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.

我们提出了一种新的方法，将因子张量映射到统一的平滑 Lie 群流形上，以使因子张量的分布在张量分解中逼近均匀，从而克服了因子张量之间固有的异质性在张量融合过程中的显著障碍，并进一步限制了链接预测的性能。