Beyond Entity Correlations: Disentangling Event Causal Puzzles in Temporal Knowledge Graphs
Authors: Qian Chen
Jinyu Zhang
Ling Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Event Prediction; Temporal Knowledge Graph; Representation Learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Existing Temporal Knowledge Graph (TKG) representation learning approaches focus on modeling entity or relation correlations. However, since TKG datasets are constructed from events, which inherently contain heterogeneous causalities, focusing solely on entity or relation level correlations is inadequate for event prediction in TKGs. Although a TKG structural causal model can be established as a theoretical framework for event level causality disentangling, practical disentanglement is non-trivial due to the lack of explicit supervision signals. To this end, we propose a Heterogeneous Event causality Disentangling Representation learning Approach (HEDRA) for TKG reasoning, which is the first work that focuses on disentangling heterogeneous causalities at the event level in TKGs. Specifically, a counterfactual detector module is proposed to disentangle non-causality by leveraging event importance and distributional discrepancies of event representations. Moreover, an Instrumental Variable (IV)-guided disentangling module is proposed to disentangle spurious causality by constructing IVs, which can produce robust event representations against spurious causality through multi-view causality subgraphs. Finally, an evolutionary orthogonal module is proposed to separate dynamic causality from static causality for event prediction. Comprehensive experiments on five real-world datasets demonstrate that HEDRA achieves the state-of-the-art performance.

Published as a conference paper at ICLR 2026
BEYOND ENTITY CORRELATIONS: DISENTANGLING EVENT CAUSAL PUZZLES IN TEMPORAL KNOWLEDGE GRAPHS
Qian Chen, Jinyu Zhang, Ling Chen
State Key Laboratory of Blockchain and Data Security
College of Computer Science and Technology. Zhejiang University, Hangzhou, China qi anchencsees zju.edu.eee cn, jy zhangêcs jju. edu.cn, i Lingchen& cs. 2 zju. edu. cn
ABSTRACT
Existing Temporal Knowledge Graph (TKG) representation learning approaches focus modeling entity or relation correlations. However, since TKG datasets are constructed from events, which inherently contain heterogeneous causalities, focusing solely entity relation level correlations is inadequate for diction in TKGs. Although a TKG structural causal model can be established as a theoretical framework for event level causality disentangling, practical disentan- glement is non-trivial due to the lack of explicit supervision signals. To this end, we propose a Meterogeneous Event causality Disentangling Representation learn- ing Approach (HEDRA) for TKG reasoning, which is the first work that focuses on disentangling heterogeneous causalities at the event level in TKGs. Specif- ically. counterfactual detector module is proposed to disentangle non non-causality by leveraging event importance and distributional discrepancies of event represen- tations. Moreover, an Instrumental Variable (IV)-guided disentangling module is proposed to disentangle spurious causality by constructing IVs, which can pro- duce robust event representations against spurious causality through multi-view causality subgraphs. Finally, an evolutionary orthogonal module is proposed to separate dynamic causality from static causality for event prediction. Comprehen- sive experiments on five real-world datasets demonstrate that HEDRA achieves the state-of-the-art performance.
pre-
INTRODUCTION
Temporal Knowledge Graphs (TKGs) are dynamic graphs composed of events (s, F, o, f), where s and denote subject and object entities, speciiies the relation between them, and indicates the timestamp (Chen & Chen 2024). TKG representation learning maps temporally evolving entities and relations into continuous low-dimensional vector space capture both temporal evolution and structural information in TKGs (Li et al. (022). The event prediction task then leverages the repre- sentations learned from historical events to infer which relations are likely occur between entities in the future. TKG representation learning underpins downstream applications, e.g., knowledge rea- soning and anomaly detection (Saxena al. (02T). The variety of correlations among entities and the complexity of temporal patterns make effective TKG representation learning challenging.
Existing TKG representation learning approaches focus on modeling correlations among entities or relations. Some approaches construct entity graphs, where entities serve as nodes and relations be- tween them serve as edges, and Iearn representations based on graph reachability (Li et al. 2022; Bai ct al. 2023 Chen et al. 2024b; Zhang et al. 2024). Other approaches introduce derived structures, e.g., entity groups, hypergraphs, and evolutionary clusters, to capture high-order correlations among entities relations that not directly connected (Zhang et al., 2022 Tang & Chen 2024 Tang eet al. 2024 [Chnn & Chen 2024). However, since TKG datasets are constructed from events, which foucsig
inherently contain heterogeneous causalities, focusing solely on entity or relation level correlations is inadequate for event prediction in TKGs.
"oorreponning author.

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EVENT
EVENT
Spurious Causality
Landfall
2023-05-15
2023-08-23
Non-causality
Typhoon "Lan'
Japan
China
EVENT
EVENT D
EVENTE
Treated Water
Causality
Treated Water
Dynamic Causality
Imports
2023 07 04
2023-05-24
2023 CD 24
JAEA
Japan
Japan
The Pacifie
China
Japan
Figure I: An example of heterogeneous causalities at the event level. IAEA denotes the International Atomic Energy Agency.
In fact, static causality and dynamic causality are ubiquitous in dynamic graphs. Here, static causal- ity refers to time-invariant causal dependencies, whereas dynamic causality captures time-dependent causal dependencies that evolve across timestamps (Zhao & Zhang 2024). In addition, TKGs also include non- non-causality that does not benefit event prediction and spurious causality that impedes the model's 's acquisition of causally relevant discriminative information for event prediction. Figure []] illustrates heterogeneous causalities at the event level, i... static causality, dynamic causality, non- causality, and spurious causality. First, the IAEA comprehensive safety review (Event A) provided the institutional framework that underpinned Japan's 's decision to begin the treated water release (Event D), exemplifying static causality. Second, when Japan initiated the discharge, China an- nounced an immediate ban on Japanese seafood imports on the same day (Event E), illustrating dynamic causality. Third, the BRIC, i.e., an international organization comprising Brazil, Russia, India, and China, summit held in Johannesburg (Event C) is non-causality with respect to these events. Fourth, Typhoon "Lan" made landfall Japan and disrupted transport (Event B). Overem- phasis on Event B could mislead the model to attribute export changes to Typhoon effects rather than the policy driven seafood ban, demonstrating spurious causality.
Although structural causal model tailored to event level causalities in TKGs can be posited, it is non-trivial to disentangle static causality, dynamic causality, non-causality, and spurious causality at the event level in TKGs. The challenge lies in identifying and estimating them from observational data, since existing TKGs lack explicit supervision signals to distinguish these causalities.
To address the aforementioned challenges, Disentangling Representation learning Approach (HEDRA) for temporal knowledge graph reason- ing. To the best of our knowledge, HEDRA is the first work that focuses disentangling heteroge- neous causalities al the event level in TKGs, which constructs event representations from quadru- ples and progressively disentangles non-causality, spurious causality, static causality, and dynamic causality among TKG events. Our contributions are summarized as follows:
propose Heterogeneous Event causality
We propose a TKG structural causal model to formally define non-causality, spurious causality, static causality, and dynamic causality, which establishes a theoretical framework for event level causality disentangling in TKGs.
We propose counterfactual detector module to disentangle non-causality in TKGs by leveraging event importance and distributional discrepancies of event representations, which includes contrastive loss to encourage event pairs with low non-causality weights to be closer and those with high non-causality weights to be more separated.
We propose Instrumental Variable (IV)-guided disentangling module to disentangle spurious causality in TKGs by constructing IVs, which can produce robust event repre- sentations against spurious causality through multi-view causality subgraphs. In addition, we propose an evolutionary orthogonal module to separate dynamic causality from static causality for downstream event prediction.
Experiments on five real-world datasets demonstrate that HEDRA achieves the state-of- the-art performance. HEDRA outperforms the runner-up by an average of 5.70%, 7.51% %, 7.21 %,, and 2.30% in MRR, Hits @ 1, Hits@3, and Hits @ 10, respectively.
