We introduce a novel hypergraph message passing framework inspired by interacting particle systems, where hyperedges act as fields inducing shared node dynamics. By incorporating attraction, repulsion, and Allen-Cahn forcing terms, particles of varying classes and features achieve class-dependent equilibrium, enabling separability through the particle-driven message passing. We investigate both first-order and secondorder particle system equations for modeling these dynamics, which mitigate over-smoothing and heterophily thus can capture complete interactions. The more stable second-order system permits deeper message passing. Furthermore, we enhance deterministic message passing with stochastic element to account for interaction uncertainties. We prove theoretically that our approach mitigates oversmoothing by maintaining a positive lower bound on the hypergraph Dirichlet energy during propagation and thus to enable hypergraph message passing to go deep. Empirically, our models demonstrate competitive performance on diverse real-world hypergraph node classification tasks, excelling on both homophilic and heterophilic datasets. Source code is available at the link.

Many datasets have inherent "multi-way" structure, where downstream tasks depend on relationships between groups of entities that ordinary graphs, whose edges are pairwise relationships, cannot represent (Bick et al., 2023; Benson et al., 2021; Schaub et al., 2021). Hypergraphs overcome this by allowing hyperedges that connect any number of vertices.

With the advancement of artificial intelligence (AI) and increasing integrated circuit (IC) design complexity, efficient chip design through electronic design automation (EDA) has become critical. Fast and accurate congestion prediction in chip layout and routing can significantly enhance automated design performance. Existing congestion modeling methods are limited by (i) ineffective processing and fusion of multi-view circuit data information, and (ii) insufficient reliability and interpretability in the prediction process. To address these challenges, we propose the Multi-view Interpretable Hypergraph for Chip (MIHC), a trustworthy multi-view hypergraph neural network framework that (i) processes both graph and image information in unified hypergraph representations, capturing topological and geometric circuit data; (ii) implements a novel subgraph Information Bottleneck mechanism, identifying critical congestion-correlated regions to guide predictions. This work is the first attempt to incorporate such interpretability into congestion prediction through informative graph reasoning. Experiments show that the MIHC method reduces NMAE by 16.67% and 8.57% in cell-based and grid-based predictions on ISPD2015, and 5.26% and 2.44% on CircuitNet-N28, respectively, compared to state-of-the-art methods. Rigorous cross-design generalization experiments further validate our method's capability to handle entirely unseen circuit designs.

Clustering is a fundamental task in both machine learning and data mining. Among various methods, edge-colored clustering (ECC) has emerged as a useful approach for handling categorical data. Given a hypergraph with (hyper)edges labeled by colors, ECC aims to assign vertex colors to minimize the number of edges where the vertex color differs from the edge's color. However, traditional ECC has inherent limitations, as it enforces a nonoverlapping and exhaustive clustering. To tackle these limitations, three versions of ECC have been studied: LOCALECC and GLOBALECC, which allow overlapping clusters, and ROBUSTECC, which accounts for vertex outliers.

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.

Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent extensions of graph neural network (GNN) architectures to hypergraphs. Most of these architectures rely on message-passing to encode higher-order information. In this paper, we propose to instead use hypergraph-level encodings based on characteristics such as hypergraph Laplacians and discrete curvature notions. These encodings can be used on datasets that are naturally parametrized as hypergraphs and on graph-level datasets, which we reparametrize as hypergraphs to compute encodings.

Hypergraph neural networks (HGNNs) have demonstrated remarkable success in learning from such higher-order relational data. While such higher-order modeling enhances relational reasoning, the effectiveness of hypergraph learning remains bottlenecked by two persistent challenges: the scarcity of labeled data inherent to complex systems, and the vulnerability to structural noise in real-world interaction patterns. Traditional data augmentation methods, though successful in Euclidean and graph-structured domains, struggle to preserve the intricate balance between node features and hyperedge semantics, often disrupting the very group-wise interactions that define hypergraph value. To bridge this gap, we present HyperMixup, a hypergraph-aware augmentation framework that preserves higher-order interaction patterns through structure-guided feature mixing. Specifically, HyperMixup contains three critical components: 1) Structure-aware node pairing guided by joint feature-hyperedge similarity metrics, 2) Context-enhanced hierarchical mixing that preserves hyperedge semantics through dual-level feature fusion, and 3) Adaptive topology reconstruction mechanisms that maintain hypergraph consistency while enabling controlled diversity expansion. Theoretically, we establish that our method induces hypergraph-specific regularization effects through gradient alignment with hyperedge covariance structures, while providing robustness guarantees against combined node-hyperedge perturbations. Comprehensive experiments across diverse hypergraph learning tasks demonstrate consistent performance improvements over state-of-the-art baselines, with particular effectiveness in low-label regimes. The proposed framework advances hypergraph representation learning by unifying data augmentation with higher-order topological constraints, offering both practical utility and theoretical insights for relational machine learning.

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension.

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.

Electronic health records (EHR) pose large-scale multi-disease modeling problems in which many outcomes are rare and strongly influenced by shared risk factors. While modern approaches achieve strong predictive performance, they often treat diseases independently or rely on black-box architectures, offering limited insight into how risk factors organize disease risk and little principled uncertainty quantification. We introduce a Bayesian hypergraph inference framework that reframes multi-disease modeling around latent, risk-factor-modulated disease pathways. Risk factors act on hyperedges, latent disease subsets with shared risk patterns, allowing diseases to participate in multiple distinct pathways and enabling interpretable, higher-order structure beyond pairwise associations. A repulsion prior encourages parsimonious and identifiable structure, while posterior inference provides calibrated uncertainty over both disease groupings and risk-factor influence. To enable scalable inference on large EHR datasets, we develop a structured variational inference algorithm that preserves logical dependencies among hyperedge existence, disease membership, and pathway-level effects. Experiments on simulated data and UK Biobank demonstrate stable and interpretable disease pathway structure, well-calibrated uncertainty, improved estimation for rare diseases, and competitive predictive performance.