TeDS: Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
Authors: Jiujiang Guo
Mankun Zhao
Wenbin Zhang
Tianyi Xu
Linying Xu
Yu Jian
Yu Mei
Yu Ruiguo
Venue: ICML 2025 poster (2025)
Keywords: Knowledge graph; Knowledge graph completion
Primary area: general_machine_learning->representation_learning
TL;DR: The paper simulates and summarizes dual perspectives of temporalized facts and designs distinct temporal perceptions based on quaternions to enhance TKGC.

Abstract: Existing research on temporal knowledge graph completion treats temporal information as supplementary, without simulating various features of facts from a temporal perspective. This work summarizes features of temporalized facts from both diachronic and synchronic perspectives: (1) Diachronicity. Facts often exhibit varying characteristics and trends across different temporal domains; (2) Synchronicity. In specific temporal contexts, various relations between entities influence each other, generating latent semantics. To track above issues, we design a quaternion-based model, TeDS, which divides timestamps into diachronic and synchronic timestamps to support dual temporal perception: (a) Two composite quaternions fusing time and relation information are generated by reorganizing synchronic timestamp and relation quaternions, and Hamilton operator achieves their interaction. (b) Each time point is sequentially mapped to an angle and converted to scalar component of a quaternion using trigonometric functions to build diachronic timestamps. We then rotate relation by using Hamilton operator between it and diachronic timestamp. In this way, TeDS achieves deep integration of relations and time while accommodating different perspectives. Empirically, TeDS significantly outperforms SOTA models on six benchmarks.

TeDS: Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
Jiujiang Guo 123 Mankun Zhao 123
Wenbin Zhang 123 Tianyi Xu 123 Linying Xu Jian Yu 123 Mei Yu 123
Ruiguo Yu 123
Abstract
1. Introduction
Knowledge graphs (KGs) technology that expresses knowledge in structured form, which is generally clas- sified into static knowledge graphs (SKGs) and temporal knowledge graphs (TKGs). SKGs and TKGs store facts as triples and quadruples. Existing KGs (e.g., ICEWS (Laut- enschlager al., 2015), NELL, and OpenIE) contain a vast amount of information, and many have been successfully applied in various domains, including community detection (Li et al., 2024), failure KGs for offshore wind power (Ding et al., 2025), and industry-oriented KGs.
Existing research on temporal knowledge graph completion treats temporal information as sup- plementary, without simulating various features of facts from temporal perspective. This work summarizes features of temporalized facts from both diachronic and synchronic perspectives: (I) Diachronicity. Facts often exhibit varying char- acteristics and trends across different temporal domains; (2) Synchronicity. In specific tempo- ral contexts, various relations between entities influence each other, generating latent semantics. To track above issues, we design quaternion- based model, TeDS, which divides timestamps into diachronic and synchronic timestamps to sup- port dual temporal perception: (a) Two composite quaternions fusing time and relation information are generated by reorganizing synchronic times- tamp and relation quaternions, and Hamilton op- erator achieves their interaction. (b) Each time point is sequentially mapped an angle and con- verted to scalar component of quaternion using trigonometric functions to build diachronic times- tamps. We then rotate relation by using Hamilton operator between it and diachronic timestamp. In this way, TeDS achieves deep integration of re- lations and time while accommodating different perspectives. Empirically, TeDS significantly out- performs SOTA models on six benchmarks.
With exponential growth of data, KGs consistently en- counter issues such as incompleteness, sparsity, and im- balance. To provide sustainable solutions, researchers focus extensively on knowledge graph completion (KGC), devel- oping a variety of robust models. However, most models focus SKGs, with less attention to TKGs with temporal information (Guo et al., 2024). Unlike SKGs, TKGs align more closely with real-world scenarios due to inclusion of time dimension, making completion process significantly more challenging. Existing temporal knowledge graph com- pletion (TKGC) research regards temporal information as supplementary, failing observe various features and tra- jectories that facts can present from a temporal perspective. To uncover characteristics of facts from temporal perspec- tive, we summarize features of temporalized facts from both diachronic and synchronic perspectives: (a) Diachronicity. Facts often exhibit varying characteristics and developmen- tal trends across different temporal domains. For example, as shown in Figure in March, James is friends with Emma and Sophia. By May and June, James starts dating Emma, and their relation progresses smoothly into a romantic one by July. Meanwhile, James remains ordinary friends with Sophia. (b) Synchronicity. In specific temporal contexts, various relations between entities often influence each other, thereby generating latent semantics. For example, as shown in Figure 1, in May and June, relation between Emma and James noticeably becomes closer, showing signs of ambigu- ity. Meanwhile, during this period, Jumes and Sophia only have one call, remaining ordinary friends. The above per- spectives are not entirely independent, they often mutually
"Equal contribution 'College Intelligence and Computing, Tianjin University, Tianjin 300354, China Tiinjin Key Labora- tory of Advanced Networking, Tianjin University, Tianjin 300354, China 'Tianjin Key Laboratory of Cognitive Computing and Appli- cation, Tianjin University, Tianjin 300354, China. Correspondence to: Ruiguo Yu <rgyu@rju.cdo .dd...
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 20255 by the author(s).

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
depend on and serve as foundations for each other. Thus, designing a unified framework simultaneously consider both diachronicity and synchronicity is an interesting work.
We empirically demonstrate that TeDS achieves signifi- cant improvements over the existing SOTA different datasets. Furthermore, TeDS underwent detailed strict constraint experiments and withstood the tests.
2. Related Work
Enmo
friced
2.1. SKGC models
James
We categorize SKGC models into five families. Transla- tion Family. TransE interprets relations as a translation between head and tail entity to achieve its modeling objec- tives. Subsequent works in this line, such as TransD (Ji et al., 2015) and TransR. Complex Family. Learning KGs in complex space has gained attention. ComplEx (Trouillon et al., 2016) and RotatE (Sun et al., 2019) extend Euclidean space into complex space. Besides, QuatE (Zhang et al., 2019) and DualE (Cao et al., 2021) treat relation as a rota- tion in quaternion space and dual quaternion space. Tensor Family. Tensor decomposition and its properties are effec- tive at deconstructing and capturing logical rules and latent semantics. RESCAL (Nickel et al., 201 1) incorporates a bilinear multiplication between embeddings for both head and tail entity, along with a full-rank matrix unique to each relation. TuckER (Balazevic et al., 2019), based on Tucker decomposition, factorizes fact into a core tensor and three member matrices in which each row is embedding of cor- responding entity or relation. Recently, BDRI (Yu et al., 2023a) leverages BTD structure and inverse patterns to en- hance forward-invert relation interactions. Compound Family. Current research integrates advantages of different geometric spaces into unified framework to get synergistic gains. CompoundF: (Ge et al., 2023) combines compound transformations to align design variants with rich relation patterns. Deep learning Family. Some models using neural networks to accomplish SKGC task gets remarkable results. For example, EIGAT (Zhao et al., 2022), HyperGatE (Pang et al., 2025), and RGAI (Shang et al., 2024a). Recently, integrating logical rules and geometric information to im- prove deep learning model interpretability has become a research focus. MGTCA (Shang et al., 2024b) integrates mixed geometry information into a trainable convolutional attention network enhance KGC.
Saphin
getasgehhr
%
memrie
meliise
T
ovarrel
relotios
Figure 1. A brief illustration reflecting diachronic and synchronic facts.
The primary purpose of our work is to introduce a novel quaternion-based model TeDS. Specifically, TeDS divides timestamp into diachronic timestamp and synchronic times- tamp to design dual temporal perception channels for track- ing synchromicity and diachronicity, as follows: (a) Syn- chronic perception. We reorganize synchronic timestamp and relation quaternions to construct two composite quater- nions that effectively blend time and relation information. We then use Hamilton operator achieve their interaction, further achieving interaction between relations and time. (b) Diachronic perception. We iterate through all timestamps, sequentially mapping each time point to an angle and con- verting it to the scalar component of a quaternion using trigonometric functions, thereby constructing diachronic timestamps to interpret timestamps continuously. We then rotate the relation using Hamilton operator between it and the diachronic timestamp, enabling the relation earry di- achronic information. In this way. TeDS can achieve deep integration of relations and time while accommodating dif- ferent temporal perspectives.
2.2. TKGC models
We divide TKGC models into five families. Translation Family. TTranSE (Jiang et al., 2016) extends TransE by incorporating timestamp, where timestamp is represented as translation operation. Several works have been pro- posed along this line. For instance, HYTE (Dasgupta et al., 2018) extends TransH by representing timestamps as a learned hyperplane. Complex Family. TComplEx (Lacroix et al., 2020), TPComplEx (Yang et al., 2024), and Joint- MTComplEE (Zhang et al., 2024b) model facts in complex
We observe the regularities of facts within tempo- ral context and summarizes two important temporal perspectives: synchronicity and diachronicity.
We utilize the representation capability of quaternions to design dual perception channels and integrate them into a unified framework to address the different per- spective features of various temporalized facts.
2

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Complction
space, Next, RotateQVS (Chen et al., 2022) and MTE (Yu et al., 2025) respectively represent temporal fact information as quaternion. Tensor Family. TASTER (Wang al., 2023) leams global and local information through sparse transfer matrices to adapt to TKGs of different scales. TeI.M (Xu et al., 2021) uses multivectors to perform 4th-order tensor factorization in TKGs. TBDRI (Yu et al., 2023b), BTDG (Lai et al., 2022), and CEC-BD (Yue et al., 2024), based on BTD, utilize different ways to represent facts, respectively. Recently, MvTuckER (Wang et al., 2024) learns multi-view representations using Tucker decomposition, transforming them into an ruth-order binary tensor. Mathematical rules Family. CDRGN-SDE (Zhang et al., 2024a) leverages the characteristics of stochastic differential equation, integrating time and dimensional data segment by segment. Deep learn- ing Family. Some works introduce neural networks into TKGC. For example, TeMP-SA (Wu et al., 2020), xERTE (Han et al., 2021), ODETKGE GF (Huang et al., 2024), DLGR (Xiao et al., 2024), SANe (Li et al., 2024), MDRQS (Zhu et al., 2025), Neo-TKGC (Qiu et al., 2025), and GLARGCN (Wang et al., 2025). A drawback of above models is that their geometric meaning is unclear.
Hamilton operator does not satisfy the commutative rule, which means that Q1 @ Q2 * Q2 @ Q1- In addition to commutative rule, the associative and distributive rules hold within quaternions. The product of Q1 = dn + +ri+ + fii Il k and Q2 = 02 + e2i + /2j + g2k is as follows:
Q1 & Q2 (a102 61 f1f2 9192)
+ (aje2 + fige 91
(2)
+ (a1f2 1192 + f102 + 91e2]
+ (a192 + e1 - fi + 9102) k.
4. TeDS for TKGC
Here, we formally introduce TeDS, which embeds TKGs in quaternion space and scores a quadruple using the Hamil- ton operator to enhance knowledge representation. Specif- ically, TeDS utilizes dual temporal perception channels as follows: (a) Synchronic perception. We reorganize syn- chronic timestamp and relation quaternions to construct two composite quaternions. We then use Hamilton operator to achieve their deep interaction.
(b) Diachronic perception. We iterate through all timestamps, sequentially mapping each time point to an angle and converting it to the scalar component of a quaternion using trigonometric functions, thus constructing diachronic timestamps for continuous in- terpretation. We then rotate the relation using Hamilton operator between it and diachronic timestamp.
3. Preliminaries
This section formally describes TKGC problem and the
relevant theoretical concepts employed in our work.
Symbol description. Suppose that G consists of N entities, M relations, and T timestamps. We use the quaternion ma- trix Q E HN to denote all entity embeddings, R E Hx to denote all relation embeddings, W E HI Txk to denote all timestamp embeddings, where each row is an embed- ding vector for specific entity of dimensionality k. Given quadruple (,, O,),, head entity relation r, and tail entity correspond to Q. = { a, + e,i + saj + g.k: ae, fs, 9o E & }. R2 = { a, + e + f.j + g,k Or, Gr. fr. Ir E IR* }. and Q. = a. + + fai + g.k Oos co: Jor 9o E R ). respectively. Timestamp T is divided into diachronic timestamp dr and synchronic timestamp ST, corresponding War and W.r, respectively.
3.1. Problem Definition
Temporal knowledge graph 9 is composed of quadruples consisting of entities, relations, and timestamps. We formu- late denote& E as the set of all entities, R as set of all relations, and T as set of all timestamps. quadruple is represented as (s, r, o, r) C CEx x R x & x T, where s E & and o E E denote head and tail entity respectively, r E R denotes the T denotes timestamp. We use II and II = E x R x & x T - II to represent the set of observed quadruples and the set of unobserved quadru- ples, respectively. Timestamp 7 has multiple cases, such as time period [n,, Te]. missing beginning time period| [-, Te], missing ending time period [T,, -] and time point T.
relation between them, and
Implementation details. TeDS mainly consists of two mod- ules, the overall architecture is as depicted in Figure 2. Synchronic perception (SP). Firstly, to achieve thorough integration of temporal and relational information, SP per- forms a composite reorganization of synchronic timestamp quaternion W.r = ast + c,rl + farj + gsrk and rela- tion quaternion R, This results in the creation of two quaternions: Qrt.p a, + e,i f.j + ger k and Qrapr Oer + Esr + fer + g, where aer: eer, for, Per E R This process is visualized in Figure 2(a) and (b). Secondly, we normalize Q to the unit quaternion QA by dividing Quar by its norm to eliminate scaling effects:
3.2. Quaternion Background
Quaternion (Hamilton, 1844) typically expressed as Q =
a + ei + fj + gk, where a, e, f.g g are real numbers, i.j. k are imaginary units that satisfy Hamilton rule.
Conjugate: The conjugate of Q is Q) a aa-el -iei--ii ei- fj- gk.
Norm: The norm of Q is [Q] / +o
Inner product: The inner product of Q1 = 01 +ei++
k and Q2 = 02 + ezi + f2i + g2k is obtained by adding the inner product of the corresponding vector component:
Qrip"
ast + E + s + g.k
Q
(3)
Q Q2- = 02) + (e1, + (2) + (9)-92)- (1)
1Q 1Qrpp]
+ 6 + f2 + 97
3

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
by doing Hamilton operator between it and R
(
(N)
[cl
Qup = Qs R
(8)
4.1. Scoring function and Loss function
S 0.4
Ome
W
Scoring function. As shown in Figure 2(f), we summarize the scoring function of TeDS as follows:
(s,,T,0,T) = (Qap + Qáp)
(9)
(d)
(e)
(
where is inner product. For the various forms of times- tamps, TeDS handles the details as follows: For facts with complete timestamp information (s, r, o, [7o, Te], TeDS splits quadruple into two instances: (s, r, O, Tb) and (8, r, o. Te). The score is computed as the average of the two:
(ps,, r, o, [To, re]) ( (,,,,, n.) + t(,, (10)
Figure 2. Illustrations of TeDS. The blue dashed arrows indicate the process flow of synchronic perceptron; The green dashed ar- rows indicate the process flow of diachronic perceptron.
For facts with missing timestamp information, i.e., either (s. r, o, [To -D) or (s, o, --yTe).. the score is taken directly from known timestamp:
Thirdly, as shown in Figure 2(c), TeDS utilizes Hamilton operator to perform rotation operations on Qrt.p via QA, Tope obtaining the representation of synchronic relations:
(s,, o, (To, -1) (s,,r,,, mo), o(,,r,o,l-,ta, = 0,
(11)
M = Qrt., & Q
(4)
Optimization. TKGs be regarded as fourth-order ten- sors, we use tensor kernel norm regularization to enhance TeDS. Thus, we propose following regularization:
where & is Hamilton operator. Meanwhile, we normalize Ml to the unit quaternion A Then, as shown in Fig- ure 2(f), we rotate the head entity Qs by doing Hamilton operator between and... Ar:
Ln = 1
+ ||, + || + I|Q.111:
(12)
where - denotes nuclear 4-norm. Furthermore, for time constraints, temporal regularizer are commonly used to smooth the representation of adjacent timestamps. Thus, we use the following linear temporal regularizer:
Q.p Q. MA
(5)
Diachronic perception (DP). Firstly, as shown in Figure 2(d), iterate through all timestamps, sequentially map- ping each time point to angle and converting it to scalar component of a quaternion using continuous trigonometric functions, thereby constructing diachronic timestamps:
N
LB W -W,,,-W,---- ww, wlll
(13)
where W6 is linear time-constrained bias, initialized ran- domly and can be learned during training. The linear time constraint can ensure that timestamps of adjacent times are close to each other, and timestamps of distant times are sig- nificantly different, ensuring the smoothness of time. And deviation term denotes sudden change of adjacent times. Loss function. Following (Trouillon et al., 2016), we regard TKGC as multi caassficaasi task, use the cross-entropy loss function:
π T + sin
π T )e'i
Wd.. = cos(
2T
2T
π TT
π Jn
+ sin(
)f'j + sin
)g'k.
2T
2T
where (e', fl, 9') represents the unit vector of the rotation axis, e', fl. g' E R²: Tn E f1,.... T} denotes time point. The benefits of above operation are twofold: 1) TeDS can interpret timestamps continuously, "smoothly" capturing time shifts rather than treating each timestamp as discrete. 2) Trigonometric functions provide smooth encoding, enabling TeDS effectively generalize between frequent and sparse events. Secondly, shown in Figure 2(e), use Hamilton operator with the diachronic timestamp War,, to rotate the relation quaternion R, into the diachronic relation Ryy.:
(-log exp(pls,
L=
Σ
Even' eap (p(8', (,0,T)
log exp (p(s,,,,,,1)
Even exp (p(8,
+ Sa + Xo
(14)
RTT, Wdr, & R,-
where II' is sampled from the set of unobserved quadruples II A is the regularization weight and \ is the temporal regularization weight.
Thirdly, we normalize R,,, to the unit quaternion R Then, as shown in Figure 2(f), we rotate the head entity Q.

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
5. Experiments and Results
5.3. Evaluation Protocol and Baselines
5.1. Datasets
We made the following preparations to evaluate TeDS: Adopting commonly metrics to evaluate models more accurately. Mean reciprocal rank (MRR) calculates the average score of the reciprocal ranks of the relevant KGs for a given query, where a higher MRR means better per- formance. Hit@n n represents the percentage of the top n, where n E {1, 10}, where a higher @it@n n indicates bet- ter performance. 2) Selecting series of state-of-the-art (SOTA) baeslines. We adopt TTransF: (2016), Tu-D (2018), TeMP -SA (2020), CyGNet (2021), RE-GCN (2019), TNTComplEx (2020), ChronoR (2021), TeLM (2021), Ro- tateQVS (2022). BTDG (2022), TBDRI (2023), CEC-BD (2024), TPComplEx (2024), Joint-MTCCopllEx (2024), CDRGN-SDE (2024), MvTuckER (2024). DLGR (2024), ODETKGE (2024), SANe (2024), MTE (2025), MDRQS (2025), Neo-TKGC (2025), and GLARGCN (2025).
We select six common TKGC benchmarks, detailed in Ta-
ble 1. ICEWS14, ICEWS05-15 and ICEWS18 are sub- sets of Integrated Crisis Early Warning System (ICEWS). ICEWS acquires and processes millions of data from vari- ous sources to aid in monitoring and responding to global events (e.g.. (Japan, Accuse, Korea, 2014-3-3)). ICEWS14, ICEWS05-15 and ICEWS18 separately collect events from 2014-1-1 to 2014-12-31, 2005-1-/ to 2015-12-31, and 2018- 1-1 to 2018- 12-31. YAGO1Ik and Wikidata12K (Dasgupta et al., 2018) are subsets of YAGO3 and Wikidata, respec- tively. YAGO3 (Mahdisoltani al., 2015) and Wikidata (Erxleben et al., 2014) are two TKGs where time anno- tations are represented in various forms, i.e., time points like (Allan, BornIn, Launceston, [2005-1-3, 2005-1333)) be- ginning or end time like (Biden, Presidency, POTUS, # # # #D), and time intervals like (Var- ick, Mayor, New York, [789-3-2, 801-3-2)). GDELT (Global Database of Events, Language, and Tone) (Trivedi et al., 2017) is global event database that offers substantial col- lection of worldwide facts from 2015-4-1 to 2016-3-31. It encompasses various events, primarily focusing on political, social, economic, and environmental occurrences.
(202/-1-2, # #
5.4. Main Results
Table 2 and 3 list results of TeDS and all baseline models on all datasets, where the optimal performance is bolded. Over- all, TeDS outperforms all baseline models across datasets. Compared with CEC-BD (tensor family), TeDS increases by 27.4 MRR points on ICEWS14, 19.0 MRR points on ICEWS05-155 17.3 MRR points on ICEWS18 88, 56.1 MRR points on YAGOI Ik, 52.2 MRR points on Wikidatal2K, and 41.9 MRR points on GDELT. Compared with TPComplEx (complex family), TeDS increases by 0.9 MRR points on ICEWS14; 2.8 MRR points on ICEWS05-15; 30.8 MRR points GDELT. Compared with SANe (deep learning family), TeDS increases by 26.9 MRR points on ICEWS14, 19.0 MRR points on ICEWS05-15, 52.3 MRR points on YAGO1IK, 52.2 MRR points on Wikidata12k.
5.2. Experimental Setup
We implement TeDS by running PyTorch. We adopt the Adagrad optimizer to train TeDS. The batch size is fixed as 1000. The regularization weights aa and A are tuned in a range of (0. ..., 0.0025, 0.005, 0.0075, 0.01, 0.1). We find the following combinations of regularization weights A, and Às to give the best results: (0.0075, 0.01) for ICEWS14: 14; (0.0025, 0)1) for ICEWS05-15; (0.1, 0.01) for ICEWS18: (0.025, 0.001) for YAGOI 1k; (0.025, 0.0025) for Wiki- data12k; (0.0000 (0.00001, 0.01) for GDELT. The optimal embed- ding dimension is k- = 100 in all benchmarks.
ICEWS14, ICEWS18 and ICEWS05-15 all belong to ICEWS and thus share similar data types. Compared to its performance ICEWS14,, TeDS shows stronger per- formance on ICEWS05-15 and ICEWS18. Compared to ICEWS14, ICEWS05-15 covers over 10 times the time span, making its data more reliant on temporal information. This supports TeDS's capability to manage long time series. Given the significant improvement of TeDS on ICEWS18 compared ICEWS14 and ICEWS05-15, we visualize dis- tribution of facts over time in ICEWS18 and ICEWS, as shown in Figure 3. We find that, at same temporal density, the number of facts in ICEWS18 is approximately 10 times that of ICEWS05-15. This significantly increases the infor- mation within the same temporal context, making TKGC more difficult. TeDS addresses this with SP, achieving top performance. Besides, compared to ICEWS, we find that TeDS demonstrates the greatest advantage over SOTA mod- els on YAGOIIK Ik and Wikidata 1 12k. To further explore the performance ad advantages of TeDS, we visualize distribution
Table 1. Statistics for the various experimental datasets.
ICEWS14
ICEWS05-15
ICEWS18
Entities
6,869
10,488
23,033
Relations
230
251
256
Facts
90,730
461,329
468,558
Pcriod(ycar)
2014
2005-2015
2018
YAGO1Ik
Wikidata12k
GDELT
Entities
10,623
12,544
500
Relations
10
24
Facts
20,507
40,621
3,419,607
Period(year)
1513-2017
1526-2020
2015-2016
5

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
Table Experimental results ICEWS14, ICEWS05-15, and ICEWS18. All results taken from the original papers. Dashes: results are not reported in the responding literature. The best results among all models are written bold.
ICEWS14
ICEWSOS-15 H@!
ICEWS18
MRR
H@!
H@@3
H@@ 10
MRR
H@@
H@@ 10
MRR
H@!
H@@
H@ 10
TTransE
25.5
7.4
60.1
27.1
8.4
61.6
TNTComplEx
60.7
51.9
65.9
77.2
66.6
58.3
71.8
81.7
TeMP-SA
60.7
48.4
68.4
84.0
68.0
55.3
76.9
91.3
TeLM
62.5
54.5
67.3
77.4
59.9
72.8
82.3
RE-NET
35.8
26.0
40.1
54.9
36.9
26.2
41.9
57.6
26.2
16.4
29.9
44.4
RE-GON
62.5
54.5
67.3
77.4
67.8
59.9
72.8
82.3
27.5
17.8
31.2
46.6
RotateQVS
59.1
50.7
64.2
75,4
63.3
52,9
70.9
81.3
TBDRI
65.2
55.2
69.7
78.5
70.9
64.6
75.7
82.1
BTDG
60.1
51.6
65.6
75.3
62.7
53.4
68.7
79.8
TPComplEx
89.8
86.5
92.5
95.4
84.5
79.4
88.2
93.4
ODETKGE
31.1
18.4
30.2
48.2
44.0
35.4
49.4
65,8
31,5
21.0
34.3
49.3
MvTuckER
65.4
57.7
69.9
79.7
69.8
61.8
74.7
84.1
DLGR
36.6
51.6
35.4
40.0
CDRGN-SDE
49.2
36.5
48.4
66.9
52.3
39.8
62.5
75.4
Doint-MTComplEx
63.6
55.6
68.1
78.1
68.3
60.1
73.6
83.2
CEC-BD
63.3
55.4
68.0
77.7
68.1
60.2
73.0
82.5
28.5
18.8
32.3
47.7
SANe
63.8
55.8
68.8
78.2
68.3
60.5
73.4
82.3
MTE
77.5
86.8
80.3
71.2
85.4
93.2
MDRQS
62.5
54.4
67.3
77.5
67.0
59.1
71.6
81.5
Neo-TKGC
64.2
53.7
70.9
83.6
72.2
61.7
79.4
90.8
GLARGCN
67.6
62.1
71.0
77.6
77.5
72.7
80.8
85.9
TeDS (ours)
90.7
90.6
90.8
91.0
87.3
85.8
88.3
90.4
45.8
45.6
46.9
48.2
Table Experimental results YAGO1Ik and Wikidatal2k. All results taken from the original papers. Dashes: results are reported in the responding literature. The best results among all models are written bold.
YAGO1
Wikidata
GDELT
MRR
H@!
H@3
H@ 10
MRR
H@
H@3
H@ 10
MRR
H@
H@3
H@ 10
TTransE
10.8
2.0
15.0
25.1
17.2
9.6
18.4
32.9
11.5
0.0
16.0
31.8
HyTE
13.6
3.3
29.8
25.3
14.7
48.3
11.8
0.0
16.5
32.6
TA-DistMult
15.5
9.8
26.7
23.0
13.0
46.1
20.6
12.4
21.9
36.5
TComplEx
18.5
12.7
18.3
30.7
33.1
23.3
35.7
53.9
29.8
21.3
32.3
46.4
TeLM
12.9
19.4
32.1
36.0
54.2
RotateQVS
18.9
12.4
19.9
32.3
27.0
17.5
29.3
45.8
CEC-BD
21.2
15.4
21.5
33,9
33,9
24.1
36.9
54.3
29.6
20.1
33.4
46.5
TPComplEx
40.7
32.9
43.1
55,9
CDRGN-SDE
22.0
12,4
20.9
34.5
MvTuckF.R
54.9
47.7
58.5
68.2
Joint-MTComplFx
22.2
15.8
22.9
35.6
36.0
27.0
39.3
54.1
SANe
25.0
18.0
26.6
40.1
43.2
33.1
48.3
64.0
30.1
21.2
32.6
47.6
MTE
39.1
32.2
40.9
52.2
MDRQS
27.1
19.9
29.6
40.4
42.4
35.0
56.3
Nco-TKGC
33.7
27.0
37.0
51.3
GLARGCN
37.3
33.8
38.5
42.3
57.1
48.4
61.3
73.0
TeDS (ours)
77.3
76.9
78.1
78.4
95.4
95.5
95.7
95.8
71.5
69.9
72.2
74.4
of facts in Wikidatal over time, shown in Figure 3. We find that facts in Wikidata12 12k span a long temporal range and exhibit pronounced long-tail distribution over time, which limits the performance of existing models. TeDS leverages the smooth embeddings provided by DP to effec- tively handle both short and long temporal spans, enabling
it to capture diverse temporal patterns and achieve perfor- mance improvements. For detailed analysis, please refer to ANALYSIS.
6

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
exhibits a slight advantage in classifying Consult across months, which may be attributed the assistance of tempo- ral embedding regularization. The above experiments and analysis further demonstrate that TeDS is better at modeling the diachronicity of facts.
10
-10
Figure 3. The distribution of facts over time in Wikidatal2k GDELT and ICEWS.
-10
SP
HTM
6. ANALYSIS
We perform ablation experiments on three benchmarks to understand how each perceptron in TeDS handles different types of facts and their benefits. Specifically, we remove the SP in TeDS, reducing DP. Next, we remove the DP, reducing TeDS SP. Besides, degrade SP into regular quaternion model named HTM, meaning that the mixing of relations and time is no longer performed.
TcDS
TeLM
Benjamin Netanyahu, 2014-32.As)
( BBrack Obamu, Consult,
Jun Feb
Mar
July
Sep
6.1. Ablation study on SP and DP
Table 4 lists specific results of SP and DP ICEWS14, Wikidata128 2k, and YAGO11k. 1k. SP and DP achieve competi- tive results compared to SOTA models across all datasets. To further explore mechanisms of different perceptrons, we first observe the distribution of same relation between enti- ties over a long time span, which helps to understand DP's performance. Thus, we extract relation Consult between Barack Obama and Benjamin Netanyahu during 2014 (i.c., (Barack Obama, Consult, Benjamin Netanyalu, 2014-*. *_ *)) and visualize the parameters of temporal relation, as shown in Figure 4. Compared to SP and HTM, TeDS enables aggre- gation Consult within each specific month while ensuring that Consult from adjacent months remains close together rather than being randomly distributed. Compared SP and HTM, TeDS is better at aggregating Consult within same month. Besides, TeDS ensures that Consult from adjacent months is kept close together rather than being randomly distributed. More specifically, compared to HTM, SP is better at aggregating Consult within same month. Unlike TeDS, SP is unable tightly group Consult from adjacent months, although it can distinguish Consult from different months to some extent. Meanwhile, compared existing baseline model MeLM, TeDS is able to aggregate data from different months as much as possible while retaining the ability to classify Consult relations across months, thereby clearly delineating the boundaries between adjacent months. is undeniable that, compared to SP and HTM, TeL.M
Figure 4. Visualizations of temporal relation embeddings learned from different months ICEWS14, where different colored dots represent the Consult in different months.
Next, we observe distribution of various relations between entities within specific temporal context to better under- stand SP's performance. Thus, we extract various relations between Barack Obama and Benjamin Netanyahu from 2014-1 to 20/4-6 and visualize the parameters of tempo- ral relation, as shown in Figure Compared to HTM and TeLM, TeDS and SP are better at distinguishing different relations. Moreover, we find that TeDS outperforms SP in distinguishing identical relations, rather than clustering them entirely together: In fact, even within the same month, identical relations can exhibit varied trends depending on the context. Thus, we believe it is crucial to cluster differ- ent relations while preserving the unique characteristics of identical relations in specific contexts.
We find that SP outperforms DP across various datasets. To explain this phenomenon, visualize relation educated at among all entities using Wikidatal 2k. As shown in Figure 6, most facts are concentrated within a specific temporal context (1850 to 2000). Clearly, this aligns with the argu- ment that SP is better at capturing the synchronicity of facts.

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
Table 4. Experimental results of ablation study. The hest results among all models are written bold.
ICEWS14
Wikidata 2k
YAGOI
MRR
H@1 1
H@3
H@ 10
MRR
H@@
H@@
H@
10
MRR
H@@
I@@3
H@ 10
HTM
56.4
47.8
58.3
67.5
30.2
21.4
33.0
44.7
28.8
17.8
30.1
44.3
79.6
76.8
80.3
83.7
67.9
59.9
72.6
83.6
48.0
38.8
53.7
64.8
DP
71.1
68.4
72.1
74.6
62.8
55.3
64.6
76.3
40.1
31.5
43.6
53.5
TeDS
90.7
90.6
90.8
91.0
95.4
95.5
95.7
95.8
77.3
76.9
78.1
78.4
Burack Obuma,"* **,, Benjamin Netanyahu, [2014-01-*5,
(i0anyah,(2044-00--., 2014-06--11)
3050
3000
-10
1000
TeDS
10
Encity
10
10+
-10
Figure 6. The visualization of the relation educated between entities comes from Wikidata12K 2k, where vertical axis represents time, the horizontal axis represents entity, and the length of green rectangles indicates the duration of relation.
SP Uegaii segutiatien
TeLM
Connatt Makea
codomee Desoaed riil Make appeeal requot
Expronsteover casperate
Figure Visualizations of the temporal relation embeddings learned within specific temporal contexts from ICEWS14, where different colored dots represent different relations.
WIS HOP STOOS WITH
HSP HUP STISS GITM
wSP Tals #RTM
6.2. Strong constraints analysis of quadruples
We extract constrained quadruples from ICEWS14 and ICEWS05-15 to simulate synchronic and diachronic sce- narios, as shown in Figure 7. Due to strong constraints of quadruples, we conduct tests using a validation set. For syn- chronicity testing, we select facts involving Barack Obama, Angela Merkel, and Russia from ICEWS14 between 2014- 01-01 and 2014-01-15. Empirically, TeDS gets most sig- nificant results. Moreover, SP consistently outperforms DP and HTM, further validating that SP excels in handling syn- chronic scenarios. For diachronicity testing, we select facts involving Barack Obama, Angela Merkel, Iran, Benjamin, and Japan from ICEWS14 and ICEWS05-15 across all time spans. Empirically, TeDS gets most significant performance. Besides, DP consistently outperforms SP and HTM, further validating that DP excels in handling diachronic scenarios. Finally, SP and DP consistently outperform HTM, indicat- ing that SP and DP have a positive impact on both diachronic and synchronic scenarios. This aligns with our motivation: the two perspectives are not entirely independent but often mutually depend on and serve foundations for each other.
10hemm Tree, 3066/11
Iitarss pabtin 201an0))
Figure 7. Evaluation results on different quadruples in test set.
Where [2014-1-1, 20114-11,0 represents the years 2014-1-1 2014-1-15; [2014-*.*] stands for the entire year of 2014; *0055 2015-*_9) represents the years 2005 2015; other * represents the rest elements of quadruples in test set that satisfy current constraints.
6.3. Analysis of the robustness and portability of TeDS
We randomly remove 10% and 20% of training of ICEWS14 (named ICEWS14 10%SPARSE and ICEWS14 20%SPARSE) to assess robustness of TeDS under sparse data conditions, as shown in Figure 8(a) and (b). Empiri- cally, TeDS remains highly competitive compared to HTM on ICEWS14 10% SPARSE and ICEWS14 20% SPARSE, which validates robustness of TeDS. To assess the porta-
8

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
bility of TeDS framework, we apply its overall concept to complex embeddings and refer to this extension as CDS. Furthermore, we simplify CDS into standard complex- valued model named CTM. Besides, we extend the overall concept of TeDS to dual quaternion space, resulting in a variant named DTeDS. The specific results are shown in Figure 8(c) and (d). Experimental results show that TeDS, CDS, and DTeDS outperform HTM and CTM in terms of performance, validating the applicability of our framework. Meanwhile, quaternion model surpasses complex model further confirming superiority of Hamilton operator over Hermitian operator. Finally, DTeDS achieves a slight perfor- mance improvement, which we attribute to dual quaternion's 's greater sensitivity to multi-relational patterns and its richer representational capacity. This will also be a key focus of our future research. The above experiments and analysis further support the portability of TeDS framework.
MRRH
TelM
ESPR
TeDS
Figure 9. Results of TeDS with different embedding dimensions on ICEWS14.
6.5. Training Time and Standard Deviation
We use NVIDIA GeForce RTX 3090 to reproduce the train- ing time for the optimal performance of TComplEx, TeLM, CDS and TeDS on YAGO1 The specific results are shown in Figure 10(a). Specifically, compared to the SOTA deep learning model (SANe, which takes about 16 hours on YAGO1Ik), our computation is efficient and control- lable. Finally, Figure 10(b) shows the standard deviations for the MRR computed over runs of TeDS on all datasets, demonstrating the stability of TeDS results.
.ToDS
SPARSE
ICEWSH4
BCTM ECDS
WTiDS aDIIDS
=CTM #CDS &HTM TTas DTvDS
.TeM TCorplts
#CB
TcDS
+ICEWSLE
+ICEWS0S IS IIEWSIS
190
123
2000
B491
WIRIBATAIKK
(b)
BENIATIO
ICEWS85-15
(c)
(d)
Figure 10. Efficiency and stability evaluation of TeDS.
Figure& 8, Analysis of the robustness and portability of TeDS
7. Conclusion
This work examines how facts behave over time, highlight- ing two perspectives: synchronicity and diachronicity. We then use quatemnio representation to design two percep- tions, integrating them into a unified framework to handle different temporal perspectives. Visualization techniques are employed to test and confirm TeDS's effectiveness in various temporal scenarios. Overall, the analysis and sum- marization of complex real-world patterns, including the periodicity of facts, remain challenging research problems. In the future, we will continue to focus on various complex scenarios involving temporal facts, such as periodic patterns and complex forms of temporal expressions, and aim to develop more interpretable and context-adaptive models to achieve higher-quality knowledge representations.
6.4. Influence of embedding dimensionality
Figure 9 illustrates MRR performance of TeLM, EHPR, and TeDS on the ICEWS14 dataset across different embedding dimensions k: = {20, 50, 75, 100, 200, 500, 1000, 2000). Compared to TeLM and EHPR, TeDS consistently achieves significantly better performance at all embedding dimen- sions and reaches its optimal performance at l = 100. In contrast, TeLM and EHPR require higher embedding di- mensions to attain their best results. This demonstrates that TeDS not only maintains high accuracy with greater parame- ter efficiency but also offers more substantial computational advantages as the scale of KGs increases.

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
Acknowledgements
8796, pp. 50-65. Springer, 2014. URL https: /doi. org/10 / (tt////.100//77-331111 9- 119-1111994444
This work supported by the National Key Research and Development Program of China (No.2024YFE0115700 and National Natural Science Foundation of China (No.62402335)
Fang. Y., Liu, X., Lu, W., Pedrycz, W., Lang, Q.. and Yang. J. Knowledge graph completion with low-dimensional gated hierarchical hyperbolic embedding. Knowl. Based Syst. 309:1 18004, 2025. doi: 10.1016/J.KNOSS, 2024.112804 URL ht ttttps:/// //t::///ooioo /tt///i..rg//1.101111/1 1 kn..ysss. 2024. 202..112804.
Impact Statement
This paper presents work whose goal is to advance the field of Knowledge Graph. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
Ge, X., Wang, Y., Wang. B., and Kuo. C. J. Knowl- edge graph embedding with 3d compound geometric transformations. CoRR, abs/2304.00378, 2023. doi: 10. 10-4855WARXV.22300000338 URL https: /to. 0tg//1..4855//r211...222 00378.
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A. Reproducibility Checklist
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If you ran experiments...
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Due to internal policy and intellectual property concerns, the source code used in this study will not be made publicly available.
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? (Yes)
(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? (Yes)
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(a) your work uses existing assets, did you cite the creators? (Yes)
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(c) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content?
The dataset used in our work is publicly available and widely used in research. To best of our knowledge, it does not contain personally identifiable information or offensive content.
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13

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
B. Appendix
B.1. HTM for TKGC
This section primarily introduces the regular quaternion model, HTM, which we proposed in ANALYSIS. For HTM, the head entity s and the tail entity correspond to Qs { as + egi + faj + gak ag Csr fx: Is E IR. } and Q. a + egi faj gok ous cor for Io IR* ). respectively, while the relation r and timestamp T correspond to R. {ar ar + fij + grk : Cr,er; Jr. E TR* and W, ar + e,i+ J-j grk ar, Cr, 17,9+
TR }. respectively. The
specifics are follows:
We first normalize timestamp Wr to the unit quaternion W by dividing W, by its norm to eliminate scaling effects:
W a +
W.(d',e.f''l
(15)
W +2
Secondly, rotate relation R2 by doing Hamilton product between it and W/ to get representation of temporal relation:
Ry R 2 W = arr + Erri + frri + gr k,
(16)
where & is Hamilton product. Next, we normalize Rgy to the unit quaternion Re..
(a" e., f" g") Rgt |RT
Orr + Crrl frrj grrk
(17)
Va / + c + f 9
We then define an intermediate variable Qarr as the result of Hamilton product between Qo and R
Q = Qs RA aerr + Carii + farrj + garzk.
(18)
Finally, the scoring function of HTM is defined by the inner product:
7(S, Qorr Qo.
(19)
B.2. CTM for TKGC
This section follows the principles upon which we built CTM, we construct a model named CTM based on complex
embeddings, For CTM, head entity and tail entity o correspond to C, a, + e,i a. e, E I and C2 = { a, + e,i ao Co E R ). respectively, while relation r and timestamp t correspond to C, a, + e,i ar, Er E R and C, = a, + e 0r, E R ), respectively. The specific steps are as follows:
We first normalize timestamp C, to C to eliminate the scaling effect by dividing C, by its norm:
C₁ = a, + i, - = |C||
(20)
Va + +
Secondly, we get the temporal relation C,r by rotating C, through the product with C,A.
Crr C, C aur + Errl,
(21)
Next, we define the Carr the result of product between C₁ and C,A:
CArr C. CA7 asrr Esrri,
(22)
where complex product. Finally, the scoring function of CTM is defined by inner product:
p(,, r. O, 7)TM Curr Co-
(23)
14

---

Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
B.3. CDS for TKGC
This section follows the overall concept of TeDS applied to complex embeddings, named CDS. For CDS, head entity relation r, and tail entity correspond to C. a, + e,i ag. R }. C, { a, + e,i ay Cr E R and == ag + coi dos Co R$ ). respectively. Timestamp is divided into diachronic timestamp dr and synchronic timestamp ST, corresponding to Car and CST. respectively. The specific steps are as follows:
Synchronic perception (SP). Firstly, to achieve a thorough integration of temporal and relational information, SP performs a composite reorganization of synchronic timestamp C.r = aar + E,r and relation Cy. This results in the creation of two complex numbers: Crrep = ar + e and Caprr = agr + e, where agrs Ear I². Secondly, we normalize Cr.pr to the unit complex 0 by dividing Q..p by its norm to eliminate scaling effects:
Crep
+ e,i
(24)
Crapel
V + e
CDS utilizes complex product to perform rotation operations on Crrup via CA relations:
Tapry obtaining representation of synchronic
Me = Crrup C
(25)
where is complex product. Meanwhile, normalize Me to the unit complex M. We then rotate head entity C, by doing complex product between it and M.:
C
(26)
Diachronic perception (DP). Firstly, we iterate through all timestamps, sequentially mapping each time point to an angle and converting it to the scalar component a complex number using trigonometric functions to construct diachronic timestamps:
T + sin
T Fn 2T
Car cos(
)e'
(27)
2T
where e' E RR: Jn E {1,-.., T} denotes time point. Secondly, we use complex product with the diachronic timestamp Cr. to rotate relation C, into diachronic relation Crr,:
Crr, -C, Cr.
(28)
Thirdly, we normalize Crr, to unit complex CA.,. We then rotate the head entity C, by doing complex product between it and CA
Cap = C2 CA
(29)
Finally, we summarize the scoring function of CDS as follows:
p(s,r,,TTTODS = (Cop + Cap) Con
(30)
where is inner product.
B.4. Analysis of TeDS under unbalanced time distribution
Figure 1l extracts facts between Barack Obama, Angela Merkel, and Russia under different time spans from ICEWS14, 14. Intuitively, DP and TeDS exhibit improved performance as the time span increases, while SP and HTM demonstrate a slight decline in performance with longer time spans. These results further support the notion that DP excels at capturing diachronic scenarios.
Figure 12 extracts different months from ICEWS14 to test temporal non-stationarity and synchronic scenarios. Intuitively, TeDS achieves significant and stable performance across all months, while DP consistently delivers the second-best results in different months. These results demonstrate that TeDS and DP excel at learning synchronic scenarios. Additionally, SP maintains good overall performance but experiences slight declines as diachronic scenarios are segmented. Overall, both DP and SP demonstrate stable and robust performance on strongly constrained datasets across different scenarios. This further supports our motivation: the two scenarios are not entirely independent but demonstrate mutual dependence and serve as foundations for each other.
15

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Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
HTM SP
TeDS
30
20
10
[01-01, 01-15]
[01-01, 03-31J
[01-01, 09-30]
Figure 11. MRR performance comparison under different time spans on ICEWS14. Where [01-01, 01-15] represents the years 2014-1-1 2014-1-15; (01-01, 03-37] represents the years 2014-1-/ to 2014-3-31; [01-01, 09-300 represents the years 2014-1-1 to 2014-9-30.
300
7d.
May
A46
000
No.
Figure 12. Comparison of MRR Performance Indicators for HTM. SP, DP, and TeDS Based on Different Monthly Data from ICEWS14.
Furthermore, we find that TeDS outperforms TPComplEx on datasets with longer time spans, which we attribute to its focus on synchronicity and diachronicity. In contrast, TPComplEx is limited to synchronic perspective, overlooking the impact of facts over time. To validate our hypothesis, we test TeDS and TPComplEx on a long-time-spar constrained dataset concerning Obama and Japan, as shown in Figure 13. The results consistently show that TeDS outperforms TPComplEx, further supporting our hypothesis.
B.5. Performance comparison between TPComplEx and TeDS
Compared to TPComplEx, TeDS demonstrates significantly better performance in MRR and Hit@l but slightly lower performance in Hit@3 and Hit@ 10 on ICEWS14. On ICEWS05-15, TeDS shows significantly better performance in MRR, Hit@1, 1, and Hit@3, 3, while slightly underperforming in Hit@ 10. Similarly, on ICEWS18, TeDS achieves significantly better performance in MRR, Hit@| I, and Hit@3, but its performance in Hit@ 10 is slightly lower. Overall, TeDS performs comparably to TPComplEx on ICEWS series datasets. The key difference lies in the fact that TeDS's performance primarily benefits from its exploration of synchronicity and diachronicity in temporal properties, with focus on selecting the unique optimal answer. In contrast, TPComplEx's 's performance mainly derived from its study of simultaneity, aggregation, and associativity in temporal properties, emphasizing the aggregation and simultaneous prediction of multiple facts, thereby focusing more on correctly predicting all possible correct answers within the ranking range. In fact, balancing the selection of the optimal answer while accounting for multiple correct answers within the ranking range an intriguing research topic.
For comprehensive comparison, we reproduce TPComplEx (selecting best result from rank E {1000, 1500, 2000}) on Wikidata 12k, YAGO11K kk and ICEWS18. Table 5 and 6 show that TeDS outperforms TPComplEx across all datasets, with significant improvements on Wikidatal 12k and YAGOIIK, which we attribute to TeDS's modeling of temporal scenarios.
Finally, we perform a computational complexity comparison between TPComplEx and TeDS. Table 7 shows TeDS's superior training speed: 43% faster per epoch on Wikidata 2k (5. (5.63s vs. 9.87s) and 35% faster on YAGO11k (2.82s vs. 4.33s)
16

---

Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
TeDS
TPComplEx
86
84
80
78
76
70
68
MRR
HIT@
HIT@
(Obama, *, Japan, [2005-*-*, 2015-*-*1)
Figure 13. Performance comparison the strongly constrained test between Obama and Japan on ICEWS05-15.
Table 5. Experimental results on YAGOIIK, 12k, and GDELT. All results are taken from the original papers. Dashes: results are not reported the responding literature. The best results among all models are written bold.
YAGO1
Wikidata 12k
GDELT
MRR
H@1
H@3
H@1 10
MRR
H@1
H@3
H@ 10
MRR
H@1
H@3
H@ 10
TPComplEx
38.5
29.4
42.6
58.6
42.1
31.5
45.7
66.1
40.7
32.9
43.1
55.9
CDS (ours)
58.1
57.4
58.7
60.8
70.7
70.3
71.9
74.1
58.6
56.1
59.0
61.5
TeDS (ours)
77.3
76.9
78.1
78.4
95.5
95.7
95.8
71.5
69.9
72.2
74.4
DTeDS (ours)
81.0
80.3
81.1
81.8
95.7
94.6
95.4
96.0
85.6
82.8
86.4
90.0
compared to TPComplEx. Crucially, these speedups are achieved alongside dramatic parameter reductions (e.g.. 90% fewer parameters on YAGO1IK). The marginally longer runtime on ICEWS05-1E (30.75s vs. 22.06s) is justified by TeDS using only 27% of baseline's parameters a favorable tradeoff for memory-comee constrained applications. Table 8 reveals TeDS's most striking advantage: achieving superior performance with just 20.64M parameters versus TPComplEx's 201 2M Wikidata12k-aa 10x improvement in parameter efficiency.
The above analysis demonstrates that TeDS is particularly well-suited for large-scale TKG applications, maintaining competitive performance while significantly reducing memory overhead and computational resource requirements
B.6. Hyperparameter analysis
Figure 14 illustrates the complete hyperparameter configuration of TeDS, where A is the regularization weight and A is the temporal regularization weight. Our observations indicate that A impacts results more than As-
Moreover, we additionally plot the loss convergence curves of TcDS on ICEWS14 and ICEWS05-15, which demonstrate its stable and efficient optimization process.
B.7. TeDS can model the synmetry/anntsymmeetyy pattern. Theorem B.1. Relation r is (anti)symmetric if T
(2,T, (2) -1,,,,,7)).
(31)
A fact with such form a (anti)symmetric pattern.
The flexibility and representational power of quaternion enable us to model various relation patterns at ease.
Proof. For symmetric pattern, if r8,, and ((0,8,7) hold, we have:
Qs 8 (RA, + +AA) Q. Qo 2 (RA, M=) Q.
(32)
17

---

Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
Table Experimental results on ICEWS14, ICEWS05-15, and ICEWS18. All results taken from the original papers. Dashes: results are not reported in the responding literature. The best results among all models are written bold.
ICEWS14
ICEWS0S-15
ICEWS18
MRR
H@!
H@@
1@@ 10
MRR
H@! 1
H@3
1@@ 10
MRR
H@ 1
H@3
H@ 10
TPComplEx (2024)
89.8
86.5
92.5
95.4
84,5
79.4
88.2
93.4
34.2
23.7
31.6
45.3
CDS (ours)
83.1
82.4
83.7
85.8
75.4
69.5
74.8
78.1
32.5
27.1
35.5
47.1
TeDS (ours)
90.7
90.6
90.8
91.0
87.3
85.8
88.3
90.4
45.8
45.6
46.9
48.2
DTeDS (ours)
92.1
91.4
92.1
92.6
95.4
90.1
91.0
92.9
56.6
55.4
58.8
60.6
Table 7. Training Time Comparison: TeDS vs. TPComplEx (seconds per epoch).
Model
ICEWS14
ICEWS05-15
Wikidata
YAGOIIk
TPComplEX TeDS(ours)
5.56
22.06 30.75
9.87
4.33
6.30
5.63
2.82
Table 8. Parameter Count Comparison: TeDS vs. TPComplEx.
Model
ICEWS14
ICEWS05-15
Wikidata12k
YAGO1Ik
TPComplEx
92,362,736
75,228.496 ,488
201.260,000 20,643,200
170,140,000 17,340,000
TeDS()urs)
12,065,600
20,396,800
The symmetry of TeDS can be demonstrated by setting the imaginary part of R + +.AA to O. Since R,,, = Wdr. @ R and Ml = Qrt,, 8 Q according to Hamilton product rule, both R2 = and R can be achieved by setting the imaginary parts of R, and Q to O.
For antisymmetric pattern, r8,, T) and -r(o, 8, hold, we have:
Qs & (RA, ++A Qo Qo (RA MA) Q.. QQ.
(33)
The antisymmetry of TeDS can be demonstrated by ensuring that the imaginary parts of R + Mr are nonzero.
B.8. Proof of Lemma 2
Theorem B.2, Relation r is inverse to relation -1 Vf V
(I, (v.r-1 ,,,,,,,,, xr, T).
(34)
A fact with such form is a inverse pattern.
Proof. For inverse pattern, if r (8, and r2(0, 8, hold, we have:
Q. 2 (RA) + +. Q. Qu @ (R + +A) Q..
(35)
For inverse property of TeDS, we need utilize the conjugation of quaternions to prove the case since conjugation of the quaternion is its inverse. Thus, formula 35 can be rewritten in the following form:
Q. 8 (RA +=A . Q. Q. 8 (RA + +AA)
Q RA Qo + Q. 0. Q Qo 8 RA Q. 10+Q. Q0 & A Q
(36)
= Q₂ & R Q. = Q. 0 RA
Q.: Q & M¹ Q. = Q. @ n Q.
18

---

Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion
0.9070
06
0.2
0.1
0.01
0,020
0.0075
0.055
0.005
0.0075
0.0025
001
0.0001
0.1
Figure 14. Performance of MRR with different da and As on ICEWS14.
ICEWS14
ICEWS05-15
LON
Epach
Epoch
Figure 15. Convergence of TeDS ICEWS14 and ICEWS05-15.
To prove Qs A4..A.A0 Qo = Qo 2 Ms. Qs we first have:
M QuTop 8 QTar [(ur(tar EpesT Jr 9sr )+ (apest - tplsr + frger 9sr it (arfer Grgor + frast + 9ST )
(37)
(0,gsr erJor frest + O
We let arst = a, Cr fofor GorIr, a, + frr frg.r fr. fret ar ferr- tor Fror 0,9or + erfer for + ar We normalize M to unit quaternion A. A,
M
Best + Crsri + frorj + Drork
(a " fd ."""
(38)
M
a2 + el + f2ar + geet
Next, we obtain the conjugate of AA:
A " -e"i f g'k.
(39)
19

---

Joint Learning of Diachronic and Synchronic Perspectives in Quaternion Space for Temporal Knowledge Graph Completion And then, we expand the left term of formula (35):
Q. 0. Qo =I(a,a" eee" S-ʃ" 9s9 3s )+
(age" tea" fag 9o i
(a,f" e,g + fsa" + got ")+
(a.9" + e - fee" + gga"") k
(a. + e, fn + gok).
=aaaa e,e" f&f 9.9 ") aot
(40)
(a.e" e,a" fag" JaS" -bot
(a,f" c " + fsa" + gst") fot
(a.g" + f - f,e" + goa" 99 .90
= (a,, (o) "e,,e",aa - (J,,J", an) - "g.9"" a.) +
(a,, e" Co) + (ex, a eo) (Sa,g" 6o) [g, s" en) +
(a,, f fol (ca. .o) + (fs.g" fol (g, .fo) +
(a.. g go) + (cs, 1² gg) (f gol (os g9))-
Finally, we expand the right term of formula (35):
10 MS. Qs = =llaaa" coe" lal + goll )
(-age" + tead" - fog + goo lit
(-aof" + cog" + foa" - goe "j+
(-and) - - + loe" + gaa")) [k] (a, + +es+ sai+ gok).
= -aoa" + coc" + foJ + 909 ) ast
(41)
(-a,e" + coa" - fog 9o (0 eet
(-aof" R + e.g" foa" g0e " fot (-aos" e.. 1 + foe" + goa") Io
= (a,, d", a.) + (eo, e" as) + (So, az) + (go. g a.)))
(a.; e", 0a) + (ea, e2) (So.g" es) + (go. 1" ee)
(a.. 8" fo) (eo.g" fe) + (fo.g" fo) (go. e" fo)
(a.. 8" gz) (co, f" 9a) + (fo,c" ga) + (go. a" .9s)-
By comparison, we can easily check the equality of left and right term. Similarly, we can derive that Q. 2 RA Qo = Qo & RA Qe. Therefore, TeDS has sufficient capability to model inverse patterns.
20


Reviews:
[{"review_id": "8XEFG72B4V", "reviewer": "Reviewer_cu6z", "summary": "The paper proposes TeDS, a novel temporal knowledge graph completion (TKGC) model that jointly learns diachronic (temporal evolution) and synchronic (cross-relation interactions) perspectives in quaternion space. The key innovations include: 1) Dual temporal perception through synchronic (time-relation composite quaternions with Hamilton operators) and diachronic (continuous time encoding via trigonometric mapping) modules; 2) A unified quaternion-based framework that deeply integrates temporal and relational information. Experiments on six benchmarks show significant improvements over SOTA models (e.g., +27.4 MRR points on ICEWS14 vs CEC-BD). The paper demonstrates thorough ablation studies and visual analysis of temporal patterns.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for all your valuable comments. Note: The pictures and tables used in response are available at https://anonymous.4open.science/r/TEDS-033A/To_Re_cu6z.pdf See: To_Re_cu6z.pdf\n\nQ1: The claim in Section 3.1 about handling various temporal constraints lacks explicit evaluation on datasets with different temporal annotations (time points vs. intervals). How does TeDS handle time interval annotations compared to time points? The experiments only show results on datasets with time points\n\nA1: We add details on handling various temporal constraints (See our response to Reviewer fTHA's A5 for details). In fact, this is a commonly used processing method in existing SOTA models (e.g., TeLM and TPComplEx). In the future, finding better ways to handle various temporal types and model dataset characteristics more effectively will be a key focus of our work.\n\n\nQ2: No evaluation on emerging temporal patterns like cyclical events\n\nA2: In our current research on TKGs, such as ICEWS, YAGO, and Wikidata, the focus is primarily on factual records (e.g., news facts, concept facts), which do not follow clear cyclical patterns like seasonal changes, economic cycles, or biological rhythms. In fact, modeling cyclical events is crucial for prediction and reasoning. Your comment broadens our future scope. We may use Fourier transforms or seasonal decomposition to enhance TeDS’s cyclical modeling. Integrating external data and known patterns could further boost performance.\n\nQ3: The appendix contains reproducibility checklist but lacks:\n\n(1)Implementation details for baselines\n\n(2)Complete hyperparameter configurations; No parameter sensitivity analysis\n\n(3)Additional case studies\n\nA3:\n\nA(1)The results of all baselines involved in comparison is taken from original papers. \n\nA(2)We add complete hyperparameter configuration (See Fig 1). We find that $𝜆_a$ impacts results more than $𝜆_b$. Even without regularization, TeDS remains highly competitive, proving its effectiveness. We add an embedding dimension analysis (See Fig 2). TeDS outperforms baselines at all dimensions, achieving best cost-performance at rank=100. Further increases bring minimal gains but higher costs.\n\nA(3)We further randomly remove 30% of ICEWS14 training set (See Fig 3) to test TeDS's robustness under extremely sparse data conditions. Besides, to test TeDS's effectiveness in industrial and sparse scenarios, we use a company's historical cost-price time-series dataset A (See our response to Reviewer C2mh's A1 for details).\n\n\n\n\nQ4: Limited analysis of computational complexity\n\nA4: Table 1 shows complexity comparison of mainstream baselines (see our response to Reviewer fTHA's A1 for details). \n\n\n\nQ5: Potential scalability issues with quaternion operations\n\nA5: To avoid impact of scaling, TeDS normalizes quaternions using Schmidt orthogonalization. Specifically, for SP, we normalize $Q_{\\tau_{sp}r}$ to unit quaternion $Q_{\\tau_{sp}r}^{\\Delta}$ by dividing $Q_{\\tau_{sp}r}$ by its norm to eliminate scaling effects $Q_{\\tau_{sp}r}^{\\Delta} =\\frac{Q_{\\tau_{sp}r}}{\\left|Q_{\\tau_{sp}r}\\right|}$\n\nNext, we use Hamilton operator $\\otimes$ to perform rotation operations on $Q_{r\\tau_{sp}}$ via $Q_{\\tau_{sp}r}^{\\Delta}$, obtaining $\\mathscr{M} = Q_{r\\tau_{sp}} \\otimes Q_{\\tau_{sp}r}^{\\Delta}.$\t\n\nMeanwhile, we normalize $\\mathscr{M}$ to unit quaternion $\\mathscr{M}^{\\Delta}$. Finally, we rotate $Q_s$ by doing $\\otimes$ between it and $\\mathscr{M}^{\\Delta}$:\n\n​\t\t$Q_{sp} = Q_{s} \\otimes \\mathscr{M}^{\\Delta}. $\n\nSimilarly, for DP, we normalize $R_{r\\tau_{n}}$ to unit quaternion $R_{r\\tau_{n}}^{\\Delta}$. Then, we rotate $Q_s$ by doing $\\otimes$ between it and $R_{r\\tau_{n}}^{\\Delta}$:\n\n​\t\t$Q_{dp} = Q_s \\otimes R_{r\\tau_{n}}^{\\Delta}.$  \n\nDetails are in Section 4 (TeDS for TKGC).\n\n\n\n\nQ6: Training time comparison limited to 4 models (Fig 9a).\n\nA6: We further compare TeDS with SOTA model TPComplEx (using the hyperparameters claimed by TPComplEx) to evaluate computational efficiency. In Table 2, we show that TeDS is 43% faster per epoch on Wikidata12k compared to TPComplEx (5.63s vs 9.87s), and 35% faster on YAGO11k (2.82s vs 4.33s). These speedups are achieved while significantly reducing the number of parameters (e.g., 90% fewer parameters on YAGO11k). The runtime on ICEWS05-15 is slightly longer (30.75s vs 22.06s), but TeDS uses only about 27% of the parameters of TPComplEx, demonstrating its efficiency advantage.\n\nParameter Comparison. Table 3 compares actual parameter counts of models: On Wikidata12k, TeDS gets superior performance with only 20.64M parameters, while TPComplEx requires 201.2M, resulting in a 10× improvement in parameter efficiency. TeDS ensures optimal performance while significantly reducing computational overhead, making it ideal for large-scale TKGs.\n\n\n\nQ7: No statistical significance testing for reported improvements.\n\nA7: In Section 6.4, we run experiments five times and calculate the standard deviation to show TeDS's stability across different datasets.", "claims_and_evidence": "The main claims are well-supported:\n- Claim of dual temporal perception: Validated through ablation studies (Table 4) showing SP and DP modules contribute 79.6/71.1 vs 90.7 combined MRR on ICEWS14\n- Claim of time-aware representation: Supported by temporal pattern visualizations (Figures 4-6) showing improved relation clustering in temporal contexts\n- Superiority over SOTA: Comprehensive comparisons across 19 baselines on 6 datasets (Tables 2-3) with clear performance gaps\n\nPotential weakness: The claim about handling various temporal constraints (Section 3.1) lacks explicit evaluation on datasets with different temporal annotations (time points vs intervals).", "methods_and_evaluation_criteria": "Methods are appropriate:\n- Quaternion operations naturally model temporal rotations and interactions\n- Dual perception aligns with temporal KG characteristics (evolution + interaction)\nEvaluation is rigorous:\n- Standard TKGC metrics (MRR, Hits@n) used consistently\n- Diverse datasets cover different temporal scenarios (ICEWS for events, YAGO/Wikidata for facts)\nMissing: No evaluation on emerging temporal patterns like cyclical events.", "theoretical_claims": "The paper contains no formal theoretical proofs. Mathematical components (quaternion operations in Section 3.2, Eqs 1-2) are correctly presented following standard quaternion algebra.", "experimental_designs_or_analyses": "Strengths:\n- Comprehensive comparisons with 19 SOTA methods\n- Detailed ablation studies (Table 4) and component analysis\n- Visualization of temporal patterns (Figures 4-7)\nWeaknesses:\n- No parameter sensitivity analysis\n- Training time comparison limited to 4 models (Figure 9a)\n- No statistical significance testing for reported improvements", "relation_to_broader_scientific_literature": "Key connections:\n- Extends quaternion KG embedding (QuatE, DualE) with temporal perception\n- Improves upon temporal KG models (TComplEx, RotateQVS) through dual perspectives\n- Combines advantages of tensor decomposition (CEC-BD) and neural approaches (SANe)", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths:\n- Novel integration of dual temporal perspectives\n- Effective quaternion-based temporal encoding\n- Comprehensive evaluation across multiple datasets\nWeaknesses:\n- Limited analysis of computational complexity\n- No evaluation on temporal constraint types (point vs interval)\n- Potential scalability issues with quaternion operations", "other_comments_or_suggestions": "None", "questions_for_authors": "How does TeDS handle time interval annotations compared to time points? The experiments only show results on datasets with time points.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zwwxF70bQd", "reviewer": "Reviewer_C2mh", "summary": "The paper introduces TeDS, a framework designed for temporal knowledge graph completion using quaternion representations to merge time and relational data. Key findings show that TeDS significantly outperforms existing models on various benchmarks, effectively managing issues like data sparsity and incompleteness. The authors emphasize the model's robustness and provide comprehensive experimental results, along with publicly available source code for reproducibility.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for taking the time to review and evaluate our manuscript. Your comments have not only helped us improve the manuscript but also given us confidence to further enhance quality of our work. Note: The pictures and tables used in response are available at https://anonymous.4open.science/r/TEDS-033A/To_Re_C2mh.pdf See: To_Re_C2mh.pdf\n\nQ1: Some claims about the model's limitations and potential societal impacts are less thoroughly discussed, which could weaken their overall persuasiveness.\n\nA1: Thank you for your valuable comment regarding need for a deeper discussion of TeDS's limitations and societal implications. To evaluate practical effectiveness of TeDS in industrial scenarios, we use a historical cost-price time-series dataset A provided by a company. This dataset includes data on resource exploration, mining operations, material consumption, labor costs, logistics and transportation, and comprehensive costs, covering production cost data from January 2000 to December 2022. With a 12-hour sampling interval, we obtain a total of 16,031 valid samples, with all monetary values denominated in 10,000 yuan.\n\nTo simulate data-missing conditions in real-world mining scenarios, we randomly remove 10%, 20%, and 30% of training data from dataset A, constructing three sparse datasets: A 10% SPARSE, A 20% SPARSE, and A 30% SPARSE. For comparison, we reproduce baseline models including TComplEx and TeLM. Fig 1 shows that TeDS gets best performance on complete dataset A, with an MRR of 71.5, significantly outperforming baseline models. On the sparse datasets, TeDS maintains high performance, demonstrating strong robustness. In contrast, TComplEx and TeLM exhibit more significant performance degradation under data-missing conditions, particularly on A 30% SPARSE, where their MRR drops to 33.0, and 34.5, respectively. These results indicate that TeDS has a clear advantage in the task of missing-value imputation for mining cost-price data, validating its potential for industrial time-series data completion scenarios.\n\nQ2: While the paper discusses several foundational models and recent advancements in knowledge graph embeddings and temporal reasoning, there are essential references that could further contextualize its contributions. For instance, the work by Zhang et al. (2020) on \"Temporal Knowledge Graph Completion\" introduces a novel approach that leverages recurrent neural networks for dynamic relationships, which could provide insights into alternative methodologies for handling temporal data. Additionally, the recent advancements in graph neural networks (GNNs) for knowledge representation, such as the work by Kipf and Welling (2017) on semi-supervised learning with GNNs, could be relevant as they offer a different perspective on embedding techniques that may complement TeDS framework. Lastly, the exploration of attention mechanisms in knowledge graphs, as seen in the paper by Wang et al. (2020) on \"Graph Attention Networks,\" could provide valuable context for understanding how attention-based approaches can enhance the representation of temporal relationships in KGs.\n\nA2: Thank you for your insightful comments on the latest developments in basic models and knowledge graph embedding and time reasoning. We have carefully included more relevant and important reference materials in our manuscripts, which inspire and complement the TeDS framework. The specific references added to manuscript are as follows: \nWelling et al. (2017) provide a different perspective on embedding technology in their Gnn semi-supervised learning work. Wang et al. (2020) apply the graph attenuation attention network to KGC, and used an efficient graph convolution method to semi-supervise the classification of graph structure data. Zhang et al. (2020) propose a relational graph neural network with hierarchical attention used for KGC, which effectively uses local neighborhood information. Xiao et al. (2024) propose a new method that uses comparative learning to break down the local and global perspectives in TKGs to obtain better reasoning. Zhu et al. (2021) use a replication generation mechanism to predict future facts by quoting historical data or generating new facts. Wang et al. (2025) combine global historical event frequencies with local temporal relative displacements to efficiently learn query representations from TKGs.  Qiu et al. (2025) enhance the capabilities of graph neural networks by integrating node weights and future information.\nThese additions not only strengthen the contextualization of our work but also provide a more comprehensive overview of the relevant literature, ensuring that our research is situated within the broader academic landscape. Thank you for your feedback, which has been instrumental in improving the quality and depth of our manuscript.", "claims_and_evidence": "The paper evaluates TeDS, a framework for temporal knowledge graph completion, using datasets like ICEWS14, ICEWS05-15, and ICEWS18. It conducts ablation studies to compare TeDS with models such as TPComplEx and HTM, employing metrics like MRR, H@1, H@3, and H@10. The motivation is to validate TeDS's effectiveness in managing temporal and relational information, showcasing its advantages in capturing complex temporal patterns. The results indicate that TeDS outperforms existing models, particularly in handling sparse and incomplete data, and the design integrating synchronicity and diachronicity significantly enhances knowledge graph completion. This motivation aligns with the experimental findings, emphasizing TeDS's innovation in processing time-related data. Most claims are well-supported by evidence, particularly regarding performance metrics and comparative analysis; however, some claims about the model's limitations and potential societal impacts are less thoroughly discussed, which could weaken their overall persuasiveness.", "methods_and_evaluation_criteria": "The proposed methods, including quaternion representation and a unified framework that integrates synchronic and diachronic perspectives, are highly relevant for addressing the complexities of temporal knowledge graphs. These methods effectively facilitate the analysis and summarization of intricate real-world scenarios involving time-dependent data. Furthermore, the evaluation criteria, which involve benchmark datasets like ICEWS14, ICEWS05-15, and ICEWS18, along with metrics such as MRR, H@1, H@3, and H@10, are appropriate for assessing the model's performance and provide a comprehensive evaluation of its effectiveness in this application.", "theoretical_claims": "Yes, the correctness of the proofs for the theoretical claims has been verified, as the appendix includes complete proofs for the theoretical results presented in the main text. This thorough documentation is intended to ensure transparency and rigor regarding the model's performance and capabilities, allowing readers to validate the theoretical foundations. Additionally, the appendix outlines the full set of assumptions underlying these results, clarifying the conditions for the applicability of the proposed methods and contextualizing the findings, while also providing supplementary details on experimental setups and an extended error analysis to enhance reproducibility and guide future research directions. There are no reported issues with the proofs or assumptions, reinforcing the credibility of the findings.", "experimental_designs_or_analyses": "The soundness and validity of the experimental designs and analyses have been thoroughly checked. \n The ablation study effectively isolates the contributions of different perceivers in the TeDS model, and the results validate the model's effectiveness without any identified issues. The performance comparison across multiple datasets is robust, demonstrating TeDS's superiority over state-of-the-art models, with no apparent flaws in the experimental setup. The standard deviation analysis provides a clear assessment of the model's robustness, and the methodology for calculating standard deviations is sound. The detailed descriptions of the training process enhance reproducibility, and the thoroughness of the training settings supports the validity of the findings. Lastly, the approach to identifying model limitations through error analysis is well-structured, offering valuable insights for future research. Overall, the experimental designs are well-founded, and no significant issues have been identified.", "relation_to_broader_scientific_literature": "The key contributions of the paper are closely related to the broader scientific literature on knowledge graph embeddings and temporal reasoning. The work builds upon foundational models like TransE and ComplEx, which established the importance of embedding techniques for static knowledge graphs, and extends these ideas to temporal contexts through models such as TTransE and TA-DistMult. By integrating insights from tensor decomposition methods like RESCAL and TuckER, the paper enhances the representation of temporal relationships, addressing limitations identified in prior research, such as the inability to effectively model dynamic interactions over time. Furthermore, the innovations presented in the TeDS framework align with recent advancements in temporal knowledge graphs, such as ChronoR and TeLM, by providing a unified approach that captures both synchronic and diachronic perspectives, thereby contributing to a more comprehensive understanding of knowledge representation in evolving contexts.", "essential_references_not_discussed": "While the paper discusses several foundational models and recent advancements in knowledge graph embeddings and temporal reasoning, there are essential references that could further contextualize its contributions. For instance, the work by Zhang et al. (2020) on \"Temporal Knowledge Graph Completion\" introduces a novel approach that leverages recurrent neural networks for dynamic relationships, which could provide insights into alternative methodologies for handling temporal data. Additionally, the recent advancements in graph neural networks (GNNs) for knowledge representation, such as the work by Kipf and Welling (2017) on semi-supervised learning with GNNs, could be relevant as they offer a different perspective on embedding techniques that may complement the TeDS framework. Lastly, the exploration of attention mechanisms in knowledge graphs, as seen in the paper by Wang et al. (2020) on \"Graph Attention Networks,\" could provide valuable context for understanding how attention-based approaches can enhance the representation of temporal relationships in knowledge graphs.", "other_strengths_and_weaknesses": "No", "other_comments_or_suggestions": "No", "questions_for_authors": "No", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "GtCojX6N6i", "reviewer": "Reviewer_fTHA", "summary": "The paper introduces a quaternion-based model for temporal knowledge graph completion that integrates diachronic and synchronic perspectives. The model demonstrates significant improvements over state-of-the-art methods on six benchmark datasets, showcasing its effectiveness in handling both short and long temporal spans.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for all your valuable comments. Note: The pictures and tables used in response are available at https://anonymous.4open.science/r/TEDS-033A/To_Re_fTHA.pdf See: To_Re_fTHA.pdf\n\nQ1: A more detailed discussion on model's computational complexity and scalability would strengthen the claims. The paper lacks in-depth analysis, particularly regarding computational overhead compared to simpler models (e.g., TransE variants)\n\nA1:\n\n(1)Complexity Comparison. In Table1, TeDS has same theoretical complexity as mainstream models (space: $\\mathcal{O}(n_ed + n_rd + n_td)$, time: $\\mathcal{O}(d)$). Compared to quaternion models (RotateQVS and EHPR, rank=2000), TeDS gets best results with rank=100, reducing dimensionality by 80-95%, improving storage and computation efficiency while maintaining theoretical completeness.\n\n(2)Training Speed Comparison. Table2 shows TeDS's superior training speed.\n\n(3)Parameter Comparison. Table3 compares actual parameter counts.\n\nFor (2) and (3), see our response to Reviewer cu6z's A6 for details TeDS ensures optimal performance while significantly reducing computational overhead, making it ideal for large-scale TKGs.\n\n\nQ2: The correctness of the quaternion operations and their application to temporal reasoning appears sound, but a deeper theoretical analysis (e.g., convergence properties, bounds on performance) would be beneficial\n\nA2: We add experiments: 1) loss function convergence curves on ICEWS14 and ICEWS05-15 (see Fig1); 2) hyperparameter sensitivity analysis (see Fig2); 3) embedding dimension analysis (See Fig3). (See our response to Reviewer cu6z's A3 for details)\n\n\nQ3: SP and DP modules underperform TeDS, but combination’s superiority is attributed to \"deep integration\" without mechanistic explanation\n\nA3: For SP and DP, we further analyze characteristics between modules through temporal relation embedding visualization (Section 6.1) and strong constraint experiments (Section 6.2). Besides, we visualize and compare temporal relation embedding of baseline TeLM (see our response to Reviewer WGeZ's A2 for details).\n\nQ4: Quaternion operations introduce complexity without clear advantages over other methods\n\nA4: We add latest baselines (e.g., MTE(2025), Neo-TKGC(2025), GLARGCN(2025)) to continuously evaluate TeDS's performance (Table4 and 5). Compared to existing models, TeDS consistently gets a significant lead. Next, we find that TPComplEx gets performance close to TeDS on ICEWS14 and ICEWS05-15. To compare the two, we reproduce TPComplEx (rank=2000) results on Wikidata12k, YAGO11k, and ICEWS18. Finally, we perform a dual comparison based on both performance (See our response to Reviewer rpDA's A1 and A2) and efficiency (See our response to your A1). Besides, we extend TeDS to complex numbers and dual quaternions, named CDS and DTeDS, respectively. Table4 and 5 show that our framework gets competitive performance, with DTeDS further improving performance when computational overhead is not considered.\n\n\n\nQ5: Fig3’s time distribution analysis could include more datasets. Clarify whether TeDS can handle time intervals beyond points\n\nA5: \n\n1)We add a data density comparison between ICEWS18 and ICEWS05-15 (Fig4), along with a fact distribution chart for YAGO11k and a data density comparison between YAGO11k and Wikidata12k (Fig5). These additions help better analyze TeDS's performance on different datasets\n\n2)For facts missing part of time (e.g., (s, r, o, [$t_b$, -]) or (s, r, o, [-, $t_e$])), the score is same as quadruple with known time, i.e., $\\phi$(s, r, o, [$t_b$, -]) = $\\phi$(s, r, o, $t_b$), $\\phi$(s, r, o, [-, $t_e$]) = $\\phi$(s, r, o, $t_e$). For facts with no missing time (e.g., (s, r, o, [$t_b$, $t_e$])), we split quadruple into (s, r, o, $t_b$) and (s, r, o, $t_e$), and score is average of the two, i.e., $\\phi$(s, r, o, [$t_b$, $t_e$]) = $\\dfrac{1}{2}$($\\phi$(s, r, o, $t_b$) + $\\phi$(s, r, o, $t_e$)). This operation ensures compatibility with different time types while minimizing computational overhead. This is a commonly used processing method in existing models (e.g., TeLM and TPComplEx)\n\n\nQ6: How does TeDS handle extremely sparse temporal data, and are there any limitations in such scenarios?\n\nA6: We further randomly remove 30% of ICEWS14 training set (see Fig 6) to test TeDS's robustness under extremely sparse data conditions. Besides, to test TeDS's effectiveness in industrial and sparse scenarios, we use a company's historical cost-price time-series dataset A (see our response to Reviewer C2mh's A1 for details). TeDS consistently outperforms, showcasing stable advantages of TeDS and high-dimensional quaternion space. \n\nQ7: How does TeDS generalize to timestamps not seen during training (e.g., future events)?\n\nA7: TKGC refers to task of completing facts by inferring missing ones from a given subset. We focus on studying missing facts rather than predicting future ones. Predicting future facts is an interesting topic, and adapting our work to it will be a key focus.", "claims_and_evidence": "The authors provide comprehensive experiments on multiple datasets, showing that TeDS outperforms existing methods in terms of metrics such as Mean Reciprocal Rank (MRR) and Hits@n. The ablation studies further validate the effectiveness of the proposed dual perception channels. However, a more detailed discussion on the computational complexity and scalability of the model would strengthen the claims.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are appropriate for the problem. The use of quaternion embeddings and the dual temporal perception channels are innovative approaches for temporal knowledge graph completion. The evaluation metrics (MRR, Hits@n) are standard in the field and suitable for assessing the model's performance.", "theoretical_claims": "The paper does not present extensive theoretical claims beyond the quaternion-based representation and its application to temporal knowledge graphs. The correctness of the quaternion operations and their application to temporal reasoning appears sound, but a deeper theoretical analysis (e.g., convergence properties, bounds on performance) would be beneficial.", "experimental_designs_or_analyses": "The authors conducted experiments on multiple benchmark datasets, including ICEWS, YAGO11k, and Wikidata12k, demonstrating the robustness of TeDS across different temporal scenarios. The ablation studies provide insights into the contributions of the synchronic and diachronic perception channels.", "relation_to_broader_scientific_literature": "The paper builds on prior work in quaternion embeddings (e.g., QuatE) and extends it to temporal knowledge graphs. The dual temporal perception channels address limitations in existing methods that often treat temporal information as supplementary.", "essential_references_not_discussed": "No critical omissions noted", "other_strengths_and_weaknesses": "Strengths:\n\n1. The dual temporal perception channels are an effective approach for capturing temporal dynamics.\n\n2. Using quaternion embeddings provides a unique way to integrate temporal and relational information.\n\nWeaknesses:\n\n1. The paper lacks a detailed discussion on the computational complexity and scalability of the model.\n\n2. Limited discussion of computational overhead compared to simpler models (e.g., TransE variants).\n\n3. SP and DP modules underperform TeDS, but the combination’s superiority is attributed to \"deep integration\" without mechanistic explanation. \n\n4. Quaternion operations introduce complexity without clear advantages over other methods.", "other_comments_or_suggestions": "1. Figure 3’s time distribution analysis could include more datasets.\n\n2. Clarify whether TeDS can handle time intervals (e.g., [start, end]) beyond points.", "questions_for_authors": "1. How does TeDS handle extremely sparse temporal data, and are there any limitations in such scenarios?\n\n2. How does TeDS generalize to timestamps not seen during training (e.g., future events)?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zkAPfTYLIi", "reviewer": "Reviewer_WGeZ", "summary": "This paper introduces TeDS, which is a unified framework to simultaneously consider both diachronic timestamp and synchronic timestamp for TKGC. TeDS achieves significant improvements over the existing SOTA on six datasets.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for all your valuable comments. The pictures and tables used in response are available at https://anonymous.4open.science/r/TEDS-033A/To_Re_WGeZ.pdf See: To_Re_WGeZ.pdf\n\nQ1: The concepts of diachronic timestamp and synchronic timestamp appear to correspond to the temporal and structural dependencies in TKGs, respectively, which are fundamental considerations in most TKGs studies. The approach of mapping these dependencies to Quaternion Space for modeling is reasonable. However, there are notable similarities between this paper and ComTR in terms of structure and equations, with the exception of Diachronic Perception component. Despite this, ComTR is not cited or discussed, which seems inappropriate. The authors should explicitly clarify the differences and similarities between their work and ComTR. Besides, TELS also adopts Quaternion Space for modeling TKGs, and a comparison with it would further strengthen paper\n\nThe related work would be more informative if it included a clearer discussion on relevance of previous studies to TeDS\n\nA1: We add above references and provide following response\n\n1)Differences in underlying technical details: TeDS uses quaternions, while ComTR uses dual quaternions. In SP, TeDS achieves a thorough integration of temporal and relational information by reorganizing the synchronous timestamp $ W_{s\\tau} = a_{s\\tau} + e_{s\\tau} \\mathbf{i} + f_{s\\tau} \\mathbf{j} + g_{s\\tau} \\mathbf{k} $ and relation $ R_r $, forming two quaternions $ Q_{r\\tau_{sp}} $ and $ Q_{\\tau_{sp}r} $. In contrast, ComTR directly applies dual quaternions without deep information interaction. Details in Section 4 (TeDS for TKGC).\n\n2)Different motivations: TeDS observes regularities of facts within a temporal context and summarizes two important temporal perspectives: synchronicity and diachronicity. In contrast, ComTR focuses on capturing multi-relational patterns in a temporal context.\n\n3)TeDS integrates dual perception channels into a unified framework to handle multi-perspective temporal facts. It is not limited to quaternions and adapts to tensors, complex numbers, dual quaternions, and homogeneous transformations. In contrast, ComTR relies on rule modeling based on dual quaternion properties.\n\nLike ComTR, TELS uses dual quaternions to: 1)model multiple relations pattern; 2)model evolutionary hierarchical pattern; 3) capture unique latent semantics based on an entity's position in a relation. Unlike ComTR, TELS maximizes dual quaternion advantages rather than just applying them. Besides, TELS components become more portable and less reliant on dual quaternion technology (e.g., latent semantic and evolutionary hierarchical awareness).\n\nTo show TeDS's portability and effectiveness, we implement it with dual quaternions as DTeDS (see Table1 and 2). Compared to baselines, DTeDS and TeDS consistently get best and second-best results. We also observe that DTeDS and TELS outperform TeDS on GDELT. Due to GDELT's high data density at same temporal granularity, many multi-relation patterns emerge. DTeDS and TELS leverage the strength of dual quaternions in capturing these patterns, aligning with our hypothesis. Besides, we implement TeDS with complex numbers as CDS, which also shows competitive results. This further confirms the portability and effectiveness of our framework.\n\n\n\nQ2: The visualizations of temporal relation embeddings should include visualizations results from some baseline methods, rather than only comparisons with variations of TeDS.\n\nA2: We enhance comparison by visualizing TeLM’s temporal relation embeddings. First, we examine distribution of same relation over time, extracting relation Consult between Obama and Netanyahu in 2014 (Fig 1). TeLM outperforms HTM in classifying Consult across months, but is less effective than TeDS in aggregating data from multiple months, with blurred boundaries between adjacent months. Next, we observe various relations between Obama and Netanyahu from Jan-Jun 2014 (Fig 2). TeDS and SP perform better than HTM and TeLM in distinguishing relations. TeDS surpasses SP in differentiating identical relations, rather than clustering them together. Even within the same month, relations may show different trends based on context. Thus, clustering different relations while preserving uniqueness of identical relations in specific contexts is key.\n\n\n\nQ3: Adding a discussion on limitations of study and potential future directions would enhance completeness of paper.\n\nA3: Our TKG research focuses on factual records, which lack clear cycles like seasons or biological rhythms. Modeling cycles is key for prediction. We may use Fourier transforms or seasonal decomposition to enhance TeDS.\n\n\n\nQ4: The text in most figures is not easily readable. Enhancing the clarity of images would improve overall readability and presentation quality.\n\nA4: We will revise paper structure and adjust the font size in figures in revised version to enhance readability of manuscript.", "claims_and_evidence": "The effectiveness of modeling TKGs from the perspectives of synchronic perception and diachronic perception has been validated in the experimental results.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are appropriate for the TKGC problem.", "theoretical_claims": "I have checked the correctness of the proofs for the theoretical claims.", "experimental_designs_or_analyses": "I have checked the soundness and validity of the experimental designs and analyses.", "relation_to_broader_scientific_literature": "Considering both diachronicity and synchronicity is beneficial for TKGC.", "essential_references_not_discussed": "Please see Weakness 1:\nSome approaches of mapping diachronicity and synchronicity to Quaternion Space for modeling are missing:\n[1] Combination of translation and rotation in dual quaternion space for temporal knowledge graph completion, IJCNN 2023\n[2] TELS: Learning time-evolving information and latent semantics using dual quaternion for temporal knowledge graph completion, KBS 2024", "other_strengths_and_weaknesses": "Strength:\nThe experiments are relatively comprehensive, and TeDS achieves the state-of-the-art performance.\n\nWeakness:\n1. The concepts of diachronic timestamp and synchronic timestamp appear to correspond to the temporal and structural dependencies in TKGs, respectively, which are fundamental considerations in most TKGs studies. The approach of mapping these dependencies to Quaternion Space for modeling is reasonable. However, there are notable similarities between this paper and ComTR [1] in terms of structure and equations, with the exception of the Diachronic Perception component. Despite this, ComTR is not cited or discussed, which seems inappropriate. The authors should explicitly clarify the differences and similarities between their work and ComTR. In addition, TELS [2] also adopts Quaternion Space for modeling TKGs, and a comparison with it would further strengthen the paper.\n[1] Combination of translation and rotation in dual quaternion space for temporal knowledge graph completion, IJCNN 2023\n[2] TELS: Learning time-evolving information and latent semantics using dual quaternion for temporal knowledge graph completion, KBS 2024\n\n2. The Related Work section would be more informative if it included a clearer discussion on the relevance of previous studies to TeDS.\n\n3. The visualizations of the temporal relation embeddings should include visualizations results from some baseline methods, rather than only comparisons with variations of TeDS.\n\n4. Adding a discussion on the limitations of the study and potential future directions would enhance the completeness of the paper.\n\n5. The text in most figures is not easily readable. Enhancing the clarity of the images would improve overall readability and presentation quality.", "other_comments_or_suggestions": "No", "questions_for_authors": "No", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EQKXeQReyZ", "reviewer": "Reviewer_rpDA", "summary": "This paper proposes TeDS, a temporal knowledge graph completion method cosidering both diachronicic and synchronic flows within and between temporalized facts. Extensive experiments demonstrate that TeDs is capable of achieving state-of-the-art performance across multiple benchmarks.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for all your valuable comments. Note: The pictures and tables used in response are available at https://anonymous.4open.science/r/TEDS-033A/To_Re_rpDA.pdf See: To_Re_rpDA.pdf\n\nQ1: The performance improment compared with baselines is more marginal on first three datasets (Table2), could the authors explain this phenomenon.\n\nA1: TeDS gets consistent performance improvements across three benchmark datasets—ICEWS14, ICEWS05-15, and ICEWS18—with particularly notable enhancements on ICEWS18. This disparity primarily stems from ICEWS18 containing approximately ten times more facts than ICEWS05-15 at the same temporal density, significantly increasing the complexity of temporal context modeling. By effectively capturing intricate dependencies among high-density facts through its Synchronous Perception (SP) mechanism, TeDS attains optimal performance on this dataset.\n\nFurthermore, TeDS demonstrates even more pronounced advantages on larger-scale TKGs with greater challenges, including YAGO11k, Wikidata12k, and GDELT. For YAGO11k and Wikidata12k, which feature long temporal spans and distinct long-tail distributions, TeDS's Diachronic Perception (DP) employs dynamic smooth embedding techniques to simultaneously model short-term fluctuations and long-term evolutionary trends, effectively addressing the challenges of sparse temporal data modeling. Meanwhile, on the extremely fact-dense GDELT dataset, TeDS significantly enhances capture of complex temporal patterns by collaboratively optimizing diachronic and synchronous feature representations. These comparative results fully demonstrate TeDS's unique strengths in handling high-density facts and complex temporal dependencies, with its synchronous and diachronic perception capabilities being more fully realized.\n\n\nQ2: TPComplEx seems to be a very strong baseline, so could the authors use its source code to produce results on remaining three datasets? It would be much helpful to make a fairer comparison.\n\nA2: To compare, we reproduce TPComplEx (selecting best result from rank $\\in$ {1000, 1500, 2000}) on Wikidata12k, YAGO11k, and ICEWS18. Table 1 and 2 show that TeDS outperforms TPComplEx across all datasets, with significant improvements on Wikidata12k and YAGO11k, which we attribute to TeDS's modeling of temporal scenarios.\n\nBesides, we compare two under strongly constrained datasets in the Appendix of our manuscript (B.6. Performance comparison between TPComplEx and TeDS).\n\nFinally, we perform a computational complexity comparison between TPComplEx and TeDS. Table 3 shows TeDS's superior training speed: 43% faster per epoch on Wikidata12k (5.63s vs. 9.87s) and 35% faster on YAGO11k (2.82s vs. 4.33s) compared to TPComplEx. Crucially, these speedups are achieved alongside dramatic parameter reductions (e.g., 90% fewer parameters on YAGO11k). The marginally longer runtime on ICEWS05-15 (30.75s vs. 22.06s) is justified by TeDS using only 27% of baseline's parameters—a favorable tradeoff for memory-constrained applications. Table 4 reveals TeDS's most striking advantage: achieving superior performance with just 20.64M parameters versus TPComplEx's 201.2M on Wikidata12k—a 10× improvement in parameter efficiency.\n\nThe above analysis demonstrates that TeDS is particularly well-suited for large-scale TKG applications, maintaining competitive performance while significantly reducing memory overhead and computational resource requirements\n\n\nQ3: It seems the authors did not upload their source code and did not commit to releasing the code after acceptance.\n\nA3: All source code used for conducting and analyzing the experiments will be publicly available upon the publication of the paper under a license that permits free use for research purposes.\n\n\nQ4: It may exists some related works this paper hasn't included.\n\nA4: We add more important references to our paper (See our response to Reviewer C2mh's A2 for details). We continue collecting latest (2025) references (e.g., MTE, Neo-TKGC, and GLARGCN) to further validate TeDS's superiority (Table 5 and 6).\n\n\nQ5: In Section 3.2, the author may briefly introduce Quaternion and Hamilton rule with examples for readibility.\n\nA5: Based on your detailed comments, we have added the following content: Quaternion is a prominent example of hypercomplex number system, extending the traditional complex number system into four-dimensional space. A quaternion $Q$ consists of one real component and three imaginary components, defined as $Q=a + e \\mathbf{i} + f \\mathbf{j} + g \\mathbf{k}$, where $a, e, f, g$ are real numbers, $\\mathbf{i}, \\mathbf{j}, \\mathbf{k}$ are imaginary units, satisfying Hamilton rule:\n\n1. $\\mathbf{i}^{2} = \\mathbf{j}^{2} = \\mathbf{k}^{2}=-1$\n\n2. $ij=k, ji=-k$\n\n3. $jk=i, kj=-i$\n\n4. $ki=j, ik=-j$\n\nQ6: The font-size of most figures is overly small.\n\nA6: We have reviewed our manuscript and accepted your suggestions. In revised version, we will adjust the font size of the figures to enhance the readability of our manuscript.", "claims_and_evidence": "The performance improment compared with baselines is more marginal on the first three datasets (Table 2), could the authors explain this phenomenon?", "methods_and_evaluation_criteria": "Yes, the paper is easy to follow, with clear writing and well-presented technical details.", "theoretical_claims": "I didn't  check all the proofs.", "experimental_designs_or_analyses": "TPComplEx seems to be a very strong baseline, so could the authors use its source code to produce results on the remaining three datasets? It would be much helpful to make a fairer comparison.", "relation_to_broader_scientific_literature": "Modeling TKGC problem from both diachronicic and synchronic perspectives is novel and highly motivated. The usage of quaternion theroies is also interesting.", "essential_references_not_discussed": "It may exists some related works this paper hasn't included.", "other_strengths_and_weaknesses": "In Section 3.2, the author may briefly introduce Quaternion and Hamilton rule with examples for readibility.", "other_comments_or_suggestions": "The font-size of most figures is overly small.", "questions_for_authors": "Please see above comments.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes TeDS, a quaternion-based model for Temporal Knowledge Graph Completion (TKGC) that jointly learns diachronic (temporal evolution) and synchronic (cross-relation interactions) perspectives. The model demonstrates significant improvements over state-of-the-art baselines on six benchmarks, achieving deep integration of temporal and relational information through quaternion operations.

Strengths:

-	The paper proposes a novel method, which effectively captures both diachronic trends (temporal evolution) and synchronic interactions (relation dependencies) in a unified quaternion framework.
-	The method shows significant performance improvements over existing methods across multiple datasets, particularly in handling complex temporal patterns and sparse data scenarios.

Weaknesses:

-	The paper lacks a detailed discussion of computational complexity and scalability.
-	There is limited analysis of how the model handles different types of temporal annotations and emerging temporal patterns.
-	Some relevant approaches of mapping diachronicity and synchronicity to quaternion space need more thorough discussion and comparison.

TeDS presents a well-motivated and empirically validated approach to TKGC, with its dual-temporal perception being a key innovation. The authors have clarified several concerns raised by the reviewers through additional experiments and explanations in their rebuttal. However, the reviewers did not provide further responses.
Decision: Accept (poster)