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2 RELATED WORK
TKG Representation Learning. TKG representation learning approaches modeling pairwise cor- relations typically combine Graph Convolutional Networks (GCNs) and Recurrent Neural Networks to capture structural information and temporal evolution, respectively (Li et al. 202Tb Sun et al.) 2021 Li et al., 2022 Bai et al. 2023; Chen et al. 2024b). addition to pairwise correlations, high-order correlations among three or more entities relations are modeled through derived struc- tures, i.., communities, hypergraphs, and evolutionary clusters (Zhang et al., 2022 Tang & Chen 2024 Tang et al. 2024| Chen & Chen 2024). However, TKG datasets, e.g.. ICEWS, S, centered on
international political events, inherently involve complex causal dependencies. Focusing solely on entity or relation level correlations is therefore inadequate for event prediction in TKGs. To address this, we propose HEDRA, the first framework to disentangle heterogeneous causalities at the event level TKGs.
Graph Causality Learning, Static graph causal learning approaches primarily focus on modeling spatial causality within static graphs. These approaches generally aim to reveal causality by gener- ating interpretable subgraphs (Luo et al. [2000] Yuan et al., [2020] Ying et al., 2019; Fan et al. [022]
Gao et al. 2023). Dynamic graphs, prevalent real-world scenarios, have motivated research on dynamic graph causal learning, which typically explores both spatial causality and temporal causal- ity (Zhao & Zhang, 2024, Chen et al., 2024a). Despite progress in dynamic graph causal learning, most approaches mainly model static and dynamic causalities while overlooking spurious causal- ity, which impedes the acquisition of causally relevant information for event prediction. Moreover, there is no theoretical framework to disentangle heterogeneous causalities at the event level in TKGs. To fill this gap, we propose HEDRA, which constructs event representations from quadruples and progressively disentangles non-causality, spurious causality, static causality, and dynamic causality among events in TKGs. The comprehensive related works can be found in Appendix A
3 PRELIMINARIES
3.1 DEFINITIONS
Definition (TKG). A TKG is defined as sequence of timestamped events, each represented as = ((s,r, o, t)ls &, r E R, E E, e TT), where E, R. and 'T denote the sets of entities, relations, and timestamps, respectively. G denotes the set of events at timestamp t.
Task (Event Prediction). The event prediction task in TKGs aims to estimate the probability distri- bution over candidate relations between subject entity and an object entity conditioned on the historical event sequence g gl:T-1, Formally, this task can be expressed as p(fls,o,g" G.:TT-1)) where T denotes the total number of historical timestamps.
3.2 EVENT LEVEL TKG STRUCTURAL CAUSAL MODEL
The event level TKG structural causal model (SCM) is shown in Figure 2, which comprises nine variables: TKG G, historical events H. non-causality N, causality C, spurious causal- ity P. dynamic causality D, static causality S, representation R, and prediction y. The di- rected edges denote cause-effecc. The explana- tions of the TKG SCM are as follows:
9 TK3
2. Hatoiical Evc 15
2
Nen-cRu calll
Coussity
Sputoos cauesity
Dycamic cauedily
Stalic caueaily
V. Depremethe
Figure 2: Event level TKG SCM.
G + H. + C: Historical events H. are derived from the TKG G. within which the genuine causal regularities distilled causality C.
P + H + N: Historical events H give rise to both non-causality / and spurious causality P. Specifically, .V' denotes correlations irrelevant to event prediction, while P denotes correlations that obstruct the model from capturing causally relevant discriminative information.
+- C + S: Causality C can be disentangled into dynamic causality and static causality S, both of which jointly drive the learning of high-quality entity and relation representations R.
N + R < P: Non-causality N and spurious causality P interfere with the representation learning process, introducing noise and consequently diminishing the quality of representation R.
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R - V: The objective of HEDRA is to leverage the learned representations R. for event pre- diction, where the target y is ideally determined by dynamic causality D and static causality S through R. with the effects of non-causality N and spurious causality P suppressed.
From the TKG SCM, two backdoor paths exist between and V/ i.e., C + H - y and + p R - V. where N and P as confounders that bias the estimation of the causal effect C + J and thereby interfere with event prediction. Moreover, when estimating the effect of makes confounder; symmetrically. when estimating the effect of S on V/ the path S + + -
H C
D on V, the path + C +
R
R + ) makes D confounder.
Backdoor Adjustment. HEDRA aims to progressively disentangle non-causality, spurious causal- ity, static causality, and dynamic causality, ultimately leveraging static and dynamic causalities for event prediction. To this end, is essential to block backdoor paths so that the model focuses on the causal effect of C. Within this framework, do-calculus (Pearl et al. 2000) provides a principled tool to eliminate the influence of confounders. Specifically, when estimating the causal effect of C on Y, adjustments for V and P are required, while estimation of the effect of D ) requires adjusting for S. Formally, the backdoor adjustment expressed as (see Appendix B for derivation):
P()) = E d)))) P(S)do(D)) E Σ P(T) Σ P(P) Σ P()IG). (I)
However, implementing such backdoor adjustments in TKGs poses significant challenges, since existing TKGs lack explicit supervision signals to distinguish non-causality, spurious causality, static causality, and dynamic causality.
Our Solution. To address the above challenge, we propose HEDRA, a framework designed to pro- gressively disentangle heterogeneous event causalities in TKGs. each timestamp, entity and re- lation representations are updated through relation-awann GCN, followed by event representation construction. The counterfactual detector module disentangles non-causality by leveraging event importance and distributional discrepancies, guided by a contrastive loss. The Instrumental Variable (IV)gguided disentangling module introduces IVs to disentangle spurious causality, with a robust- ness loss based multi-view causality subgraphs. The evolutionary orthogonal module further disentangles dynamic and static causalities under orthogonality constraints, while an evolutionary loss preserves the temporal dependence of dynamic components and the temporal independence of static components. Finally, by modeling dynamic and static causalities across timestamps, an event graph is constructed and processed with event GCNs to refine entity and relation representations for event prediction. The framework of HEDRA is illustrated in Figure 3
4 METHODOLOGY
4.1 EVENT REPRESENTATION CONSTRUCTION MODULE
Relational Message Passing. Structural dependencies among entities and re- lations timestamp t are modeled by a relation-aware GCN RReLU (1, Wi (M! + h.tt) + W2hh"). where Nº = ((s,,) E G') denotes the set of subject-relation pairs forming incoming edges to object at timestamp t. h h and h represent the layer-l representations of subject, object, and relation at timestamp t, respectively. Wi and W₂ are learnable parameters for neighbor aggregation and the self-loop, respectively. d, is the in-degree of object. Entity and relation representations are randomly initialized. For brevity, the layer index / is omitted in subsequent sections.
htfll
Relation Update. The relation representation at timestamp & is influenced jointed by the r-related entity representations at the same timestamp and its historical representation. Formally, let hú, v denote the r-related entity representations at timestamp t. The update of relation representation is formulated as h = ([ himato; ; h h,-1)), ]), where [;] denotes concatenation. pool is mean pooling.
Event Representation Construction. To capture the semantic interactions among subjects, rela- tions, and objects at each timestamp, event representations constructed by jointly encoding the three components of a TKG fact. Formally, for the quadruple (s, r, f) with subject representation hi, relation representation ht, and object representation hgg the event representation is formulated as h SMLP (I h;;; h;: 16 }), where fMLP denotes a multi-layer perceptron.
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Timestamp
importance Low Datritufoonl Dicrepencyy
Non causality
Spurious Causaliyy
Event
High Distibutiona
Rotation
Static
Event Graph
Disentangling Heterogeneous Causalities
Losses
1
Importance
Disriutton
Alliadive
4
Unscard
Enilyy Graph
3
Repullivo Farce
Countorfachua Detector Module
Contraetive Loss
Ensode
Instumerral
Mull-noww
Varadiis
S Atsecivv Porce
Prediction Timestamp
Diseard
Caussilly
IV-giided Disentanginn Module
Robusiness
Dynam Frendwr
Orthogonaity
Updated Eritly Graph
GRI
Dynamio Cauasityy
Event GCN
State
Stanc
Evolutonary Orthogonal Module
Evolutionary Loss
Figure The framework of HEDRA, illustrated with timestamp T' 1 as an example.
