Deep hyperbolic convolutional model for knowledge graph embedding

Recent advancements in knowledge graph embedding have enabled the representation of entities and relations in continuous vector spaces. Performing link prediction on incomplete knowledge graphs using these embeddings has emerged as a challenging task, drawing considerable research interest. Knowledge graphs in the real world typically exhibit a natural hierarchical structure. Hyperbolic embedding methods have shown promising results in modeling hierarchical data, especially in low-dimensional representations. However, existing hyperbolic models for knowledge graph embedding are generally shallow, resulting in limited expressiveness. Additionally, some deep hyperbolic models exist but are often constrained to fixed curvature spaces, which may not optimally capture varying hierarchical structures. In this work, we propose DeER, a novel multi-layer hyperbolic model that leverages a trainable curvature space, marking an advancement in the depth and adaptability of hyperbolic modeling for knowledge graph embeddings. We specifically design a hyperbolic convolutional neural network to learn the heterogeneous interactions between entities and relations within this adaptable hyperbolic space. Additionally, we introduce a hyperbolic feedforward neural network to transform hyperbolic features across multiple layers, enhancing the model's ability to capture complex hierarchical relationships. Experimental results on three benchmark datasets demonstrate that DeER significantly enhances expressiveness and hierarchical modeling performance when compared to both shallow and other deep baseline approaches.