Hyperbolic Geometry is Not Necessary: Lightweight Euclidean-Based Models for Low-Dimensional Knowledge Graph Embeddings

Abstract

Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation based on hyperbolic geometry is much more complicated than Euclidean operations. In this paper, based on the state-of-the-art hyperbolic-based model RotH, we develop two lightweight Euclideanbased models, called RotL and Rot2L. The RotL model simplifies the hyperbolic operations while keeping the flexible normalization effect. Utilizing a novel two-layer stacked transformation and based on RotL, the Rot2L model obtains an improved representation capability, yet costs fewer parameters and calculations than RotH. The experiments on link prediction show that Rot2L achieves the stateof-the-art performance on two widely-used datasets in low-dimensional knowledge graph embeddings. Furthermore, RotL achieves similar performance as RotH but only requires half of the training time.

Ultrahyperbolic Knowledge Graph Embeddings

“…where Although circular rotation is theoretically able to infer symmetric patterns [36] (i.e., by setting rotation angle 𝜃 = 𝜋 or 𝜃 = 0), circular reflection can more effectively represent symmetric relations since their second power is the identity. AttH [36] combines circular rotations and circular reflections by using an attention mechanism learned in the tangent space, which requires additional parameters. We also combine circular rotation and circular reflection operators but in a different way.…”

Swift and Sure: Hardness-aware Contrastive Learning for Low-dimensional Knowledge Graph Embeddings

“…We further improve the Hardness-aware Activation by multiplying the similarity score with a relation-specific trainable parameter. Applied by previous low-dimensional KGE models, this technology is beneficial to encoding hierarchical relationships and improves prediction accuracy [28]. Finally, given a query (𝑒, 𝑟 ) and its target entity 𝑒 𝑝 , the triple score based on 𝐿 2 distance via the Hardness-aware Activation is defined as:…”

“…To verify the performance of our HaLE framework, we select five representative KGE models: TransE [3], DistMult [34], RotatE [22], RotE [5], and RotL [28]. These models utilize five different transform functions to generate the query vector in the Euclidean space, which are formulated as follows:…”

“…To reduce the space complexity, low-dimensional hyperbolic-based KGE models have drawn attention, such as MuRP, RotH, RefH and AttH [2,5]. Although they can achieve good performance when using 32 or 64 dimensions, the calculations in the hyperbolic space are much more complicated than those in the Euclidean space [28].…”

“…Best viewed in color.to replace the multiplication operation between the head entity and relation vectors. Based on the RotH model, Wang et al[28] propose two Euclidean-based lightweight models, RotL and Rot2L. Eliminating complex hyperbolic operations, the two models have lower computational complexity and faster convergence speed.Replacing Negative Sampling.…”