4.2 COUNTERFACTUA DETECTOR MODULE
Candidate Graph. To avoid the quadratic complexity of fully connecting all event pairs, candidate graph is constructed through k-nearest-newe neighbbrss (Cover Hart 1967) the representation space. Let (vem,, 1 denote the set of event representations at timestamp where E is the number of events. The binary adjacency matrix is Ce (0, 1}, with Cū indicating candidate edge j-
Event Importance. Higher edge importance implies increased probability of causal dependency between events. For each candidate edge i +.j, the event importance is computed as:
Cạj LeakyyeLLU (aaeeeuuua""WWhahheeehe
[Waheeem. Wafhevemss): A. ExENings exp(er,)*
exp(e:j)
(2)
where W3, W4, and a are learnable parameters. (j) = {k Ckz = 1} means the in-degree of event j. A, E (0, 1] is the importance weight on edge i-jj.
Distributional Diserepancy. Larger distributional discrepancy between event representations im- plies decreased probability of causal dependency. Each event representation is mapped to parameterss of diagonal Gaussian posterior through multi-layer perceptrons fr and fa as:
14, ())
a; softplus (eo(hesem:)))
where μ4 and d, are the mean and standard deviation vectors of the Gaussian q; = Nu,, diag o )), respectively. For a candidate edge i + j. the distributional discrepancy is the Hellback-Leiblee divergence (Kullback & Leibler 195T) between y; and 4j as:
of L.a + (pid U5,a)² log
DiJ = KT. (4: (1)
(4)
2
of
33d
where is the dimension of representations.
Non-causality Mask. Event importance and distributional discrepancy are fused on the candidate graph to produce soft non-causality mask as:
8 (Qatta logit(A +) 8KL D) C, NN = -
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where Oattnn and SKL fixed loss-weight coefficients satisfying Gattn + 6KL 1 and set to 0.5 in all experiments to give equal weight to event importance and distributional discrepancy. is small constant for numerical stability. a is the sigmoid function and logit is its inverse. C denotes the Hadamard product. is the all ones matrix. The larger Aij decreases M and indicates higher causal dependency likelihood, whereas the larger Dij increases Mry and indicates higher non-causality likelihood.
Contrastive Loss. A contrastive loss is proposed to encourage event pairs with low non-causality weights to be closer and those with high non-causality weights to be more separated. Let 8ij cos (vent, j denote cosine similarity, let 7 > 0 be the temperature, and let P {(1,5) i + j. Cij- = = be the set of candidate pairs. The contrastive loss is formulated as:
Lcon
[11 (1-M5 (lggoogosss - M log(1 - ((sr/T))))
(6)
IPI
4.3 IV-GUIDED DISENTANGLING MODULE
Instrumental Variable Score. After non-causality has been disentangled, edges between event
pairs may still mix genuine and spurious causalities. In causal learning, the Instrumental Variable (IV) approach is commonly employed disentangle them (Gao al. (023). Accordingly, IV encoder fiv, implemented as a multi-layer perceptron, is adopted produce the IV score for each edge i i as:
m, fiv( fiv(he ho logit(Ar; + +), -Dis).
Herein, only standard TKG quadruples are observed, and no causality labels are available. The IV encoder produces scores that are used solely inside the IV-guided disentangling module (IVDM) to separate genuine from spurious causalities. This design enforces a neural analogue of the exclusion restriction, since I1 does not directly enter the final scoring function. Conditioned on the observed history graph and current event representations, Ha is assumed to be approximately independent of the unobserved noise the genuine- versussspurious split, playing the role of the standard IV independence assumption.
Spurious Causality Mask. Let M = 1 MC denote the complement of the non-causality mask. Based on the IV score, the gated matrix II = M @ is employed to disentangle genuine and spurious causalities
0. Quantile, (Mi My 03),
M If 11122000 0.1).
1-=1-M²
(8)
where a E (0, 1) specifies the fraction of top-scoring edges. 0, is the a--uantile of IV scores. MP selects the top-ar edges as genuine causality while M" retains the remainder as spurious causality.
Multi-view Propagation. Although the spurious causality mask partitions the edges into genuine and spurious causalities, the IV scores may be imperfect in practice. To enhance robustness, three subgraphs are constructed: the genuine-view subgraph Ggen with M the spurious-view subgraph
Gspur with M" and the all-view subgraph Gall combining both. Heterogeneous convolution is applied on each subgraph to derive complementary event representations, which is formulated as:
H HConv (Ggm, Heven): H HConv (CCovv Hevem),
H HConv (Gan, Hevex).
where HConv(-) denotes heterogeneous event convolution.
Robustness Loss. To enhance robustness under imperfect IV estimation, robustness loss is de- signed based on different subgraph propagation views, consisting of alignment and separation terms. The alignment term draws the all-view representations toward the genuine-view representations, while the separation term pushes the spurious-view representations away from the genuine-view representations. This process is formulated as:
F
Loob Aaalgn E
|- log o (s(han.s. [/Tr]
+ damp E
[- log (1 (s(hipu,s hgon.)) s))T))]
Calign
Comp
(10)
where Àalign and Asep are fixed trade-off off coefficients with Aalign + Asep and are set to 0.5 in all experiments to give equal weight to the alignment and separation terms.

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4.4 EVOLUTIONARY ORTHOGONAL MODULE
Static and Dynamic Causalities Masks. To disentangle static and dynamic causalities, each event representation projected into static component and raw dynamic component by two multi-layer perceptron encoders fstat and fayn as:
S.1 eveni
Setas (et
D.A gvent.
-day (Fagen.))
(11)
Then, the dynamic component is obtained by orthogonalizing the raw dynamic component with respect to the static component as:
D.t (h oowee Avees..
Fevent
1 Agvent,
Fevent
(12)
[b ovent, +
A classifier fMLP is employed distinguish dynamic from static causality, follows:
Pij o [fUL [ h g
[h ovene
h (mmmrlll))
(13)
Herein, the dynamic causality mask is defined as M = H(p > 0.5} 3 M and the static causality mask M = -
Evolutionary Loss. An evolutionary loss is designed to preserve the temporal dependence of dy- namic components and the temporal independence of static components as:
Levo Adya
G
Revent
fGRU - I1
(Peeenl.
+
[9]
h Revent
h eveeni
S,1:t-1
||
(14)
BEG
9E9
Cayn
Catat
where Adyn and Astat are fixed trade-off coefficients satisfying Aayn + Astat and are set to 0.5 in all experiments to give equal weight to the dynamic and static components. G is the set of r, groups. h denotes the group-level mean of the static components, and h hevent. is the historical memory of the dynamic components.
Static and Dynamic Causalities Modeling. Static and dynamic causalities are essential for event prediction in TKGs. To exploit them explicitly, message passing is conducted in the static-view subgraph Gsa and the dynamic-view subgraph Gayn- Heterogeneous convolution applied to the genuine-vies representations H ge and the resulting statie-view and dynamic-view representations are fused and normalized to update event representations as:
H Norm Ws [HConv(Guy) H HConv HTa)))
(15)
Updated entity and relation representations H. and H, are obtained via inverse event construction.
4.5 EVENT PREDICTION
ConvTransE Shang et al. 2019) is employed as the decoder to estimate the relation probability distribution for given entity pair p( (, g1: a oHH, ConyTransE(e,, where & denotes
the predicted probability vector over relations and H, the relation representation matrix. The training objective for event prediction is to minimize the cross-entropy loss:
N₂ Σ
1
LTKG
(yis log + (1 logs) pi.)).
(16)
Ns
where Ny and N, denote the number of training samples and relations, respectively. Va is the ground-truth label for relation j in sample (1 if the event occurs, O otherwise), and Pij is the predicted probability. The overall training objective of HEDRA integrates multiple components:
L (1 Acon Arob
Xevo) CTKG + Xcon Geon + ArehCrob + Aevo
(17)
where Acony Arbb and Aevo are scalar coefficients for contrastive, robustness, and evolutionary losses, respectively. All hyperparameters constrained within (0, 1).

