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

arXiv: https://arxiv.org/abs/2404.09155 · HTML: https://mlsanity.com/paper/2404.09155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 14 Apr 2024.

## Builds on (most cited first, 19 of 19)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Learning Sequence Encoders for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1809.03202/) (2018)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [TeMP: Temporal Message Passing for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2010.03526/) (2020)
- [Deep Learning on Lie Groups for Skeleton-based Action Recognition](https://mlsanity.com/paper/1612.05877/) (2016)
- [Temporal Knowledge Graph Reasoning with Historical Contrastive Learning](https://mlsanity.com/paper/2211.10904/) (2022)
- [Tangent Space Backpropagation for 3D Transformation Groups](https://mlsanity.com/paper/2103.12032/) (2021)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Temporal Knowledge Graph Completion using Box Embeddings](https://mlsanity.com/paper/2109.08970/) (2021)
- [Efficient Derivative Computation for Cumulative B-Splines on Lie Groups](https://mlsanity.com/paper/1911.08860/) (2019)
- [EvoKG: Jointly Modeling Event Time and Network Structure for Reasoning over Temporal Knowledge Graphs](https://mlsanity.com/paper/2202.07648/) (2022)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2203.07993/) (2022)
- [How Knowledge Graph and Attention Help? A Quantitative Analysis into Bag-level Relation Extraction](https://mlsanity.com/paper/2107.12064/) (2021)

## Abstract (arXiv)

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.