduce a comprehensive robustness evaluation protocol tailored to assess the robustness of GCL models. We subject these models to adaptive adversarial attacks targeting the graph structure, specifically in the evasion scenario. We evaluate node and graph classification tasks using diverse real-world datasets and attack strategies. With our work, we aim to offer insights into the robustness of GCL methods and hope to open avenues for potential future research directions.
Our work combines aspects of three promising paradigms in machine learning, namely, attention mechanism, energy-based models, and associative memory. Attention is the power-house driving modern deep learning successes, but it lacks clear theoretical foundations. Energy-based models allow a principled approach to discriminative and generative tasks, but the design of the energy functional is not straightforward. At the same time, Dense Associative Memory models or Modern Hopfield Networks have a well-established theoretical foundation, and allow an intuitive design of the energy function. We propose a novel architecture, called the Energy Transformer (or ET for short), that uses a sequence of attention layers that are purposely designed to minimize a specifically engineered energy function, which is responsible for representing the relationships between the tokens. In this work, we introduce the theoretical foundations of ET, explore its empirical capabilities using the image completion task, and obtain strong quantitative results on the graph anomaly detection and graph classification tasks.
The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classification, clustering, or eigenmode analysis. Recently, the Hodge Laplacian has come into focus as a generalisation of the ordinary Laplacian for higher-order graph models such as simplicial and cellular complexes. Akin to the traditional analysis of graph Laplacians, many authors analyse the smallest eigenvalues of the Hodge Laplacian, which are connected to important topological properties such as homology. However, small eigenvalues of the Hodge Laplacian can carry different information depending on whether they are related to curl or gradient eigenmodes, and thus may not be comparable. We therefore introduce the notion of persistent eigenvector similarity and provide a method to track individual harmonic, curl, and gradient eigenvectors/-values through the so-called persistence filtration, leveraging the full information contained in the Hodge-Laplacian spectrum across all possible scales of a point cloud. Finally, we use our insights (a) to introduce a novel form of Hodge spectral clustering and (b) to classify edges and higher-order simplices based on their relationship to the smallest harmonic, curl, and gradient eigenvectors.
Traditional methods like Graph Convolutional Networks (GCNs) face challenges with limited data and class imbalance, leading to suboptimal performance in graph classification tasks during toxicity prediction of molecules as a whole. To address these issues, we harness the power of Graph Isomorphic Networks, Multi Headed Attention and Free Large-scale Adversarial Augmentation separately on Graphs for precisely capturing the structural data of molecules and their toxicological properties. Additionally, we incorporate Few-Shot Learning to improve the model's generalization with limited annotated samples. Extensive experiments on a diverse toxicology dataset demonstrate that our method achieves an impressive state-of-art AUC-ROC value of 0.816, surpassing the baseline GCN model by 11.4%. This highlights the significance of our proposed methodology and Few Shot Learning in advancing Toxic Molecular Classification, with the potential to enhance drug discovery and environmental risk assessment processes.
While graph neural networks have achieved state-of-the-art performances in many real-world tasks including graph classification and node classification, recent works have demonstrated they are also extremely vulnerable to adversarial attacks. Most previous works have focused on attacking node classification networks under impractical white-box scenarios. In this work, we will propose a non-targeted Hard Label Black Box Node Injection Attack on Graph Neural Networks, which to the best of our knowledge, is the first of its kind. Under this setting, more real world tasks can be studied because our attack assumes no prior knowledge about (1): the model architecture of the GNN we are attacking; (2): the model's gradients; (3): the output logits of the target GNN model. Our attack is based on an existing edge perturbation attack, from which we restrict the optimization process to formulate a node injection attack. In the work, we will evaluate the performance of the attack using three datasets, COIL-DEL, IMDB-BINARY, and NCI1.
This survey paper presents a brief overview of recent research on graph data augmentation and few-shot learning. It covers various techniques for graph data augmentation, including node and edge perturbation, graph coarsening, and graph generation, as well as the latest developments in few-shot learning, such as meta-learning and model-agnostic meta-learning. The paper explores these areas in depth and delves into further sub classifications. Rule based approaches and learning based approaches are surveyed under graph augmentation techniques. Few-Shot Learning on graphs is also studied in terms of metric learning techniques and optimization-based techniques. In all, this paper provides an extensive array of techniques that can be employed in solving graph processing problems faced in low-data scenarios.
Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods face challenges in consistently achieving satisfactory performance and often lack interpretability, which hinders our understanding of anomaly detection decisions. In this paper, we propose a novel approach to graph anomaly detection that leverages the power of interpretability to enhance performance. Specifically, our method extracts an attention map derived from gradients of graph neural networks, which serves as a basis for scoring anomalies. Notably, our approach is flexible and can be used in various anomaly detection settings. In addition, we conduct theoretical analysis using synthetic data to validate our method and gain insights into its decision-making process. To demonstrate the effectiveness of our method, we extensively evaluate our approach against state-of-the-art graph anomaly detection techniques on real-world graph classification and wireless network datasets. The results consistently demonstrate the superior performance of our method compared to the baselines.
Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these graph models with topological features via persistent homology (PH) has gained prominence, but identifying the class of attributed graphs that PH can recognize remains open. We introduce a novel concept of color-separating sets to provide a complete resolution to this important problem. Specifically, we establish the necessary and sufficient conditions for distinguishing graphs based on the persistence of their connected components, obtained from filter functions on vertex and edge colors. Our constructions expose the limits of vertex- and edge-level PH, proving that neither category subsumes the other. Leveraging these theoretical insights, we propose RePHINE for learning topological features on graphs. RePHINE efficiently combines vertex- and edge-level PH, achieving a scheme that is provably more powerful than both. Integrating RePHINE into MP-GNNs boosts their expressive power, resulting in gains over standard PH on several benchmarks for graph classification.
Graph pooling methods have been widely used on downsampling graphs, achieving impressive results on multiple graph-level tasks like graph classification and graph generation. An important line called node dropping pooling aims at exploiting learnable scoring functions to drop nodes with comparatively lower significance scores. However, existing node dropping methods suffer from two limitations: (1) for each pooled node, these models struggle to capture long-range dependencies since they mainly take GNNs as the backbones; (2) pooling only the highest-scoring nodes tends to preserve similar nodes, thus discarding the affluent information of low-scoring nodes. To address these issues, we propose a Graph Transformer Pooling method termed GTPool, which introduces Transformer to node dropping pooling to efficiently capture long-range pairwise interactions and meanwhile sample nodes diversely. Specifically, we design a scoring module based on the self-attention mechanism that takes both global context and local context into consideration, measuring the importance of nodes more comprehensively. GTPool further utilizes a diversified sampling method named Roulette Wheel Sampling (RWS) that is able to flexibly preserve nodes across different scoring intervals instead of only higher scoring nodes. In this way, GTPool could effectively obtain long-range information and select more representative nodes. Extensive experiments on 11 benchmark datasets demonstrate the superiority of GTPool over existing popular graph pooling methods.
Graph Neural Networks (GNNs) are powerful in learning semantics of graph data. Recently, a new paradigm "pre-train and prompt" has shown promising results in adapting GNNs to various tasks with less supervised data. The success of such paradigm can be attributed to the more consistent objectives of pre-training and task-oriented prompt tuning, where the pre-trained knowledge can be effectively transferred to downstream tasks. Most existing methods are based on the class prototype vector framework. However, in the few-shot scenarios, given few labeled data, class prototype vectors are difficult to be accurately constructed or learned. Meanwhile, the structure information of graph is usually exploited during pre-training for learning node representations, while neglected in the prompt tuning stage for learning more accurate prototype vectors. In addition, they generally ignore the impact of heterophilous neighborhoods on node representation and are not suitable for heterophilous graphs. To bridge these gaps, we propose a novel pre-training and structure prompt tuning framework for GNNs, namely PSP, which consistently exploits structure information in both pre-training and prompt tuning stages. In particular, PSP 1) employs a dual-view contrastive learning to align the latent semantic spaces of node attributes and graph structure, and 2) incorporates structure information in prompted graph to construct more accurate prototype vectors and elicit more pre-trained knowledge in prompt tuning. We conduct extensive experiments on node classification and graph classification tasks to evaluate the effectiveness of PSP. We show that PSP can lead to superior performance in few-shot scenarios on both homophilous and heterophilous graphs. The implemented code is available at https://github.com/gqq1210/PSP.
Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred to as signals) defined on the vertices of a single graph. These tasks require networks designed differently from those designed for traditional GNN tasks. Indeed, traditional GNNs rely on localized low-pass filters, and signals of interest may have intricate multi-frequency behavior and exhibit long range interactions. This motivates us to introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. Our network is able to capture both local and global signal structure and is able to capture both low-frequency and high-frequency information. We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data.
Graph data widely exists in real life, with large amounts of data and complex structures. It is necessary to map graph data to low-dimensional embedding. Graph classification, a critical graph task, mainly relies on identifying the important substructures within the graph. At present, some graph classification methods do not combine the multi-granularity characteristics of graph data. This lack of granularity distinction in modeling leads to a conflation of key information and false correlations within the model. So, achieving the desired goal of a credible and interpretable model becomes challenging. This paper proposes a causal disentangled multi-granularity graph representation learning method (CDM-GNN) to solve this challenge. The CDM-GNN model disentangles the important substructures and bias parts within the graph from a multi-granularity perspective. The disentanglement of the CDM-GNN model reveals important and bias parts, forming the foundation for its classification task, specifically, model interpretations. The CDM-GNN model exhibits strong classification performance and generates explanatory outcomes aligning with human cognitive patterns. In order to verify the effectiveness of the model, this paper compares the three real-world datasets MUTAG, PTC, and IMDM-M. Six state-of-the-art models, namely GCN, GAT, Top-k, ASAPool, SUGAR, and SAT are employed for comparison purposes. Additionally, a qualitative analysis of the interpretation results is conducted.