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Table 1: The performance of HEDRA and the compared approaches on ICEWSI4 and ICEWSI8. An asterisk ("*") indicates that HEDRA significantly outperforms the compared approaches based on pairwise t-tests at 95% confidence level. The best performance highlighted in bold, while the runner-up is underlined.
ICEWS14
ICEWS18
Appreach
@its@
Hits@3
Hits
Hits@
Hits@
Hitx@
TTransE (WWW 2018)
22.36*
13,41*
24.40*
64
16.39
8.43*
17.21
31.72*
TA-TransE (EMNLP 2018)
20.94*
13.77
24.11*
36.06*
21.64*
14.11
24.89*
37.64
RE-NET (FMNTT 2020)
38.53*
22.53*
44.47a
74.05*
45.70*
Glean (KDD 2020)
36.07*
22.17*
39.524
64,75*
35.15*
22.02
38.017 28.07*
64.24*
RE-GON (SIGIR 2021)
40.85*
28.154
45.334
6%..3*
40.68*
27.01
46.31
69.51*
DACHA (TKDD 1022)
40.69*
27.28*
45.79*
68.44*
40.50*
27.83*
45.26*
69.21
(UCAAI 2022)
29.524
70.66*
30.19*
46.99*
73.90*
EvoExplore (KBS 2022)
28.119 19
13.97
33.45*
57.67*
29.8 29.829
18.50*
30,08%
58.01
GTRL (TKDE 2024)
38.57
27.36*
42.15*
66.35*
38.43*
27.48*
43.06*
67.82*
DHyper (TOIS 2024)
41.71*
29.37
45.69*
69.32*
42,84*
29.96*
47.52*
70.82*
DECRL (NeurIPS 2024)
42.90
30:49
47.06*
70.01
43.36*
30.64*
47.96*
71.124
HEDRA
47.86
35.28
53.32
75.65
46.77
33.66
52.33
Improvement
11.56%
15.71%
13.30%
2.16%
7.86%
9.86%
9.12%
+0.03%
5 EXPERIMENTS
5.1 EXPERIMENTAL SETUP
Datasets and Experimental Settings. HEDRA is evaluated on five widely adopted real-world TKG datasets: ICEWS14, ICEWS18, GDELT, WIKI, and YAGO (Trivedi et al.] 2017 Li et al.) 20216). ICEWS14 and ICEWS18 are derived from the Integrated Crisis Early Warning System [Boschee et al. 2015). which records political events at daily granularity. GDELT, sourced from the Global Database of Events, Language. and Tone (Leetaru & Schrodt 2013). captures human activities with timestamps at 15-minute intervals. WIKI and YAGO are organized at the yearly level, which are constructed from Wikipedia and YAGO3 (Mahdisoltani et al. 2013), respectively. The Mean Reciprocal Rank (MRR) and Hits@ 1/3/10 are adopted as evaluation metrics. Detailed statistics of the datasets and other experimental settings are provided in Appendix C.I Unless otherwise stated, all loss-weigth coefficients in HEDRA, including Qattn and 3KL, and aalign and Asep are treated as fixed design choices and set to 0.5 in all experiments. They are introduced to balance the corresponding components and keep them dataset-specific tuning knobs. A representative sensitivity study on Cattn and Aalign on ICEWS 14 dataset is reported in Appendix C.4 indicating that HEDRA is robust moderate changes of these coefficients within a reasonable range.
comparable scale, rather than to serve as
Baselines. HEDRA is compared with eleven representative TKG representation learning ap- proaches, grouped as follows: shallow encoder based approaches, i.e., TTransE (Leblay & Chekol 2018 and TA-TTannEE
Starcia-urras et al., 2018);; GNN based approaches, i.e., RE-NET (Jin al., 2020 Glean (Deng et al.) (2020). RE-GCN (Li et al., 2021b), DACHA (Chen et al. [021)) )), and
TiRGN (Li et al.] 2022)); and derived structure approaches, i.e., EvoExplore (Zhang et al. 2022). GTRL. (Tang & Chen 2 DHyper (Tang et al. 2024), and DECRI. (Chen & Chen 2024). De- tailed descriptions of these baselines are provided in Appendix [c.] Since some approaches do not target event prediction task and others collapse relations into four coarse-grained categories that differs from our settings, to ensure a fair comparison, we follow the official implementations of all baselines and tune hyperparameters report the results.
5.2 PERFORMANCE COMPARISON
The performance of HEDRA with the compared approaches on the ICEWS14, ICEWSI8, WIKI, YAGO, and GDELT datasets presented in Tables 2 and It can be observed that HEDRA achieves average improvements of 5.70%, 7.51%, 7.21% and 2.30% over the runner-up in terms of MRR and Hits 1/3/10 on five datasets, respectively. On ICEWS18 dataset, HEDRA yields a slightly lower Hits @ 10 than RE-NET. This difference can be attributed to RE-NET's global graph mechanism, which aggregates broader historical information and tends to retain more potentially relevant candidates within the top- 10 range, whereas HEDRA is designed to emphasize event level causality disentanglement and improve the quality of the top ranks, leading to more pronounced gains in MRR, Hits@ 1, and @. Overall, these results show that disentangling heterogeneous
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Table The performance of HEDRA and the compared approaches on WIKI and YAGO. Since the YAGO dataset contains only 10 relation types, the @its@) 10 metric is not statistically meaningful and is therefore denoted "_" Other notations follow Table
WIKI
YAGO
Approach
MRR
Hits 1
Hits
Hits 10
MRR
Hits @1
Hits
Hits 10
TTransE (WWW 2018)
69 60.64
62.54
71.57*
84.84*
88.35
$1.49*
94.24
TA-Trans (EMNLP 2018)
70.76*
66.26*
74.32*
88,47*
87.16"
85.53*
90.50*
RE-NET (EMNLP 2020)
75.29*
57.08*
90.25*
97.64*
92.24
89.43*
92.43*
Glean (KDD 2020)
91.76*
86.18*
90.55*
92.84
90.19
88.90*
91.71*
GCN (SIGIR 2021)
24
99.414
DACHA (TKDD 2022)
75.86*
68,91
78.79*
90.91
92.54"
89.17"
94,77*
TIRGN (UCAA 2022)
99.00*
98.53*
99.35*
99.51*
98.53
97.91*
98 90*
EvoExplore (KBS 2022)
78.71
73.13*
81.42*
88.43
93.92
91 477
2
GTRI. GTRI. (TKDE 2024)
92.68*
89.18*
92.34
95.63*
92.36"
90.71
93.95*
DHyper (TOIS 2024)
OOM
OOM
0OM
OOM
94,38"
96.01*
DECRL (NeurIPS 2024)
93.20
90.91
94.33*
14"
844
15*
97.09*
HEDRA
99.14
98.73
99.48
99.79
99.12
98.77
99.31
Improvement
0.14%
0.20%
0.13%
0.26%
0.60%
0.88 %
0.41%
Table 3:
The performance of HEDRA and the compared approaches on GDELT. "TLE" indicates single epoch exceeded 24 hours. "OOM" indicates out of memory. Other notations follow Table !
Approach
MRR
Hits@
Hits@3
Hits@ 10
I'TranSE (WWW WWW 2018)
15.09* 20.674
4.71* 10,23*
13,69*
39.72*
TA TransE (EMNLP 2018)
19.88
35.89*
RE-NET (EMNLP 2020)
TLE
TLE
TLE
TLE
Glean (KDD 2020)
17.91
8.21
16.65*
39.18 19.18
RE-GCN (SIGIR 2021)
21.35*
11,20*
21.73*
44.53*
DACHA (TKDD 2022)
TLE
TLE
TLE
TLE
TiRGN (UCAA 2022)
22.46*
12
22.13*
45.89*
Evelixporre (KBS 2022)
18.72
7.71+
18.374
43.87+
GTRL (TKDE 2024)
19.51
8.40
19,26*
41.074
DHyper (TOIS 2024)
0OM
DECRL (NeurlPS 2024)
22.74
12.56*
22,57
45.07*
HEDRA
24.64
13,93
25.53
49.02
Improvement
8.36%
10.91 %
13.11%
6.82 %
event level causalities while discarding non-causality and spurious causality enables HEDRA to capture more discriminative entity and relation representations. The computational complexity of The observed runtime increase is acceptable in light of the
HEDRA can be found in Appendix C.3 significant performance gains.
