Graph Anomaly Detection (GAD) identifies deviant patterns including anomalous nodes, edges, and subgraphs in graph data, with significant applications in social networks, cybersecurity, and financial risk control. While spectral methods have proven effective for homogeneous graph anomaly detection, their application to heterogeneous graphs remains challenging due to structural complexity and semantic richness. Existing heterogeneous graph anomaly detection methods either rely on manually designed meta-paths or decompose the graph into homogeneous subgraphs, leading to limited flexibility or loss of structural integrity. To address these limitations, we propose the Graph Wavelet Transformer (GWT), a novel spectral-based approach that integrates global graph properties and spectral analysis without requiring meta-path information. GWT employs a three-stage process: heterogeneous-to-homogeneous graph conversion, global dependency modeling via graph transformers, and spectral-aware feature enhancement focusing on frequency band components. Extensive experiments on multiple benchmarks demonstrate that GWT significantly outperforms ten baseline methods, providing a new paradigm for heterogeneous graph anomaly detection that preserves structural completeness while achieving computational efficiency.

Cross-domain recommendation (CDR) has gained significant attention for its ability to address data sparsity issue. However, most existing CDR methods focus primarily on improving recommendation accuracy while largely overlooking fairness considerations, which can lead to biased outcomes and unfair treatment of different user groups. To solve this critical problem, we investigate whether fairness can be transferred from the source domain to the target domain. Our analysis suggests that fairness can be effectively transferred if the fairness of the source domain is ensured and the distributions of the source and target domains are well aligned. Based on this, we propose the FairCDR, a novel framework that can achieve the knowledge transfer of fairness and user preferences simultaneously. FairCDR owns two phases: single-domain fairness guarantee and inter-domain distribution alignment. In the first phase, we employ an adversarial learning-based recommender (ALR) to disentangle user preferences from sensitive attributes in the source domain. In the second phase, we introduce a new mutual learning-based diffusion model (MLDiff), which engages in mutual learning with ALR to progressively align the distributions of the source and target domains. This improves ALR's adaptability to distribution shifts, ultimately ensuring fairness and recommendation performance in the target domain. Extensive experiments on multiple real-world cross-domain datasets demonstrate that FairCDR surpasses existing strong baselines in both fairness and recommendation quality.

Multimodal recommendation, which utilizes rich multimodal information to learn user preferences, has attracted significant attention. Most works focus on designing powerful encoders for extracting multimodal features, and simply aggregate the learned features together to make prediction. Consequently, they have a limited capacity to learn the inter-modality knowledge including the modality-shared and modality-unique knowledge. In fact, learning the modality-shared knowledge enables us to align cross-modality data for fusing heterogeneous modality features. Learning the modality-unique knowledge is equally important when recommendation tasks only involve a small amount of shared features and the necessary information is contained within specific modality. In this article, we propose Contrastive Modality-Disentangled Learning (CMDL) to overcome this critical limitation. CMDL exactly captures the inter-modality knowledge by achieving modality disentanglement. Specifically, CMDL first disentangles the initial representation into the modality-invariant and modality-specific representations. Afterwards, CMDL introduces a novel manner of contrastive learning to approximate the MI upper bounds for achieving disentanglement regularization. Building upon the proposed regularization, CMDL encourages the modality-invariant and modality-specific representations to capture the modality-shared and modality-unique knowledge respectively and to be statistically independent to each other. Empirically, extensive experiments are conducted on benchmark datasets, demonstrating the superior performance of CMDL compared with strong multimodal recommenders.

Methods based on graph neural networks for solving combinatorial optimization (CO) problems have exhibited promising results in tackling a range of NP-hard problems, eliminating the necessity for reliance on manually created domain knowledge. Existing models including reinforcement learning (RL) framework assume that combinatorial instances in the training set contribute equally during training. Nevertheless, there is considerable variation in the quality of training instances, and the performance of models may suffer from the inclusion of low-quality training instances. This paper expands the current scope of neural solvers for CO problems through the incorporation of curriculum learning (CL). To alleviate the adverse impact of low-quality training instances, we propose CL4CO which utilizes CL strategy, a selective training method, to train models based on the rank of instances' quality in neural Combinatorial Optimization framework. Also, we introduce several candidate topology-aware metrics based on heterophily ratio and evaluation of clustering for the training scheduler. Furthermore, it is noteworthy to emphasize that it has potential to enhance the generalization capacity of RL-based baselines and we give a experimental validation. This enhancement plugin from the fact that CL empowers the acquired RL-based solver to effectively leverage commonly shared features within the same class of CO. Empirically, we conduct a case study on MaxCut, a classical discrete Oil-vector CO, to verify our findings and our results demonstrate that CL4CO is efficient and superiority with good generalization ability.