For graph self-supervised learning (GSSL), masked autoencoder (MAE) follows the generative paradigm and learns to reconstruct masked graph edges or node features. Contrastive Learning (CL) maximizes the similarity between augmented views of the same graph and is widely used for GSSL. However, MAE and CL are considered separately in existing works for GSSL. We observe that the MAE and CL paradigms are complementary and propose the graph contrastive masked autoencoder (GCMAE) framework to unify them. Specifically, by focusing on local edges or node features, MAE cannot capture global information of the graph and is sensitive to particular edges and features. On the contrary, CL excels in extracting global information because it considers the relation between graphs. As such, we equip GCMAE with an MAE branch and a CL branch, and the two branches share a common encoder, which allows the MAE branch to exploit the global information extracted by the CL branch. To force GCMAE to capture global graph structures, we train it to reconstruct the entire adjacency matrix instead of only the masked edges as in existing works. Moreover, a discrimination loss is proposed for feature reconstruction, which improves the disparity between node embeddings rather than reducing the reconstruction error to tackle the feature smoothing problem of MAE. We evaluate GCMAE on four popular graph tasks (i.e., node classification, node clustering, link prediction, and graph classification) and compare with 14 state-of-the-art baselines. The results show that GCMAE consistently provides good accuracy across these tasks, and the maximum accuracy improvement is up to 3.2% compared with the best-performing baseline.
Abstract— DeepFake detection aims to differentiate falsified faces from real ones. Most approaches formulate it as a binary classification problem by solely mining the local artifacts and inconsistencies of face forgery, which neglect the relation across local regions. Although several recent works explore local relation learning for DeepFake detection, they overlook the propagation of relational information and lead to limited performance gains. To address these issues, this paper provides a new perspective by formulating DeepFake detection as a graph classification problem, in which each facial region corresponds to a vertex. But relational information with large redundancy hinders the expressiveness of graphs. Inspired by the success of masked modeling, we propose Masked Relation Learning which decreases the redundancy to learn informative relational features. Specifically, a spatiotemporal attention module is exploited to learn the attention features of multiple facial regions. A relation learning module masks partial correlations between regions to reduce redundancy and then propagates the relational information across regions to capture the irregularity from a global view of the graph. We empirically discover that a moderate masking rate (e.g., 50%) brings the best performance gain. Experiments verify the effectiveness of Masked Relation Learning and demonstrate that our approach outperforms the state of the art by 2% AUC on the cross-dataset DeepFake video detection. Code will be available at https://github.com/zimyang/MaskRelation. Index Terms— Multimedia forensics, DeepFake detection, masked learning, relation feature.
Graph Neural Networks (GNNs) have shown remarkable merit in performing various learning-based tasks in complex networks. The superior performance of GNNs often correlates with the availability and quality of node-level features in the input networks. However, for many network applications, such node-level information may be missing or unreliable, thereby limiting the applicability and efficacy of GNNs. To address this limitation, we present a novel approach denoted as Ego-centric Spectral subGraph Embedding Augmentation (ESGEA), which aims to enhance and design node features, particularly in scenarios where information is lacking. Our method leverages the topological structure of the local subgraph to create topology-aware node features. The subgraph features are generated using an efficient spectral graph embedding technique, and they serve as node features that capture the local topological organization of the network. The explicit node features, if present, are then enhanced with the subgraph embeddings in order to improve the overall performance. ESGEA is compatible with any GNN-based architecture and is effective even in the absence of node features. We evaluate the proposed method in a social network graph classification task where node attributes are unavailable, as well as in a node classification task where node features are corrupted or even absent. The evaluation results on seven datasets and eight baseline models indicate up to a 10% improvement in AUC and a 7% improvement in accuracy for graph and node classification tasks, respectively.
Graph representation learning has now become the de facto standard when handling graph-structured data, with the framework of message-passing graph neural networks (MPNN) being the most prevailing algorithmic tool. Despite its popularity, the family of MPNNs suffers from several drawbacks such as transparency and expressivity. Recently, the idea of designing neural models on graphs using the theory of graph kernels has emerged as a more transparent as well as sometimes more expressive alternative to MPNNs known as kernel graph neural networks (KGNNs). Developments on KGNNs are currently a nascent field of research, leaving several challenges from algorithmic design and adaptation to other learning paradigms such as self-supervised learning. In this paper, we improve the design and learning of KGNNs. Firstly, we extend the algorithmic formulation of KGNNs by allowing a more flexible graph-level similarity definition that encompasses former proposals like random walk graph kernel, as well as providing a smoother optimization objective that alleviates the need of introducing combinatorial learning procedures. Secondly, we enhance KGNNs through the lens of self-supervision via developing a novel structure-preserving graph data augmentation method called latent graph augmentation (LGA). Finally, we perform extensive empirical evaluations to demonstrate the efficacy of our proposed mechanisms. Experimental results over benchmark datasets suggest that our proposed model achieves competitive performance that is comparable to or sometimes outperforming state-of-the-art graph representation learning frameworks with or without self-supervision on graph classification tasks. Comparisons against other previously established graph data augmentation methods verify that the proposed LGA augmentation scheme captures better semantics of graph-level invariance.