5.3 ABLATION STUDY
To assess the contribution of each com- ponent in HEDRA, ablation studies are
Table The performance of HEDRA and its variants.
The best performance is highlighted in bold.
performed on the ICEWS14 dataset,
as shown in Table 4 Specifically, HEDRA-W/O-CDM removes the coun- terfactual detector module with the contrastive loss. HEDRA-w/O-El and HEDRA-w/O-DD remove the event im- portance and the distributional discrep- ancy for constructing the non-causality mask, respectively. HEDRA-W/O-IVE removes the IV- guided disentangling module with the robustness loss, and SEDDRA-W/OEEOM excludes the evolu- tionary orthogonal module with the evolutionary loss. Since all ablated variants still share the same event level causality disentanglement framework, which provides a strong backbone compared with traditional entity level baselines, module-wist ablations tend to result in numerically modest perfor- mance drops and at the same time reflect the robustness of HEDRA.
Approach
MRR
Hits@1
Hits@3
Hits 10
HEDRA w/o CDM
47.11
34.25
$2.12
75.04
HEDRA-W/O-F
47.34
34.65
52.33
75
HEDRA A w/o DD
47.25
34.46
52.63
75.35
HEDRA w/o IVDM
46.47
33.77
51.65
74.75
HEDRA- NEDRA-W/O-EOM.
46.24
33.49
$1.79
74.10
HEDRA
47.86
35.28
53.32
The ablation results show that HEDRA-W/O-CDM exhibits only modest performance drop, sug- gesting that the con-causality removed by the counterfactual detector module provides limited ben- efit to event prediction. In contrast, HEDRA-w/O-IVDD suffers substantial performance degra- dation, demonstrating that the IV-guided disentangling module plays a critical role eliminating spurious causality that impedes the model's acquisition of causally relevant discriminative informa-

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Table 5: Top-5 predicted relations for two representative test samples on ICEWS14. Correctly predicted relations are indicated by leading check mark (v) and highlighted in bold.
Test sample 1: (Barack Obama, ?, Xi Jinping, 2014 2014/11/13)
DECRL
HEDRA
Sign formal agreement
v Sign formal agreement
Host a visit
Express intent to meet or negotiate regeiin
Express intent to meet or negotiate
Make statement
v Cousult
v Make visit
Make statement
v Consult
sample 2: (Police (Hong Kong),
Protester (Hong Kong), 2014/11/29)
DECRL
HEDRA
// statement
// Make statement detain. charge logal action Fight with small arms light weapons conventional military Investigale
Arrest, detain. Investigate
logal action
Return release person(s)
conventional military
tion, which is essential for event prediction in TKGs. The hyperparameter sensitivity analysis can be found in Appendix C.4 The results indicate that the performance of HEDRA is insensitive the history window length but shows notable dependence on the neighbor count which is defined in the candidate graph.
5.4
CASE STUDY
Table compares the predictions of HEDRA and the runner-up approach DECRL two representative ICEWS14 test samples, one exhibiting a positive relational trend and the other a negative trend. Specifically, the table lists the top five predicted lations for test sample 1 (Barack Obama, ?, Xi Jinping, 2014/11/13) and test sample (Police (Hong Kong), ? Protester (Hong Kong), 2014/11/29). For test sample more ground- truth relations are correctly identified by HEDRA, which predicts "Make a visit" rather than the inverse "Host visit". indicating that event level causal disentangling better models relation direc- tionality. By contrast, DECRL, which primarily captures entity correlations, struggles to distinguish relation directions. For test sample 2, only negative relations are predicted by HEDRA, whereas DECRL outputs the positive relation "Return, release person(s)". likely because it does not con- sider heterogeneous causalities at the event level in TKGs, which can lead to predictions with senti- ment opposite to the ground-truth relations. In Appendix C.5 additional diagnostics of the training dynamics and IV-guided disentangling behavior are presented, together with few-shot robustness experiments ICEWS14 and ICEWS18 datasets. Another case study be found in Appendix
C.6
CONCLUSIONS AND FUTURE WORK
In this paper, based TKG structural causal model that establishes the theoretical framework for event level causality disentangling, a Heterogeneous Event causality Disentangling Representation learning Approach (HEDRA) is proposed, which is the first work that focuses on disentangling heterogeneous causalities at the event level in TKGs. Comprehensive experiments are conducted on five real-world datasets, including the comparison with baselines, ablation study, hyperparameter sensitivity analysis, running time analysis, training dynamics analysis, few-shot relations prediction, and case studies, which demonstrate the superior performance of HEDRA.
Future work includes replacing the fixed quantile rule in the IV-guided module with learned, data- driven calibration mechanism for selecting genuine edges, designing lightweight global memory modules to enhance long-range history modeling and Hits 10 on large-scale datasets, and fur- ther reducing computational overhead via sparser causal subgraph construction, more efficient event causality disentangling, and sparsity- Another promising direction is to combine HEDRA with using LLMs to provide semantic priors for event and relation representations and to leverage tex- tual context for data-sparse and long-tail relations, while preserving explicit event level causality disentangling.
distributed implementations event prediction frameworks,
datasets such GDELT.
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ACKNOWLEDGMENT
This work was funded by the National Key Research and Development Program of China (No. 2024YFB3312900).
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A
COMPREHENSIVE RELATED WORK
A.1 TKG REPRESENTATION LEARNING
Current TKG representation learning approaches primarily aim to model correlations among entities or relations, which can be categorized into two main categories: modeling pairwise correlations between entities relations and modeling high-order correlations among entities relations.
TKG representation learning approaches modeling pairwise correlations typically combine Graph Convolutional Networks (GCNs) and Recurrent Neural Networks capture structural information and temporal evolution, respectively (Li al. 2021b) 2022; Bai et al. 2023). For example, RE-GCN (Li al. 2021b) combines GCNs with Gated Recurrent Units (GRUs) to capture structural and tem- poral information, respectively. Similarly. TiRGN (Li et al. 2022 uses multi-relational GCNs and
GRUs capture the structural information of entities across different temporal patterns. These ap- proaches generally stack multiple layers of networks to model pairwise correlations between distant entities, which can result in over-smoothing. To address this, some TKG representation learning approaches introduce paths or subgraphs to model pairwise correlations between distant entities or relations more effectively (Li et al. 2021a] [Sun et al., 2021 Chen al., 2024b Zhang al. 2024). For example, CluSTeR (Li et al.) 2021a) and TiTer (Sun et al.) (021) utilize reinforcement learn- ing discover tross-tempprra clue paths that model pairwise correlations between entities. LogCL
(Chen et al. 2024b) constructs both local and global subgraphs based on queries to achieve a similar goal.
In addition to pairwise correlations, high-order correlations among three or more entities or relations are modeled through derived structures, i.c., communities, hypergraphs, and evolutionary clusters (Zhang et al. 2022; Tang & Chen 2024 Tang et al. 2024 Chen & Chen 2024). For example, EvoExplore (Zhang et al. 2022) leverages dynamic communitiss based on soft modularity to model implicit correlations among multiple entities. DHyper (Tang et al. (2224) introduces hypergraph neu- ral networks to capture high-order correlations among entities and among relations. DECRL (Chen) & Chen 2024) uses deep evolutionary clustering construct evolutionary clusters for capturing
high-order correlations among entities.
However, TKG datasets, e.g., ICEWS, centered on international political events, inherently involve complex causal dependencies. Focusing solely on entity or relation level correlations is therefore inadequate for event prediction TKGs. To address this, propose HEDRA, the first framework to disentangle heterogeneous causalities at the event level in TKGs.
A.2 GRAPH CAUSALITY LEARNING
Graph causal learning approaches can divided into static graph causal learning approaches and dynamic graph causal learning approaches.
Static graph causal learning approaches primarily model spatial causality in static graphs by gen- erating interpretable subgraphs (Luo et al.) 2020 Yuan et al.) 2020 Ying et al. 2019 Fan et al.) 2022
Gao et al. 2023). For example, PGExplainer (Luo et al. (020) employs prior knowledge static graphs. XGNN (Yuan et al.) 2020) employs reinforcement learning to iteratively expand interpretable subgraphs. More recent approaches generate subgraphs using learnable methods. For example, GNNExplainer (Ying al.) 2019) uses mutual information to add or remove nodes and edges to generate subgraphs. RCGRL
to pre-define subgraphs. thereby providing interpretability
(Gao et al. 2023) relies GNN-derived edge weights for generating subgraphs.
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Table 6: The statistics of datasets.
Daraset
#Entity
#Relation
#Training
#Validation
#Test
Interval
ICEWS14
7.128
230
74,845
8,514
7,371
24 bours
ICEWS18
23,033
256
373.018
45,995
49.545
24 bours
GDELT
7,691
1.734,399
238.765
WIKI
12.554
$39.286
67.538
63.110
year
YAGO
10,623
10
161,540
19.523
20,026
year
Dynamic graphs, prevalent in real-world scenarios, have motivated research on dynamic graph causal learning, which typically explores both spatial causality and temporal causality (Zhao & Zhang 2024 Chen et al. 2024a). For example, DyGNNExplainer (Zhao & Zhang, 2024) utilizes
disentangling methods uncover spatio-temporal causality. CSI (Chen al., (2024a) generates causal subgraphs by deriving query-related subgraphs and applying attention mechanisms to model spatio-temporal causality within dynamic graphs.
Despite progress in dynamic graph causal learning, most approaches mainly model static and dy- namic causalities while overlooking spurious causality, which impedes the acquisition causally relevant information for event prediction. Moreover, theoretical framework exists disentangle heterogeneous causalities the event level TKGs. To fill this gap, we propose HEDRA, which constructs event representations from quadruples and progressively disentangles non-causality, spu- rious causality, static causality, and dynamic causality among events in TKGs.
B BACKDOOR ADJUSTMENT DERIVATION
The detailed derivation process of backdoor adjustment shown as follows:
P())d)(D) Σ d) do()))
Σ P())do(()) P(S)
P(S) Σ P())), P(T,P)do(C)
(18)
-EP(S) E P(VIg) P(T,P)
P(S) P(T) Σ P(P) Σ P(yIS).
This derivation illustrates how the adjustment effectively blocks the backdoor paths involving N, P. and S, thereby ensuring unbiased estimation of causal effects.
C EXPERIMENTS APPENDIX
C.I DATASET STATISTICS AND EXPERIMENTAL SETTINGS
Detailed statistics of the datasets are summarized Table 6 HEDRA implemented in Python with PyTorch and trained an NVIDIA RTX 5090 GPU. The Neural Network Intelligence (NNT) toolkit is employed to automatically explore hyperparameter configurations. The search spaces of key hyperparameters are defined as follows: Mayer the number of layers, ranges from 1 to 5 with a step size of 1; NWindow, the length of historical windows, ranges from 1 to 14 with a step size of 1; and the number k-nearest neighbors in the candidate graph, ranges from to 15 with step size of 2. A maximum of 30 trials are conducted in the NNI search process, with the Tree-structured Parzen Estimator (Bergstra et al. 2015) employed as the optimization algorithm. The final selected hyperparameters are summarized in Table
Hyperparameters Xoons Ayob. and Aevo are all set 0.1, controlling the magnitude of contrastive, robustness, and evolutionary losses, respectively. The Adam optimizer (Kingma & Ba 2014) is applied with an initial learning rate of 0.01. The batch size 16, and the representation dimension 200. Results averaged over five independent runs.
https://github.r http:/twww...ccoccccoooooo/t//// /o
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Table 7: The final choices key hyperparameter values.
Hyperparameterr
Scarch space
ICEWS14
ICEWSI8
GDELT
WIKI
YAGO
Muser
[1. 2, 3. 4,
2
2
2
f1,2,3, 4.5,
13.
10
(3, (3,5,7 7, 9, 11, 13, 15)
13
11
9
7
C.2 DESCRIPTION OF BASELINES
To validate the effectiveness of HEDRA, compare it against eleven representative TKG repre- sentation learning approaches, which are summarized as follows:
Shallow Encoder based Approaches:
TTransE (Leblay & Chekol, 2018) augments TransE by embedding temporal information into entity representations.
TA-TransE (Garcia-Duran et al. 2018) extends TransE by incorporating RNN-based mod- eling to capture time-aware relation representations.
GNN based Approaches:
2020) combines GCNs for capturing structural information together with RNNs to model temporal dependencies.
RE-NET Tin al.
Glean (Deng et al.
2020
leverages composition- based GCNs to encode entity interactions
and employs GRUs to model temporal evolution.
integrates relation-aware GCNs with autoregressive GRUs to jointly capture structural and temporal dependencies.
RE-GCN (Li et al.
2021b)
DACHA (Chen et 2021) introduces dual GCNs for structure information encoding and
incorporates self aelf-attentive mechanism to learn relation aware temporal representations.
TiRGN (Li et al. 2022) introduces RGCNs to capture graph structural information and double recurrent mechanism model temporal dependencies.
Structure Derived Approaches:
EvoFxplore (Zhang et al. 2022) employs dynamic community structure to characterize the evolution of local structural patterns.
introduces group structure to model distant and indirectly connected entities, and integrates GRUs for temporal reasoning.
GTRL [Tang & Chen 2024
DHyper (Tang et al.
2024) leverages hypergraph neural networks to model high-order
dependencies among entities and relations.
represents the SOTA structure derived approach by employ- ing deep evolutionary clustering to trace the temporal evolution of high-order correlations
DECRL (Chen & Chen 2024
among entities.
C.3 COMPLEXITY ANALYSIS
The time complexity of relation-awan GCN is O((N, + N2) where No and N, are the numbers of entities and relations, respectively. is the dimension of representations. The time complexity of the event representation construction module is O(E + ED²), where E is the number of events. The time complexity of the counterfactual detector module ((F + FDD2). The time complexity of the IV-guided disentangling module is D(EE + D²). The time complexity of the evolutionary orthogonal module is OEED²). For the event prediction module, the time complexity OD)). Therefore, the total time complexity of HEDRA is OEE" D + (Ne + N E)D²).
comparison of the per-epoch training and inference times of DHyper, DECRL, and HEDRA on the ICEWS14 dataset is provided in Table Compared with DECRL, HEDRA improves MRR and Hits@1 by 1.566 and 15.71%, respectively, and provides more accurate predictions of relation directionality and sentiment, which crucial for real-world applications. Plotted as latency-MRR
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Table Running time (in seconds) comparison.
Approach
Traning
Inference
Dilyper (TOIS 2024) DECRL (NeurIPS 2024)
636.85
91.43
142.82
HEDRA
1226.63
195.15
48
IEDRA
46
MRR
44
DECRL
DHlyper
42
600
800
1000
1200
Training Latency (8)
Figure 4: Latency-MRR Pareto frontier comparing DHyper, DECRL, and HEDRA.
points, these three approaches form a clear Pareto frontier, as shown in Figure 4 DHyper occupies the low-latency, lower-accuracy end, DECRL provides an intermediate trade-off, and HEDRA lies at the high-accuracy, higher-latency corner. On ICEWS14 dataset, HEDRA improves MRR over DHyper from 41.71 to 47.86, yielding an absolute gain of 6.15 MRR points (approximately 15% relative improvement), and over DECRL from 42.90 to 47.86, corresponding to an absolute gain of 4.96 MRR points (approximately 12% relative improvement). These gains come the cost of roughly 2 and 1.3x higher training latency. respectively. Overall, this latency- accuracy trade- off suggests that the additional runtime of HEDRA justified when higher predictive accuracy prioritized over absolute latency.
To quantify the resource footprint of HEDRA across datasets, Table 9 summarizes the parame- ter counts, peak CUDA memory, and wall-clock training time on ICEWS14 and GDELT datasets. On ICEWS14 dataset, HEDRA uses 20.7M parameters, reaches peak CUDA memory footprint of 2.95 GB, and requires 1226.63 (+= 0.34 GPU hours) of training time, with inference time of 195.15 s. On GDELT dataset, whose number of events is about 20x that of ICEWS14 dataset, HEDRA uses MM parameters, reaches a peak CUDA memory of 9.91 GB, and requires 14274.41 8 (= 3.97 GPU hours) of training time. Consequently, when moving from ICEWS14 to GDELT, the parameter count increases only modestly (~ 6%). peak memory grows by about 3.4x, and wall-clock training time increases by about 11.6x, which is substantially sub-linear in the dataset size increase.
C.4 HYPERPARAMETE SENSITIVITY ANALYSIS
The sensitivity analysis of the key hyperparameters of HEDRA, i.c., the length of historical windows Nwindow and the number of neighbors k. the ICEWS14 dataset is shown in Figure It can be observed that the length of historical windows has only a minor impact on performance, indicating that disentangling event level causalities enables HEDRA learn robust entity and relation repre- sentations. In contrast, the number of neighbors has a significant effect, as it directly determines the size of the candidate graph. As k increases, the performance gradually improves and then re- mains relatively stable when k > 7. In addition, Figure 6 reports a representative sensitivity study on the loss-weight coefficients Qatta and Aalign on ICEWS14 dataset, using the same curve-based visualization, indicating that HEDRA is robust to moderate changes of these coefficients within reasonable range and that the default symmetric setting around 0.5 lies near-optimal region.
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Published as a conference paper at ICLR 2026
Table Resource statistics of HEDRA ICEWSI4 and GDELT.
Dataset
Prameters (M)
Peak CUDA memorr (GB)
Trainning time (s)
ICEWS14 GDELT
2.95
1226.62 14274.41
22.1
9.91
70
70
Resulla of Mestics
Results of Metsics
60
60
50
50
40
40
30
.00
3
3
15
(a) Hyperparameter Nwindww
(b) Hyperparameter
Figure 5: Hyperparameter sensitivity analysis.
C.5 MODEL ANALYSIS
This subsection reports additional diagnostics on training dynamics and IV-guided disentangling behaviour on ICEWS14 dataset, as well as the robustness of HEDRA few-shot relations ICEWS14 and ICEWS18 datasets.
Training Dynamics and IV-guided Module. Four loss are monitored during training: the event prediction loss LTKG, the contrastive loss Leous the robustness loss Lyob, and the evolutionary loss Levo- To quantify how mass evolves on spurious causal edges inside the causal branch, diagnostic statistic p, is introduced as:
Po(e.
(19)
Eg
cEE,
where Eg denote the set of edges currently assigned to the spurious-causalie set, and (e()) denote the probability that edge belongs to spurious causality.
Table 10 reports the evolution of the loss terms and p. over the 10 epochs on ICEWS14 dataset. All four losses decrease smoothly over epochs without noticeable oscillation or divergence, indicating that the interactions among the contrastive, robustness, and evolutionary losses keep the optimiza- tion process stable. P. increases from 0.817 at epoch I to approximately 0.852 by epochs 7 and then saturates. Since the fraction of edges assigned to the spurious set is approximately fixed by construction, this increase in P. indicates that the IV-guided module becomes progressively more
90
70
70
VRR
Results of Mesries
Hludd
Rosults of Meazies
60
60
50
50
10
40
30
0.1
0.3
0.5
0.7
0.9
0.1
0.3
0.5
0.7
0.9
(a) Coefficient Clasto
(b) Coefficient Antign
Figure 6: Coefficient sensitivity analysis.
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Published as a conference paper at ICLR 2026
Table 10: Training dynamics and spurious-mas mass diagnostic on ICEWS14. The epoch marked with corresponds to the best validation MRR.
Epuch LyKG
Leon
Lyoh
Levo
3.8341
0.5589
0.8724
0.3108
0.817
3.2442
0,2644
3,1236
4 3.0461
0.2308
0.2262
0.0024
0.847
5
2.9763
0.2260
0,2210
0,0018
0.830
2.9166
0.2225
0,2182
0,0016
0.851
7
8
2,8230
0.2197
0.2150
0.0014
0.852
9 2,7895
0.2192
0,2140
0,0013
0.852
Table 11: Few-shot relation performance of HEDRA on ICEWS14 and ICEWS18.
Dataset
MRR
Hits0'1
Hitses
@1
ICEWS14
26.68
11.96
29.79
62.63
ICEWS18
17.44
8.53
38.44
confident about which edges spurious and concentrates spurious-causality result, these edges are more strongly down-weighted during message passing and decoding, which the intended behaviour. The best validation MRR ICEWS14 dataset is reached around epoch 8, when p. has essentially flattened, suggesting that performance gains coincide with the model's improved ability identify and suppress spurious causality, while later epochs mainly refine repre- sentations on top of this learned peeaiine-veruu-ssurrion partition.
them. As
Few-shot Relations. To examine robustness on relations with limited supervision, a few-shot re- lation setting is constructed ICEWS14 and ICEWS18 datasets. For each dataset, 20% of the relations are randomly selected, only 20% of their quadruples are retained for training, and evalua- tion is performed solely on this subset of relations. Under this highly sparse supervision, HEDRA achieves the results in Table IT indicating that the model retains non-trivial level of robustness for relations with limited training data.
C.6 ANOTHER CASE STUDY
For each entity the ICEWS14 dataset, all associated events are first grouped by timestamp, and only one event per timestamp is randomly chosen and retained. The most recent 20 distinct times- tamps are then chronologically ordered to construct trajectories that characterize the temporal evo- lution the entity. Figure 7 illustrates the stepwise magnitudes of change in both dynamic and static components between consecutive events. For China and Japan, the dynamic component is observed to vary more and by larger amounts than the static component, indicating that short-term shocks absorbed by the dynamic component while long-term semanties remain stable in the static component, consistent with the goal of HEDRA to disentangle dynamic and static causalities.
clange berwoonn aaccuu events
1.2 change between accent ovents
0.4
0.4
HAN
IMP
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
10
15
Event step
Event step
(a) Entity "China": || A PI| vs. |
(b) Entity "Japan": A vs. |
Figure 7: Case study of stepwise changes over the last 20 events. between consecutive events and denotes the Euclidean norm.
