Mitigating Heterogeneity among Factor Tensors via Lie Group Manifolds for Tensor Decomposition Based Temporal Knowledge Graph Embedding

TL;DR

This work addresses heterogeneity among factor tensors in tensor-decomposition-based Temporal Knowledge Graph Embedding (TKGE), which hinders tensor fusion and link prediction. It introduces a Lie group manifold mapping to enforce a unified, homogeneous-like distribution across entity, relation, and timestamp factors, supported by theoretical analysis that homogeneous factors approximate the target more efficiently. The method integrates into existing TKGE models without adding parameters and demonstrates improved link prediction performance across multiple baselines on ICEWS and GDELT datasets, including robust reductions in heterogeneity measures. The approach offers a scalable, geometry-inspired solution to a core bottleneck in TKGE, with practical implications for more accurate temporal reasoning in knowledge graphs.

Abstract

Recent studies have highlighted the effectiveness of tensor decomposition methods in the Temporal Knowledge Graphs Embedding (TKGE) task. However, we found that inherent heterogeneity among factor tensors in tensor decomposition significantly hinders the tensor fusion process and further limits the performance of link prediction. To overcome this limitation, we introduce a novel method that maps factor tensors onto a unified smooth Lie group manifold to make the distribution of factor tensors approximating homogeneous in tensor decomposition. We provide the theoretical proof of our motivation that homogeneous tensors are more effective than heterogeneous tensors in tensor fusion and approximating the target for tensor decomposition based TKGE methods. The proposed method can be directly integrated into existing tensor decomposition based TKGE methods without introducing extra parameters. Extensive experiments demonstrate the effectiveness of our method in mitigating the heterogeneity and in enhancing the tensor decomposition based TKGE models.

Figures (4)

• Figure 1: (a) illustrates the heterogeneity in the distribution of entities, relations and timestamps within TKGs, as evidenced by the differing distribution curves. (b) illustrates the homogeneous distribution curves of entities, relations and timestamps when using our method to mitigate the heterogeneity among these three elements.
• Figure 2: An illustration of the relation between the Lie group and the Lie algebra. The Lie algebra $\mathfrak{so}(n)$ is the tangent space to the Lie group’s manifold $S(n)$.
• Figure 3: Visualisations of the learned entity, relation and timestamp embeddings on ICEWS14.
• Figure 4: Results of TeAST and TeAST$+{log}(f(\cdot))$ with different rank on ICEWS14.