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    <abstract>The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like metrics, which addressed the limitations of the Euclidean embedding models. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. However, the performance of the hyperbolic KG embedding models for non-transitive relations is still unpromising, while the complex hyperbolic embeddings do not deal with multi-relations. This paper aims to utilize the representation capacity of the complex hyperbolic geometry in multi-relational KG embeddings. To apply the geometric transformations which account for different relations and the attention mechanism in the complex hyperbolic space, we propose to use the fast Fourier transform (FFT) as the conversion between the real and complex hyperbolic space. Constructing the attention-based transformations in the complex space is very challenging, while the proposed Fourier transform-based complex hyperbolic approaches provide a simple and effective solution. Experimental results show that our methods outperform the baselines, including the Euclidean and the real hyperbolic embedding models.</abstract>
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%0 Conference Proceedings
%T Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform
%A Xiao, Huiru
%A Liu, Xin
%A Song, Yangqiu
%A Wong, Ginny
%A See, Simon
%Y Goldberg, Yoav
%Y Kozareva, Zornitsa
%Y Zhang, Yue
%S Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing
%D 2022
%8 December
%I Association for Computational Linguistics
%C Abu Dhabi, United Arab Emirates
%F xiao-etal-2022-complex
%X The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like metrics, which addressed the limitations of the Euclidean embedding models. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. However, the performance of the hyperbolic KG embedding models for non-transitive relations is still unpromising, while the complex hyperbolic embeddings do not deal with multi-relations. This paper aims to utilize the representation capacity of the complex hyperbolic geometry in multi-relational KG embeddings. To apply the geometric transformations which account for different relations and the attention mechanism in the complex hyperbolic space, we propose to use the fast Fourier transform (FFT) as the conversion between the real and complex hyperbolic space. Constructing the attention-based transformations in the complex space is very challenging, while the proposed Fourier transform-based complex hyperbolic approaches provide a simple and effective solution. Experimental results show that our methods outperform the baselines, including the Euclidean and the real hyperbolic embedding models.
%R 10.18653/v1/2022.emnlp-main.349
%U https://aclanthology.org/2022.emnlp-main.349
%U https://doi.org/10.18653/v1/2022.emnlp-main.349
%P 5228-5239

Markdown (Informal)

[Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform](https://aclanthology.org/2022.emnlp-main.349) (Xiao et al., EMNLP 2022)

• Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform (Xiao et al., EMNLP 2022)

ACL

• Huiru Xiao, Xin Liu, Yangqiu Song, Ginny Wong, and Simon See. 2022. Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 5228–5239, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics.