CID-TKG: Collaborative Historical Invariance and Evolutionary Dynamics Learning for Temporal Knowledge Graph Reasoning

Shuai-Long Lei; Xiaobin Zhu; Jiarui Liang; Guoxi Sun; Zhiyu Fang; Xu-Cheng Yin

cs.AIMar 9, 2026

CID-TKG: Collaborative Historical Invariance and Evolutionary Dynamics Learning for Temporal Knowledge Graph Reasoning

Authors: Shuai-Long Lei, Xiaobin Zhu, Jiarui Liang, Guoxi Sun, Zhiyu Fang, Xu-Cheng Yin

Organizations: University of Science and Technology Beijing, Haidian, Beijing, China

Abstract

Temporal knowledge graph (TKG) reasoning aims to infer future facts at unseen timestamps from temporally evolving entities and relations. Despite recent progress, existing approaches still suffer from inherent limitations due to their inductive biases, as they predominantly rely on time-invariant or weakly time-dependent structures and overlook the evolutionary dynamics. To overcome this limitation, we propose a novel collaborative learning framework for TKGR (dubbed CID-TKG) that integrates evolutionary dynamics and historical invariance semantics as an effective inductive bias for reasoning. Specifically, CID-TKG constructs a historical invariance graph to capture long-term structural regularities and an evolutionary dynamics graph to model short-term temporal transitions. Dedicated encoders are then employed to learn representations from each structure. To alleviate semantic discrepancies across the two structures, we decompose relations into view-specific representations and align view-specific query representations via a contrastive objective, which promotes cross-view consistency while suppressing view-specific noise. Extensive experiments verify that our CID-TKG achieves state-of-the-art performance under extrapolation settings.

Figures & tables

Figure 1. An illustrative example of CID-TKG on the ICEWS dataset. The blue region denotes the historical invariance graph, while the green region denotes the evolutionary dynamics graph. Darker colors indicate higher attention scores in both graphs. Illustration of CID-TKG on the ICEWS dataset, showing historical invariance and evolutionary dynamics graphs with attention intensities.

Notations	Descriptions
$\mathcal{E},\mathcal{R},\mathcal{T},\mathcal{F}$	Entity, relation, timestamp, and temporal fact set in a TKG.
$\mathcal{G}_{t}$	Temporal knowledge graph snapshot at timestamp $t$ .
$\mathbf{e}_{s,t},\mathbf{r}_{t},\mathbf{e}_{o,t}$	Subject, relation, and object embeddings at timestamp $t$ .
$\mathbf{E}_{t},\mathbf{R}_{t}$	Entity and relation embedding matrices at timestamp $t$ .
$\mathcal{G}^{D},\mathcal{G}^{I}$	Evolutionary dynamics and historical invariance graph.
$\mathbf{e}^{D},\mathbf{e}^{I}$	Entity embeddings of both graphs.

Table 1. Summary of Important Notations

Figure 2. Overall architecture of CID-TKG (a). The framework consists of spatio-temporal initialization, relation decomposition (c), a historical invariance graph encoder, and an evolutionary dynamics graph encoder with time-aware attention scores (b), followed by contrastive alignment for collaborative representation learning.

Dataset	Entities $\|E\|$	Relations $\|R\|$	Training Facts	Validation Facts	Testing Facts	Time granularity
ICEWS14s	6,869	230	74,845	8,514	7,371	24 hours
ICEWS18	23,033	256	373,018	45,995	49,545	24 hours
ICEWS05-15	10,094	251	368,868	46,302	46,159	24 hours
GDELT	7,691	240	1,734,399	238,765	305,241	15 mins

Table 2. Statistics of datasets

Type	Model	ICEWS14s				ICEWS18				ICEWS05-15				GDELT
Type	Model	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
$\clubsuit$	TLogic	43.04	33.56	48.27	61.23	29.82	20.54	33.95	48.53	46.97	36.21	53.13	67.43	–	–	–	–
	TR-Rules	43.32	33.96	48.55	61.17	30.41	21.10	34.58	48.92	47.64	37.06	53.80	67.57	–	–	–	–
	INFER	44.46	35.03	49.37	62.31	32.22	22.39	36.41	51.52	48.73	38.32	54.61	68.48	–	–	–	–
$\diamondsuit$	GenTKG	–	36.85	47.95	53.50	–	24.25	37.25	42.10	–	–	–	–	–	–	–	–
	LLM-DA	47.10	36.90	52.60	67.10	–	–	–	–	52.10	41.60	58.60	72.80	–	–	–	–

Table 3. Performance of TKG entity extrapolation on ICEWS14s, ICEWS18, ICEWS05-15 and GDELT. The time-filtered MRR, Hits@1, Hits@3, and Hits@10 metrics are multiplied by 100. The best results are marked in bold and the second results are underlined . We use

\clubsuit

\diamondsuit

, and

\spadesuit

to denote path-based, LLM-based, and embedding-based methods, respectively.

Variant	ICEWS14s			ICEWS18
Variant	MRR	Hits@1	Hits@10	MRR	Hits@1	Hits@10
CID-TKG	51.93	41.49	72.32	38.88	27.66	61.16
-w/o- $\mathcal{G}^{D}$	49.54	38.82	70.00	36.88	25.53	59.40
-w/o- $\mathcal{G}^{I}$	50.29	39.75	70.55	36.98	25.81	58.92
-w/o-(CoA & ReD)	50.96	40.44	71.10	38.42	27.15	60.80
-w/o-CoA	51.37	41.04	71.15	38.62	27.46	60.57

Table 4. Ablation results on ICEWS14s and ICEWS18.

Panel of Figure 3 — Figure 3. Effect of the upper bound $N$ on the evolutionary dynamics graph. Effect of the upper bound $N$ on the evolutionary dynamics graph.

Panel of Figure 4 — Figure 4. Effect of the contrastive alignment weight $\mu$ . Effect of the contrastive alignment weight $\mu$ .

Query	CID-TKG-w/ $\mathcal{G}^{D}$		CID-TKG-w/ $\mathcal{G}^{I}$		CID-TKG
Query	Hits@5 Entity	Score	Hits@5 Entity	Score	Hits@5 Entity	Score
$e_{s}:Head\_of$ $\_Government\_(India)$ $r:Praise\_or\_endorse$ $t:2014-12-01$	$Member\_of\_Parliament\_(India)$	5.1521	$Citizen\_(India)$	4.6465	$\bm{Employee\_(India)}$	9.5145
	$Governor\_(India)$	5.1514	$Company\_-\_Owner$ $\_or\_Operator\_(India)$	4.4339	$Member\_of$ $\_Parliament\_(India)$	9.1098
	$\bm{Employee\_(India)}$	5.1435	$Indigenous\_People\_(India)$	4.4003	$Governor\_(India)$	8.9817
	$Labor\_Union\_(India)$	4.4350	$\bm{Employee\_(India)}$	4.3710	$Citizen\_(India)$	8.7354
	$Administrative\_Body\_(India)$	4.3371	$Villager\_(India)$	4.2844	$Labor\_Union\_(India)$	7.9872

Table 5. Case study of CID-TKG’s entity extrapolation performance on the ICEWS14s dataset. The ground-truth entity is highlighted in bold, and the corresponding prediction scores are provided.

Panel of Figure 5 — Figure 5. Robustness analysis under Gaussian noise perturbations. Robustness analysis under Gaussian noise perturbations.

Panel of Figure 6 — Figure 6. Efficiency–performance trade-off comparisons. Efficiency–performance trade-off of different methods.

Variant	ICEWS14s			ICEWS18
Variant	MRR	Hits@1	Hits@10	MRR	Hits@1	Hits@10
TTransE	13.72	2.98	35.74	8.31	1.92	21.89
TA-DisMult	25.80	16.94	42.99	16.75	8.61	33.59
DE-simlE	33.36	24.85	49.82	19.30	11.53	34.80
TNTComplEX	34.05	24.85	49.82	21.23	13.28	36.91
ECEformer	34.84	25.60	52.67	26.01	16.67	44.33

Table 6. Additional Comparison with Temporal Modeling Baselines on ICEWS14s and ICEWS18.

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CHE-TKG: Collaborative Historical Evidence and Evolutionary Dynamics Learning for Temporal Knowledge Graph Reasoning

Shuai-long Lei, Xiaobin Zhu, Jiarui Liang, Guoxi Sun+2

University of Science and Technology Beijing

Temporal Link Prediction Dynamic Graph Learning Temporal KGs

Open paper AskPDF arXiv

Temporal knowledge graph (TKG) reasoning aims to predict future events from historical facts. A key challenge lies in jointly capturing two sources of predictive information in TKGs: historical evidence and evolutionary dynamics. However, existing methods typically focus on only one of these sources, which limits the ability to fully exploit the complementary predictive signals in TKGs. To address this, we propose CHE-TKG, a novel collaborative dual-view learning framework for TKG reasoning. CHE-TKG explicitly separates and jointly models historical evidence and evolutionary dynamics, aiming to learn and exploit their complementary predictive signals. Specifically, CHE-TKG constructs a historical evidence graph to capture long-term structural regularities and stable relational constraints, alongside an evolutionary dynamics graph to model temporal transitions and recent changes, with dedicated encoders for each view. We further employ relation decomposition and a contrastive alignment objective to better capture the predictive signals across the two views. Extensive experiments demonstrate that CHE-TKG achieves state-of-the-art performance on multiple benchmarks.

Abstract

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