# Biquaternionic Space with Complex-valued Attention for Temporal Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2609.14279 · HTML: https://mlsanity.com/paper/2609.14279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 13 Sep 2026.

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

- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [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)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [InteractE: Improving Convolution-based Knowledge Graph Embeddings by Increasing Feature Interactions](https://mlsanity.com/paper/1911.00219/) (2019)
- [TeRo: A Time-aware Knowledge Graph Embedding via Temporal Rotation](https://mlsanity.com/paper/2010.01029/) (2020)
- [ChronoR: Rotation Based Temporal Knowledge Graph Embedding](https://mlsanity.com/paper/2103.10379/) (2021)
- [Temporal Knowledge Graph Completion using Box Embeddings](https://mlsanity.com/paper/2109.08970/) (2021)
- [Tucker decomposition-based Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2011.07751/) (2020)
- [Dual-Geometric Space Embedding Model for Two-View Knowledge Graphs](https://mlsanity.com/paper/2209.08767/) (2022)
- [HGE: Embedding Temporal Knowledge Graphs in a Product Space of Heterogeneous Geometric Subspaces](https://mlsanity.com/paper/2312.13680/) (2023)
- [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)
- [Logic and Commonsense-Guided Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2211.16865/) (2022)
- [Simple but Effective Compound Geometric Operations for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2408.06603/) (2024)

## Abstract (arXiv)

Temporal knowledge graph embedding (TKGE) models infer missing facts in knowledge graphs that evolve over time. Many existing models use a single geometric space, which can limit their ability to represent diverse relational patterns, or treat entity representations as static. We propose Biquaternionic Space with Complex-valued Attention (BSCA), a TKGE model that combines circular and hyperbolic rotations within a unified biquaternionic framework. A complex-valued attention mechanism adaptively fuses time-conditioned and relation-conditioned entity representations, allowing them to vary with temporal and relational context. Experiments on five benchmark datasets show competitive performance across datasets, with the largest improvement on GDELT: BSCA achieves an MRR of 52.1%, compared with 38.1% for the strongest baseline in our comparison.