Thus,hypergraph-guided embedding can capture functional relations in learned representations.

In the supplementary material, we provide additional information and details in A.1. This section covers the introduction of data, key parameter settings, comparisons with baselines, optimization methods, and the algorithm process of our method. The statistical information of the aforementioned four real-world datasets is presented in Table 4. These datasets primarily consist of daily spatio-temporal statistics in the United States. We perform 2 dynamic routing iterations.

Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which rely on message-passing between nodes over hyperedges to learn latent representations, have emerged as the method of choice for predictive tasks in many of these domains. These approaches typically perform only a small number of message-passing rounds to learn the representations, which they then utilize for predictions. The small number of message-passing rounds comes at a cost, as the representations only capture local information and forego long-range high-order dependencies. However, as we demonstrate, blindly increasing the message-passing rounds to capture long-range dependency also degrades the performance of hyper-graph neural networks. Recent works have demonstrated that implicit graph neural networks capture long-range dependencies in standard graphs while maintaining performance. Despite their popularity, prior work has not studied long-range dependency issues on hypergraph neural networks. Here, we first demonstrate that existing hypergraph neural networks lose predictive power when aggregating more information to capture long-range dependency. We then propose Implicit Hypergraph Neural Network (IHNN), a novel framework that jointly learns fixed-point representations for both nodes and hyperedges in an end-to-end manner to alleviate this issue. Leveraging implicit differentiation, we introduce a tractable projected gradient descent approach to train the model efficiently. Extensive experiments on real-world hypergraphs for node classification demonstrate that IHNN outperforms the closest prior works in most settings, establishing a new state-of-the-art in hypergraph learning.

Deep graph models have achieved great success in network representation learning. However, their focus on pairwise relationships restricts their ability to learn pervasive higher-order interactions in real-world systems, which can be naturally modeled as hypergraphs. To tackle this issue, Hypergraph Neural Networks (HNNs) have garnered substantial attention in recent years. Despite the proposal of numerous HNNs, the absence of consistent experimental protocols and multi-dimensional empirical analysis impedes deeper understanding and further development of HNN research. While several toolkits for deep hypergraph learning (DHGL) have been introduced to facilitate algorithm evaluation, they provide only limited quantitative evaluation results and insufficient coverage of advanced algorithms, datasets, and benchmark tasks. To fill the gap, we introduce DHG-Bench, the first comprehensive benchmark for HNNs. Specifically, DHG-Bench systematically investigates the characteristics of HNNs in terms of four dimensions: effectiveness, efficiency, robustness, and fairness. We comprehensively evaluate 17 state-of-the-art HNN algorithms on 22 diverse datasets spanning node-, edge-, and graph-level tasks, under unified experimental settings. Extensive experiments reveal both the strengths and limitations of existing algorithms, offering valuable insights and directions for future research. Furthermore, to facilitate reproducible research, we have developed an easy-to-use library for training and evaluating different HNN methods. The DHG-Bench library is available at: https://github.com/Coco-Hut/DHG-Bench.

Many real-world interactions are group-based rather than pairwise such as papers with multiple co-authors and users jointly engaging with items. Hypergraph neural networks have shown great promise at modeling higher-order relations, but their reliance on a fixed number of explicit message-passing layers limits long-range dependency capture and can destabilize training as depth grows. In this work, we introduce Implicit Hypergraph Neural Networks (IHGNN), which bring the implicit equilibrium formulation to hypergraphs: instead of stacking layers, IHGNN computes representations as the solution to a nonlinear fixed-point equation, enabling stable and efficient global propagation across hyperedges without deep architectures. We develop a well-posed training scheme with provable convergence, analyze the oversmoothing conditions and expressivity of the model, and derive a transductive generalization bound on hypergraphs. We further present an implicit-gradient training procedure coupled with a projection-based stabilization strategy. Extensive experiments on citation benchmarks show that IHGNN consistently outperforms strong traditional graph/hypergraph neural network baselines in both accuracy and robustness. Empirically, IHGNN is resilient to random initialization and hyperparameter variation, highlighting its strong generalization and practical value for higher-order relational learning.

Relational databases (RDBs) are ubiquitous in enterprise and real-world applications. Flattening the database poses challenges for deep learning models that rely on fixed-size input representations to capture relational semantics from the structured nature of relational data. Graph neural networks (GNNs) have been proposed to address this, but they often oversimplify relational structures by modeling all the tuples as monolithic nodes and ignoring intra-tuple associations. In this work, we propose a novel hypergraph-based framework, that we call rel-HNN, which models each unique attribute-value pair as a node and each tuple as a hyperedge, enabling the capture of fine-grained intra-tuple relationships. Our approach learns explicit multi-level representations across attribute-value, tuple, and table levels. To address the scalability challenges posed by large RDBs, we further introduce a split-parallel training algorithm that leverages multi-GPU execution for efficient hypergraph learning. Extensive experiments on real-world and benchmark datasets demonstrate that rel-HNN significantly outperforms existing methods in both classification and regression tasks. Moreover, our split-parallel training achieves substantial speedups -- up to 3.18x for learning on relational data and up to 2.94x for hypergraph learning -- compared to conventional single-GPU execution.

Irregular multivariate time series (IMTS) are characterized by irregular time intervals within variables and unaligned observations across variables, posing challenges in learning temporal and variable dependencies. Many existing IMTS models either require padded samples to learn separately from temporal and variable dimensions, or represent original samples via bipartite graphs or sets. However, the former approaches often need to handle extra padding values affecting efficiency and disrupting original sampling patterns, while the latter ones have limitations in capturing dependencies among unaligned observations. To represent and learn both dependencies from original observations in a unified form, we propose HyperIMTS, a Hypergraph neural network for Irregular Multivariate Time Series forecasting. Observed values are converted as nodes in the hypergraph, interconnected by temporal and variable hyperedges to enable message passing among all observations. Through irregularity-aware message passing, HyperIMTS captures variable dependencies in a time-adaptive way to achieve accurate forecasting. Experiments demonstrate HyperIMTS's competitive performance among state-of-the-art models in IMTS forecasting with low computational cost.