Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy

Graph autoencoders (Graph-AEs) learn representations of given graphs by aiming to accurately reconstruct them. A notable application of Graph-AEs is graph-level anomaly detection (GLAD), whose objective is to identify graphs with anomalous topological structures and/or node features compared to the majority of the graph population. Graph-AEs for GLAD regard a graph with a high mean reconstruction error (i.e. mean of errors from all node pairs and/or nodes) as anomalies. Namely, the methods rest on the assumption that they would better reconstruct graphs with similar characteristics to the majority. We, however, report non-trivial counter-examples, a phenomenon we call reconstruction flip, and highlight the limitations of the existing Graph-AE-based GLAD methods. Specifically, we empirically and theoretically investigate when this assumption holds and when it fails. Through our analyses, we further argue that, while the reconstruction errors for a given graph are effective features for GLAD, leveraging the multifaceted summaries of the reconstruction errors, beyond just mean, can further strengthen the features. Thus, we propose a novel and simple GLAD method, named MUSE. The key innovation of MUSE involves taking multifaceted summaries of reconstruction errors as graph features for GLAD. This surprisingly simple method obtains SOTA performance in GLAD, performing best overall among 14 methods across 10 datasets.

Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphs

Graph Neural Networks (GNNs) have gained significant attention as a powerful modeling and inference method, especially for homophilic graph-structured data. To empower GNNs in heterophilic graphs, where adjacent nodes exhibit dissimilar labels or features, Signed Message Passing (SMP) has been widely adopted. However, there is a lack of theoretical and empirical analysis regarding the limitations of SMP. In this work, we unveil some potential pitfalls of SMP and their remedies. We first identify two limitations of SMP: undesirable representation update for multi-hop neighbors and vulnerability against oversmoothing issues. To overcome these challenges, we propose a novel message passing function called Multiset to Multiset GNN(M2M-GNN). Our theoretical analyses and extensive experiments demonstrate that M2M-GNN effectively alleviates the aforementioned limitations of SMP, yielding superior performance in comparison

Exploring Edge Probability Graph Models Beyond Edge Independency: Concepts, Analyses, and Algorithms

Desirable random graph models (RGMs) should (i) be tractable so that we can compute and control graph statistics, and (ii) generate realistic structures such as high clustering (i.e., high subgraph densities). A popular category of RGMs (e.g., Erdos-Renyi and stochastic Kronecker) outputs edge probabilities, and we need to realize (i.e., sample from) the edge probabilities to generate graphs. Typically, each edge (in)existence is assumed to be determined independently. However, with edge independency, RGMs theoretically cannot produce high subgraph densities unless they "replicate" input graphs. In this work, we explore realization beyond edge independence that can produce more realistic structures while ensuring high tractability. Specifically, we propose edge-dependent realization schemes called binding and derive closed-form tractability results on subgraph (e.g., triangle) densities in graphs generated with binding. We propose algorithms for graph generation with binding and parameter fitting of binding. We empirically validate that binding exhibits high tractability and generates realistic graphs with high clustering, significantly improving upon existing RGMs assuming edge independency.

Tackling Prevalent Conditions in Unsupervised Combinatorial Optimization: Cardinality, Minimum, Covering, and More

Combinatorial optimization (CO) is naturally discrete, making machine learning based on differentiable optimization inapplicable. Karalias & Loukas (2020) adapted the probabilistic method to incorporate CO into differentiable optimization. Their work ignited the research on unsupervised learning for CO, composed of two main components: probabilistic objectives and derandomization. However, each component confronts unique challenges. First, deriving objectives under various conditions (e.g., cardinality constraints and minimum) is nontrivial. Second, the derandomization process is underexplored, and the existing derandomization methods are either random sampling or naive rounding. In this work, we aim to tackle prevalent (i.e., commonly involved) conditions in unsupervised CO. First, we concretize the targets for objective construction and derandomization with theoretical justification. Then, for various conditions commonly involved in different CO problems, we derive nontrivial objectives and derandomization to meet the targets. Finally, we apply the derivations to various CO problems. Via extensive experiments on synthetic and real-world graphs, we validate the correctness of our derivations and show our empirical superiority w.r.t. both optimization quality and speed.

A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications, and thus investigation of deep learning for HOIs has become a valuable agenda for the data mining and machine learning communities. As networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural networks (HNNs) have emerged as a powerful tool for representation learning on hypergraphs. Given the emerging trend, we present the first survey dedicated to HNNs, with an in-depth and step-by-step guide. Broadly, the present survey overviews HNN architectures, training strategies, and applications. First, we break existing HNNs down into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. Second, we examine how HNNs address and learn HOIs with each of their components. Third, we overview the recent applications of HNNs in recommendation, biological and medical science, time series analysis, and computer vision. Lastly, we conclude with a discussion on limitations and future directions.

HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs

Hypergraphs are marked by complex topology, expressing higher-order interactions among multiple nodes with hyperedges, and better capturing the topology is essential for effective representation learning. Recent advances in generative self-supervised learning (SSL) suggest that hypergraph neural networks learned from generative self supervision have the potential to effectively encode the complex hypergraph topology. Designing a generative SSL strategy for hypergraphs, however, is not straightforward. Questions remain with regard to its generative SSL task, connection to downstream tasks, and empirical properties of learned representations. In light of the promises and challenges, we propose a novel generative SSL strategy for hypergraphs. We first formulate a generative SSL task on hypergraphs, hyperedge filling, and highlight its theoretical connection to node classification. Based on the generative SSL task, we propose a hypergraph SSL method, HypeBoy. HypeBoy learns effective general-purpose hypergraph representations, outperforming 16 baseline methods across 11 benchmark datasets.

FlowerFormer: Empowering Neural Architecture Encoding using a Flow-aware Graph Transformer

The success of a specific neural network architecture is closely tied to the dataset and task it tackles; there is no one-size-fits-all solution. Thus, considerable efforts have been made to quickly and accurately estimate the performances of neural architectures, without full training or evaluation, for given tasks and datasets. Neural architecture encoding has played a crucial role in the estimation, and graphbased methods, which treat an architecture as a graph, have shown prominent performance. For enhanced representation learning of neural architectures, we introduce FlowerFormer, a powerful graph transformer that incorporates the information flows within a neural architecture. FlowerFormer consists of two key components: (a) bidirectional asynchronous message passing, inspired by the flows; (b) global attention built on flow-based masking. Our extensive experiments demonstrate the superiority of FlowerFormer over existing neural encoding methods, and its effectiveness extends beyond computer vision models to include graph neural networks and auto speech recognition models. Our code is available at http://github.com/y0ngjaenius/CVPR2024_FLOWERFormer.

SLADE: Detecting Dynamic Anomalies in Edge Streams without Labels via Self-Supervised Learning

To detect anomalies in real-world graphs, such as social, email, and financial networks, various approaches have been developed. While they typically assume static input graphs, most real-world graphs grow over time, naturally represented as edge streams. In this context, we aim to achieve three goals: (a) instantly detecting anomalies as they occur, (b) adapting to dynamically changing states, and (c) handling the scarcity of dynamic anomaly labels. In this paper, we propose SLADE (Self-supervised Learning for Anomaly Detection in Edge Streams) for rapid detection of dynamic anomalies in edge streams, without relying on labels. SLADE detects the shifts of nodes into abnormal states by observing deviations in their interaction patterns over time. To this end, it trains a deep neural network to perform two self-supervised tasks: (a) minimizing drift in node representations and (b) generating long-term interaction patterns from short-term ones. Failure in these tasks for a node signals its deviation from the norm. Notably, the neural network and tasks are carefully designed so that all required operations can be performed in constant time (w.r.t. the graph size) in response to each new edge in the input stream. In dynamic anomaly detection across four real-world datasets, SLADE outperforms nine competing methods, even those leveraging label supervision.

Self-Guided Robust Graph Structure Refinement

Recent studies have revealed that GNNs are vulnerable to adversarial attacks. To defend against such attacks, robust graph structure refinement (GSR) methods aim at minimizing the effect of adversarial edges based on node features, graph structure, or external information. However, we have discovered that existing GSR methods are limited by narrowassumptions, such as assuming clean node features, moderate structural attacks, and the availability of external clean graphs, resulting in the restricted applicability in real-world scenarios. In this paper, we propose a self-guided GSR framework (SG-GSR), which utilizes a clean sub-graph found within the given attacked graph itself. Furthermore, we propose a novel graph augmentation and a group-training strategy to handle the two technical challenges in the clean sub-graph extraction: 1) loss of structural information, and 2) imbalanced node degree distribution. Extensive experiments demonstrate the effectiveness of SG-GSR under various scenarios including non-targeted attacks, targeted attacks, feature attacks, e-commerce fraud, and noisy node labels. Our code is available at https://github.com/yeonjun-in/torch-SG-GSR.

Feature Distribution on Graph Topology Mediates the Effect of Graph Convolution: Homophily Perspective

How would randomly shuffling feature vectors among nodes from the same class affect graph neural networks (GNNs)? The feature shuffle, intuitively, perturbs the dependence between graph topology and features (A-X dependence) for GNNs to learn from. Surprisingly, we observe a consistent and significant improvement in GNN performance following the feature shuffle. Having overlooked the impact of A-X dependence on GNNs, the prior literature does not provide a satisfactory understanding of the phenomenon. Thus, we raise two research questions. First, how should A-X dependence be measured, while controlling for potential confounds? Second, how does A-X dependence affect GNNs? In response, we (i) propose a principled measure for A-X dependence, (ii) design a random graph model that controls A-X dependence, (iii) establish a theory on how A-X dependence relates to graph convolution, and (iv) present empirical analysis on real-world graphs that aligns with the theory. We conclude that A-X dependence mediates the effect of graph convolution, such that smaller dependence improves GNN-based node classification.