Few-shot node classification on hypergraphs requires models that generalize from scarce labels while capturing high-order structures. Existing hypergraph neural networks (HNNs) effectively encode such structures but often suffer from overfitting and scalability issues due to complex, black-box architectures. In this work, we propose ZEN (Zero-Parameter Hypergraph Neural Network), a fully linear and parameter-free model that achieves both expressiveness and efficiency. Built upon a unified formulation of linearized HNNs, ZEN introduces a tractable closed-form solution for the weight matrix and a redundancy-aware propagation scheme to avoid iterative training and to eliminate redundant self-information. On 11 real-world hypergraph benchmarks, ZEN consistently outperforms eight baseline models in classification accuracy while achieving up to 696x speedups over the fastest competitor. Moreover, the decision process of ZEN is fully interpretable, providing insights into the characteristic of a dataset.

Heterogeneous hypergraph is a kind of structural data that contains multiple types of nodes and multiple types of hyperedges. Each hyperedge type corresponds to a specific multi-ary relation (called hyper-relation) among subsets of nodes, which goes beyond traditional pair-wise relations in simple graphs. Existing representation learning methods for heterogeneous hypergraphs typically learn embeddings for nodes and hyperedges based on graph neural networks. Although achieving promising performance, they are still limited in capturing more complex structural features and richer semantics conveyed by the composition of various hyper-relations. To fill this research gap, in this work, we propose the concept of hyper-meta-path for heterogeneous hypergraphs, which is defined as the composition of a sequence of hyper-relations. Besides, we design an attention-based heterogeneous hypergraph neural network (HHNN) to automatically learn the importance of hyper-meta-paths. By exploiting useful ones, HHNN is able to capture more complex structural features to boost the model's performance, as well as leverage their conveyed semantics to improve the model's interpretability. Extensive experiments show that HHNN can achieve significantly better performance than state-of-the-art baselines, and the discovered hyper-meta-paths bring good interpretability for the model predictions.

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. Furthermore, A.2 presents supplementary experiments for our model, including visualization experiments and replication studies. Additionally, we discuss the reasons behind utilizing hypergraphs as the temporal encoder in A.3. Finally, the limitations and broader impacts of our work are discussed in A.4. A.1 Data and Implementation Details Data. The statistical information of the aforementioned four real-world datasets is presented in Table 4.

In this section, we conduct experiments to explore the effect of hyperparameters. There are two important tradeoff parameters α, and β in our proposed method. We select four representative datasets to perform the ablation study. For each data set, when varying one parameter, the other is set as constant. To investigate the effect of α, we search its value in the range of {0.1, 0.2, 0.5, 1.0}. The experimental results are summarized in Table 1. From the table, we can find that α is able to improve the performance in a wide range of hyper-parameters (0.1-0.5).

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.