Knowledge Hypergraphs (KHs) have recently emerged as a knowledge representation for retrieval-augmented generation (RAG), offering a paradigm to model multi-entity relations into a structured form. However, existing KH-based RAG methods suffer from three major limitations: static retrieval planning, non-adaptive retrieval execution, and superficial use of KH structure and semantics, which constrain their ability to perform effective multi-hop question answering. To overcome these limitations, we propose PRoH, a dynamic Planning and Reasoning over Knowledge Hypergraphs framework. PRoH incorporates three core innovations: (i) a context-aware planning module that sketches the local KH neighborhood to guide structurally grounded reasoning plan generation; (ii) a structured question decomposition process that organizes subquestions as a dynamically evolving Directed Acyclic Graph (DAG) to enable adaptive, multi-trajectory exploration; and (iii) an Entity-Weighted Overlap (EWO)-guided reasoning path retrieval algorithm that prioritizes semantically coherent hyperedge traversals. Experiments across multiple domains demonstrate that PRoH achieves state-of-the-art performance, surpassing the prior SOTA model HyperGraphRAG by an average of 19.73% in F1 and 8.41% in Generation Evaluation (G-E) score, while maintaining strong robustness in long-range multi-hop reasoning tasks.

Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing such "higher order" relationships is as a hypergraph. However, efforts to apply machine learning techniques to hypergraph structured datasets have been limited thus far. In this paper, we address the problem of link prediction in knowledge hypergraphs as well as simple hypergraphs and develop a novel, simple, and effective optimization architecture that addresses both tasks. Additionally, we introduce a novel feature extraction technique using node level clustering and we show how integrating data from node-level labels can improve system performance. Our self-supervised approach achieves significant improvement over state of the art baselines on several hyperedge prediction and knowledge hypergraph completion benchmarks.

Knowledge hypergraphs generalize knowledge graphs using hyperedges to connect multiple entities and depict complicated relations. Existing methods either transform hyperedges into an easier-to-handle set of binary relations or view hyperedges as isolated and ignore their adjacencies. Both approaches have information loss and may potentially lead to the creation of sub-optimal models. To fix these issues, we propose the Hyperbolic Hypergraph Neural Network (H2GNN), whose essential component is the hyper-star message passing, a novel scheme motivated by a lossless expansion of hyperedges into hierarchies. It implements a direct embedding that consciously incorporates adjacent entities, hyper-relations, and entity position-aware information. As the name suggests, H2GNN operates in the hyperbolic space, which is more adept at capturing the tree-like hierarchy. We compare H2GNN with 15 baselines on knowledge hypergraphs, and it outperforms state-of-the-art approaches in both node classification and link prediction tasks.

Existing knowledge hypergraph embedding methods mainly focused on improving model performance, but their model structures are becoming more complex and redundant. Furthermore, due to the inherent complex semantic knowledge, the computation of knowledge hypergraph embedding models is often very expensive, leading to low efficiency. In this paper, we propose a feature interaction and extraction-enhanced 3D circular convolutional embedding model, HyCubE, which designs a novel 3D circular convolutional neural network and introduces the alternate mask stack strategy to achieve efficient n-ary knowledge hypergraph embedding. By adaptively adjusting the 3D circular convolution kernel size and uniformly embedding the entity position information, HyCubE improves the model performance with fewer parameters and reaches a better trade-off between model performance and efficiency. In addition, we use 1-N multilinear scoring based on the entity mask mechanism to further accelerate the model training efficiency. Finally, extensive experimental results on all datasets demonstrate that HyCubE consistently outperforms state-of-the-art baselines, with an average improvement of 4.08%-10.77% and a maximum improvement of 21.16% across all metrics. Commendably, HyCubE speeds up by an average of 7.55x and reduces memory usage by an average of 77.02% compared to the latest state-of-the-art baselines.

Knowledge graphs store facts using relations between pairs of entities. In this work, we address the question of link prediction in knowledge bases where each relation is defined on any number of entities. We represent facts in a knowledge hypergraph: a knowledge graph where relations are defined on two or more entities. While there exist techniques (such as reification) that convert the non-binary relations of a knowledge hypergraph into binary ones, current embedding-based methods for knowledge graph completion do not work well out of the box for knowledge graphs obtained through these techniques. Thus we introduce HypE, a convolution-based embedding method for knowledge hypergraph completion. We also develop public benchmarks and baselines for our task and show experimentally that HypE is more effective than proposed baselines and existing methods.