Knowledge hypergraph embedding, which projects entities and n-ary relations into a low-dimensional continuous vector space to predict missing links, remains a challenging area to be explored despite the ubiquity of n-ary relational facts in the real world. Currently, knowledge hypergraph link prediction methods are essentially simple extensions of those used in knowledge graphs, where n-ary relational facts are decomposed into different subelements. Convolutional neural networks have been shown to have remarkable information extraction capabilities in previous work on knowledge graph link prediction. In this paper, we propose a novel embedding-based knowledge hypergraph link prediction model named HyConvE, which exploits the powerful learning ability of convolutional neural networks for effective link prediction. Specifically, we employ 3D convolution to capture the deep interactions of entities and relations to efficiently extract explicit and implicit knowledge in each n-ary relational fact without compromising its translation property. In addition, appropriate relation and position-aware filters are utilized sequentially to perform two-dimensional convolution operations to capture the intrinsic patterns and position information in each n-ary relation, respectively. Extensive experimental results on real datasets of knowledge hypergraphs and knowledge graphs demonstrate the superior performance of HyConvE compared with state-of-the-art baselines.

Knowledge hypergraph representation learning , which projects entities and $n$ -ary relations into a low-dimensional vector space, remains a challenging area to be explored despite the ubiquity of $n$ -ary relational facts in the real world. Current methods are always extensions of those used for knowledge graphs with shallow or deep structures. However, shallow and linear models limit the extraction capacity of the latent knowledge, while deep and non-linear models lead to the overabundance of parameters. In this paper, we propose a novel knowledge hypergraph completion model called HJE, which utilizes the powerful capability of convolutional neural networks for efficient representation learning. Interaction-enhanced 3D convolution and relation-aware 2D convolution are jointly utilized by HJE to extract explicit and implicit global knowledge and semantic information effectively without compromising the translation property of the model. Moreover, HJE constructs a unified learnable embedding matrix to capture entity position information in knowledge tuples. The entity mask mechanism can naturally couple the multilinear scoring approach for $n$ -ary facts to speed up the training convergence of the model. Extensive experimental results on real datasets of knowledge hypergraphs and knowledge graphs demonstrate the superior performance of HJE compared with state-of-the-art baselines.

Knowledge hypergraph embedding models are usually computationally expensive due to the inherent complex semantic information. However, existing works mainly focus on improving the effectiveness of knowledge hypergraph embedding, making the model architecture more complex and redundant. It is desirable and challenging for knowledge hypergraph embedding to reach a trade-off between model effectiveness and efficiency. In this paper, we propose an end-to-end efficient knowledge hypergraph embedding model, HyCubE, which designs a novel 3D circular convolutional neural network and the alternate mask stack strategy to enhance the interaction and extraction of feature information comprehensively. Furthermore, our proposed model achieves a better trade-off between effectiveness and efficiency by adaptively adjusting the 3D circular convolutional layer structure to handle $n$-ary knowledge tuples of different arities with fewer parameters. In addition, we use a knowledge hypergraph 1-N multilinear scoring way to accelerate the model training efficiency further. Finally, extensive experimental results on all datasets demonstrate that our proposed model consistently outperforms state-of-the-art baselines, with an average improvement of 8.22% and a maximum improvement of 33.82% across all metrics. Meanwhile, HyCubE is 6.12x faster, GPU memory usage is 52.67% lower, and the number of parameters is reduced by 85.21% compared with the average metric of the latest state-of-the-art baselines.