Decision-focused learning (DFL) combines both machine learning and combinatorial optimization so as to enhance the quality of decision-making. In general, DFL adds an optimization layer after the neural network and solves a focused combinatorial optimization problem. The optimization layer is usually based on KKT conditions or surrogate functions. However, the optimizer associated with the DFL is inflexible and requires a large amount of expert knowledge. Furthermore, it has been shown that the optimizer exhibits a lack of robustness and differentiability when confronted with complex tasks, especially in the graph domain. To solve this problem, we study a more generic situation by taking the optimization layer as a black-box operator on graphs. Then, we design a mixed zeroth-order optimization to differentiate the layer. Specifically, we combine DFL with graph neural networks and present a decision-focused graph neural network named ZO4Graph based on a mixed zeroth-order optimizer. Empirically, we conduct extensive experiments compared with two-stage models on community detection. Numerical results demonstrate that our proposed framework outperforms its peers.

Anomaly detection in multi-type event sequences is a crucial and challenging problem with important applications in various domains, including cybersecurity, finance and healthcare. Temporal point process has emerged as a powerful technique for modeling event sequences and has gained considerable attention in the field of anomaly detection. However, existing temporal point process approaches are either inapplicable to multi-type event sequence data or incur the loss of valuable information in subsequences associated with specific event types. To this end, we propose a novel Multiple Hypothesis Testing based Anomaly Detection method (MultiAD) to detect anomalous multi-type event sequences. The basic idea of MultiAD is to capture the underlying distribution of normal sequences using a neural multivariate point process, based on which the original hypothesis testing problem can be converted into a multiple hypothesis testing using the multivariate time rescaling theorem. By conducting multiple hypothesis tests on the time-rescaled subsequences, MultiAD makes full use of the valuable information contained within individual subsequences. Moreover, we claim that the existing test statistic ignores the sequential information of inter-event time intervals and propose new statistics to address this shortcoming. Finally, we employ the kernel method to obtain a smooth estimator of the distribution of the proposed statistics under the null hypothesis. This ensures a more accurate and reliable computation of the p-value, providing robust statistical inference. Extensive experimental results demonstrate that MultiAD significantly outperforms the state-of-the-art methods on both synthetic and real-world data.

Markov logic network (MLN) is a powerful statistical modeling framework for probabilistic logic reasoning. Despite the elegancy and effectiveness of MLN, the inference of MLN is known to suffer from an efficiency issue. Even the state-of-the-art MLN engines can not scale to medium-size real-world knowledge bases in the open-world setting, i.e., all unobserved facts in the knowledge base need predictions. In this work, by focusing on a certain class of first-order logic rules that are sufficiently expressive, we develop a highly efficient MLN inference engine called MLN4KB that can leverage the sparsity of knowledge bases. MLN4KB enjoys quite strong theoretical properties; its space and time complexities can be exponentially smaller than existing MLN engines. Experiments on both synthetic and real-world knowledge bases demonstrate the effectiveness of the proposed method. MLN4KB is orders of magnitudes faster (more than 103 times faster on some datasets) than existing MLN engines in the open-world setting. Without any approximation tricks, MLN4KB can scale to real-world knowledge bases including WN-18 and YAGO3-10 and achieve decent prediction accuracy without bells and whistles.

Graph neural networks (GNNs) are powerful models to handle graph data and can achieve state-of-the-art in many critical tasks including node classification and link prediction. However, existing graph neural networks still face both challenges of over-smoothing and over-squashing based on previous literature. To this end, we propose a new Curvature-based topology-aware Dropout sampling technique named CurvDrop, in which we integrate the Discrete Ricci Curvature into graph neural networks to enable more expressive graph models. Also, this work can improve graph neural networks by quantifying connections in graphs and using structural information such as community structures in graphs. As a result, our method can tackle the both challenges of over-smoothing and over-squashing with theoretical justification. Also, numerous experiments on public datasets show the effectiveness and robustness of our proposed method. The code and data are released in https://github.com/liu-yang-maker/Curvature-based-Dropout.