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

Rushan Geng; Cuicui Luo

cs.LGSep 13, 2026

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

Authors: Rushan Geng, Cuicui Luo

Organizations: School of Computer Science and Technology University of Chinese Academy of Sciences Beijing, China · International College University of Chinese Academy of Sciences Beijing, China

Abstract

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.

Figures & tables

Datasets	Entities	Relations	Timestamps	Time Span	Granularity	Training	Validation	Test
ICEWS14	6,869	230	365	A.D.2014	1 day	72,826	8,941	8,963
ICEWS05-15	10,094	251	4,017	A.D.2005-A.D.2015	1 day	368,962	46,275	46,092
GDELT	500	20	366	A.D.2015-A.D.2016	1 day	2,735,685	341,961	341,961
YAGO11k	10,623	10	237	453 B.C.-A.D.2844	1 year	16,406	2,050	2,051
Wikidata12k	12,554	24	232	A.D.1709-A.D.2018	1 year	539,286	67,538	63,110

Table 1. Statistics of the experimental datasets.

Method		ICEWS05-15				ICEWS14				GDELT				YAGO11k				Wikidata12k
Method		MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10
	TTransE	27.1	8.4	-	61.6	25.5	7.4	-	60.1	11.5	0.0	16.0	31.8	10.8	2.0	15.0	25.1	17.2	9.6	18.4	32.9
	TA-DistMult	47.4	34.6	-	72.8	47.7	36.3	-	68.6	20.6	12.4	21.9	36.5	15.5	9.8	-	26.7	23.0	13.0	-	46.1
	HyTE	31.6	11.6	44.5	68.1	29.7	10.8	41.6	65.5	11.8	0.0	16.5	32.6	13.6	3.3	-	29.8	18.0	9.8	19.7	33.3
	DE-SimplE	51.3	39.2	57.8	74.8	52.6	41.8	59.2	72.5	23.0	14.1	24.8	40.3	-	-	-	-	-	-	-	-
	TComplEx	66.0	59.0	71.0	80.0	61.0	53.0	66.0	76.0	34.0	24.9	36.1	49.8	18.5	12.7	18.3	30.7	33.1	23.3	35.7	53.9

Table 2. Link prediction results (%) on five TKG datasets. Baseline results are taken from the original papers. Bold and underlining indicate the best and second-best results, respectively. Dashes indicate unavailable results.

Method		ICEWS05-15				ICEWS14				YAGO11k				Wikidata12k
Method		MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10
	BSCA	69.3	61.3	74.3	83.8	64.7	56.6	69.4	79.6	20.9	14.2	21.7	34.4	34.3	24.3	37.2	55.6
	w/o $e_{\tau}^{\blacktriangledown}$	68.7	60.7	73.7	83.1	64.3	56.2	69.2	79.4	20.4	13.7	21.0	33.3	33.6	23.3	36.9	55.4
	w/o $e_{r}^{\blacktriangledown}$	68.4	60.3	73.4	83.2	64.2	55.9	69.2	79.6	20.3	13.7	21.0	34.5	33.7	23.2	37.3	55.7
	w/o $e_{\tau}^{\blacktriangledown}+e_{r}^{\blacktriangledown}$	68.9	60.8	74.0	83.8	63.9	55.7	68.9	79.4	20.1	13.6	20.6	33.3	33.7	23.0	37.2	56.1
	w/o $e_{\tau}^{\blacktriangle}$	68.8	60.8	73.8	83.3	64.3	56.2	68.9	79.5	20.5	13.7	21.2	34.8	34.2	23.5	37.6	56.2

Table 3. Ablation results (%) on four TKG datasets. The full BSCA model is shown in bold for reference; w/o denotes removal of the indicated component.

Panel of Figure 1 — Figure 1. Histograms of learned relation and timestamp representations for the relation “Consult” at timestamp $\tau=$ 2014-03-29. Three histograms show the joint relation–time representation, the multiplicative timestamp component, and their Hamilton product for Consult on March 29, 2014.

Figure 2. Training curves over 300 epochs on ICEWS14 and YAGO11k. Two panels show BSCA link prediction performance over 300 training epochs on ICEWS14 and YAGO11k.

Figure 3. Sensitivity to embedding regularization (a) and temporal regularization (b) on ICEWS14, and to embedding dimension on ICEWS14 (c) and YAGO11k (d). Four panels compare link prediction performance across embedding regularization weights, temporal regularization weights, and embedding dimensions on ICEWS14 and YAGO11k.

Relation	Pattern	w/o Attn	w/ Attn
Consult	Symmetric	87.07	87.11
Discuss by telephone	Symmetric	87.53	87.21
Engage in negotiation	Symmetric	89.97	90.68
Make a visit	Asymmetric	89.47	89.90
Make optimistic comment	Asymmetric	52.82	55.09
Reject	Asymmetric	57.92	57.90

Table 4. MRR (%) with and without attention for selected ICEWS14 relations and entities. Bold indicates the higher score in each row.

Method	# Params (M)	Train Time
TComplEx	31.81	7.9 min
TNTComplEx	32.65	8.4 min
TeAST	33.28	8.2 min
TLT-KGE( $\mathbb{C}$ )	58.56	8.2 min
TLT-KGE( $\mathbb{Q}$ )	31.28	14.1 min
TeLM	63.63	17.1 min

Table 5. Comparison of model complexity and training efficiency. All experiments were conducted on the ICEWS14 dataset using a single NVIDIA GeForce RTX 3090 (24GB).

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TeRoR: Decoupled Temporal Rotation with Relational Circular Region for Temporal Knowledge Graph Embedding

Peijia Xie, Yike Liu, Chao He, Huiling Zhu

South China Normal University, Guangzhou, China

KG Embedding Temporal Link Prediction Temporal KGs

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In recent years, with the emergence of Temporal Knowledge Graphs (TKGs), research on learning entity and relation representations in TKGs has attracted increasing attention, giving rise to a large number of TKG embedding methods. TeRo is a simple and efficient temporal knowledge graph embedding approach. However, TeRo does not do well in modeling the mapping properties of various relations, such as one-to-many, many-to-one, and many-to-many. Meanwhile, it also has limitations in the expression of temporal information. To address these issues, we propose a novel TKG embedding method named TeRoR. This method divides the temporal evolution of entity embeddings, and conducts independent rotation transformations on head and tail entities in the complex vector space to strengthen temporal information modeling capacity. In terms of relational characteristics, we train a radius to constrain the rotated and translated head entities within a circular region centered on the tail entity, which effectively captures the diverse mapping properties of relations. Experimental results demonstrate that TeRoR achieves competitive performance against state-of-the-art models on four distinct TKG datasets.

Abstract

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