Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality: whether a higher-order relation is compositional, emergent, or inhibitory with respect to its observed or unobserved sets. In polypharmacy, the regime decides whether a drug should be dropped, kept, or excluded: a compositional drug triple can be safely simplified, an emergent triple requires all drugs jointly, and an inhibitory triple flags a drug that disrupts an existing interaction. However, existing hypergraph learning methods, which merely propagate messages over observed hyperedges, leave this compositional signal unmodeled, allowing dangerous drug combinations to slip through and be misclassified. To this end, we propose the Hypergraph Pattern Machine (HGPM), shifting the paradigm from message passing to learning the compositional pattern of subsets. It tokenizes compositional subsets, organizes them in an inclusion DAG, and trains an inclusion-aware Transformer under masked reconstruction. On ten hypergraph benchmarks, HGPM matches or exceeds state-of-the-art methods. Notably, in a real adverse-event prediction case, HGPM correctly identifies the drug addition that inhibits the side effect among feature-identical candidates, a discrimination existing methods cannot make. The code and data are in https://github.com/KryieZhao/HGPM.git.
Large language models (LLMs) have recently shown strong potential in modeling relational structures. However, existing approaches remain fundamentally graph-centric: they focus on processing pairwise graph structures into tokens that LLMs can understand. In contrast, many real-world relational patterns do not naturally conform to the pairwise-edge assumption, and are better modeled as high-order associations in hypergraphs. For hypergraph structures, existing methods often fail to preserve the native semantics that multiple objects are jointly connected by the same high-order relation, limiting their ability to exploit complex structures. To address this limitation, we put forth the "Hypergraph as Language" perspective and propose Hyper-Align, a hypergraph-native alignment framework for large language models. Hyper-Align compiles the query-object-centered hypergraph context into hypergraph tokens directly consumable by a base LLM. Specifically, we introduce Hypergraph Incidence Detail Template with Overview (HIDT-O), which serializes high-order association structures into a fixed-shape hybrid template combining local incidence details and overview-level summaries. We then design a Hypergraph Incidence Projector (HIP), which maps native high-order incidence structures into the LLM token space through explicit semantic-structural decoupling and bidirectional message passing between vertices and hyperedges. We further define a concrete Hypergraph-as-Language input protocol, which jointly feeds hypergraph tokens and textual prompts into a frozen base LLM, supporting both vertex-level and hyperedge-level tasks under a unified question-answering paradigm. To systematically evaluate different methods in hypergraph structural modeling, we introduce HyperAlign-Bench. Extensive experiments show that Hyper-Align significantly outperforms existing methods across in-domain and zero-shot evaluations.
Hypergraphs provide a principled framework for modeling polyadic interactions, with applications in recommendation systems, social networks, and molecular modeling. Hypergraph generation remains challenging because incidence structures are discrete, sparse, and governed by heterogeneous higher-order interactions. Existing generators often rely on implicit latent spaces or continuous incidence decoders, which provide limited mechanistic interpretation of how node-hyperedge incidences arise. To address these limitations, we propose HYVINT, an intensity-driven hypergraph generative framework. Our key innovations are twofold: (i) we develop an intensity-driven incidence formation mechanism for hypergraphs that links latent interaction strength to binary incidence, and (ii) we derive a tractable lower-bound variational estimator for learning latent representations. We provide generation error bounds with asymptotic convergence rates and empirically show that HYVINT achieves strong fidelity while maintaining substantial novelty and diversity on synthetic and real-world hypergraphs.
Continuous optimization methods for learning Directed Acyclic Graphs (DAGs) operate on weighted adjacency matrices and are therefore limited to pairwise causal relationships. We propose a framework for learning Directed Acyclic Hypergraphs (DAHGs) from observational data, capturing joint parental influences that pairwise models cannot represent. Our approach rests on three components: (i) a generalized linear structural equation model (SEM) with multiplicative interaction terms whose non-zero weights correspond one-to-one with directed hyperedges; (ii) a weighted adjacency tensor representation whose acyclicity is characterized via nilpotency under the tensor t-product; and (iii) a differentiable acyclicity constraint derived through the Fourier decomposition of the t-product, which reduces tensor nilpotency to slice-wise matrix nilpotency and enables least-squares learning via the augmented Lagrangian method.