A denotes the first difference
18


Reviews:
[{"review_id": "l0gbCRs5YU", "reviewer": "Reviewer_9HRi", "summary": "HEDRA proposes an event-level structural causal model for temporal knowledge graphs that separates four kinds of signals: non-causality, spurious causality, static causality, and dynamic causality. Backdoor adjustment is used as the conceptual guide for blocking confounding paths between causality and prediction. The framework instantiates three coordinated modules. First, a counterfactual detector uses an attention-style event importance term and a KL divergence term to construct a non-causality mask and trains with a contrastive loss. Second, an instrumental-variable guided module computes an IV score per candidate edge, selects top-quantile edges as genuine, builds multi-view subgraphs, and applies a robustness loss with alignment and separation terms. Third, an evolutionary orthogonal module projects event representations into static and dynamic components with an orthogonality step and an evolutionary loss that encourages temporal dependence of the dynamic component and temporal stability of the static component. Experiments on ICEWS14, ICEWS18, GDELT, WIKI, and YAGO show consistent gains and report average improvements over the runner-up on MRR and Hits. The paper includes a complexity analysis and a per-epoch runtime comparison on ICEWS14, and provides sensitivity studies that emphasize the effect of the neighbor count used to build the candidate graph.", "questions": "1.\tInstrumental variable assumptions and checks\nWhat empirical evidence can you provide that the candidate IVs used to build Π satisfy the intended exclusion and independence intuitions in practice, and what failure modes arise when these conditions are weakened. A brief diagnostic report would be valuable. \n2.\tComprehensive resource profile\nCan you report parameter counts, FLOPs if available, wall-clock time, GPU hours and peak memory for each dataset, and position HEDRA on a latency–MRR Pareto against at least two strong baselines. The ICEWS14 table is helpful, and similar measurements on GDELT would be informative. \n3.\tThreshold sensitivity and calibration\nHow sensitive are results to the quantile level α in the IV mask and to the stability constant and temperature used in the non-causality mask. Do learned thresholds or adaptive calibration outperform fixed quantiles for precision of the presumed genuine set. \n4.\tTraining dynamics and loss interactions\nWould you add training curves for the contrastive loss, the robustness loss with alignment and separation, the evolutionary loss, and the total objective, to document stability and to show how mass shifts from spurious edges to genuine ones during training. \n5.\tExplanation of the small negative improvement in one metric\nTable 1 shows a very small negative change on Hits at ten for ICEWS18 in the improvement row. Can you analyze which queries contribute to this dip and whether it is linked to rank-tail behavior or to the size of the candidate graph on this dataset.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "1.\tEvent-level causal formalization\nThe SCM clearly separates non-causality and spurious causality from the static and dynamic components that should drive prediction, and articulates backdoor paths that motivate the design of the modules. \n2.\tConcrete module designs with explicit masks and losses\nThe counterfactual detector fuses importance and distributional discrepancy to form a non-causality mask and optimizes a contrastive objective. The IV-guided module defines an IV score from observable features, selects top-quantile genuine edges, builds three propagation views, and regularizes with alignment and separation. The evolutionary module performs orthogonalization and trains with a two-part evolutionary loss. Each step has precise formulas. \n3.\tComprehensive empirical coverage\nResults on five datasets with detailed tables, significance marks on ICEWS14 and ICEWS18, and a case study support the claims. The sensitivity section highlights that performance depends strongly on the neighbor count while being relatively insensitive to the history window length. \n4.\tTransparent reporting of one-dataset runtime and end-to-end complexity\nThe complexity analysis enumerates per-module terms, and the runtime table compares HEDRA against two strong baselines on ICEWS14. \n5.\tClear writing and figures\nThe framework figure and mask definitions make the pipeline easy to follow, and the derivation for backdoor adjustment is provided in the appendix.", "weaknesses": "1.\tIV validity and diagnostics are under-specified\nThe IV-guided module defines an IV score and uses an α-quantile rule to select genuine edges, then relies on robustness via multi-view propagation. The paper does not state explicit conditions under which the constructed IVs satisfy the usual exclusion and independence intuitions, nor does it include simple falsification checks such as placebo variables or outcome-on-IV tests. Adding a short subsection or appendix that names the identifying conditions and reports basic diagnostics would make the IV part more convincing. \n2.\tRuntime and memory profiling are limited to one dataset\nTable 8 reports per-epoch training and inference times on ICEWS14 only. Given the large E-squared and D-squared terms summarized in the complexity section, a resource profile on GDELT and WIKI or YAGO would help readers judge practical scalability. Module-wise wall-clock, peak memory, and parameter counts would be particularly useful. \n3.\tMask thresholds and calibration are not analyzed\nThe non-causality mask combines attention weights and KL divergence with fixed balancing coefficients and a small constant for stability. The IV mask then selects the top-α edges as genuine by a quantile rule. The paper does not present precision–recall calibration for the presumed genuine set under different α values or compare fixed quantiles with learned thresholds. Sensitivity and calibration of these gates would clarify robustness. \n4.\tPer-loss training dynamics and attribution are not shown\nThe robustness loss has alignment and separation terms, and the evolutionary loss has dynamic and static terms, yet the paper does not provide per-term ablations or training curves that illustrate convergence and interactions with the main prediction loss. Adding curves for the contrastive, robustness, evolutionary, and total losses would strengthen the optimization narrative. \n5.\tDefinition and parity of evaluation protocols could be clearer in the main text\nThe use of MRR and Hits is standard, and the tables mark significance on ICEWS14 and ICEWS18. It would help to define time-aware evaluation choices in the main body and to extend significance reporting beyond ICEWS to all tables with multi-run results, so that parity with baselines is fully transparent. \n6.\tGDELT comparison is affected by timeouts and OOM\nThe GDELT table shows several baselines timing out or running out of memory, which complicates margin interpretation. A breakdown by relation family and time granularity, plus a note on candidate-graph size and subgraph convolution memory use at fifteen-minute intervals, would contextualize the reported gains.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "0V2Sv35hqC", "reviewer": "Reviewer_ujzc", "summary": "This paper proposes HEDRA, the first framework to disentangle heterogeneous event-level causalities in Temporal Knowledge Graphs. By developing a structural causal model and three specialized modules—counterfactual detection, IV-guided disentanglement, and evolutionary orthogonalization—it effectively separates static, dynamic, non-, and spurious causalities. Comprehensive experiments on five benchmarks demonstrate state-of-the-art performance, with significant improvements over existing methods, while maintaining practical computational efficiency.", "questions": "See weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Proposes the first framework for event-level causal disentangling in temporal knowledge graphs.\n\nComprehensive experiments on five datasets show consistent SOTA performance.", "weaknesses": "Ablation results show only minor drops.\n\nThe method introduces multiple complex modules, resulting in high training complexity and long runtime, especially on large-scale datasets such as GDELT.\n\nIt is unclear whether the proposed method can represent or generalize to unseen entities or relations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "PxqXpg5z2c", "reviewer": "Reviewer_xmQG", "summary": "Existing Temporal Knowledge Graph (TKG) methods mainly focus on modeling entity-level correlations, learning the relationships among entities through graph structures (nodes and edges) or higher-order structures such as hypergraphs and clusters. However, since events themselves exhibit diversity and causal heterogeneity, relying solely on entity correlations is insufficient to capture event-level causal mechanisms, thereby limiting the reliability of event prediction. HEDRA is the first TKG representation learning approach that achieves heterogeneous causality disentanglement at the event level. By incorporating counterfactual detection, instrumental variable guidance, and dynamic orthogonal decomposition, HEDRA effectively distinguishes non-causality, spurious causality, static causality, and dynamic causality, significantly enhancing both the performance and interpretability of event prediction tasks.", "questions": "1. Why does the paper not include comparisons with TiRGN and large-model-based approaches?\n2. In the introduction, the paper states:“Other approaches introduce derived structures, e.g., entity groups, hypergraphs, and evolutionary clusters, to capture high-order correlations among entities that are not directly connected (Zhang et al., 2022; Tang & Chen, 2024; Tang et al., 2024; Chen & Chen, 2024).” However, Tang & Chen (2024) proposed DHyper, which does not merely focus on entity-level correlations but jointly models high-order dependencies among both entities and relations.Why, then, is DHyper categorized under methods that primarily model entity correlations? Moreover, does its joint modeling capability potentially challenge the claimed novelty of this paper’s approach?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. HEDRA is the first to elevate the research focus to the event-level causal relationships.\n2. The paper theoretically formalizes four types of event-level causality, providing a solid theoretical foundation for future studies on temporal knowledge graphs based on causal reasoning.", "weaknesses": "1. The paper does not include a comparison with traditional methods based on GCN and GRU, such as TiRGN[1].\n2. It also lacks comparisons with recent large-model approaches specifically designed for event prediction, such as MIRAI[2].\n3. The anonymous GitHub repository is empty.\n4. The notation is abundant and overly complex, which slightly reduces readability.\n5. The text above the figure, such as in Figure 1, is too small.\n\n[1] Li Y, Sun S, Zhao J. Tirgn: Time-guided recurrent graph network with local-global historical patterns for temporal knowledge graph reasoning[C]//IJCAI. 2022: 2152-2158.\n\n[2] Ye C, Hu Z, Deng Y, et al. Mirai: Evaluating llm agents for event forecasting[J]. arXiv preprint arXiv:2407.01231, 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "Df8PAKbG6b", "reviewer": "Reviewer_nNKS", "summary": "The paper introduces HEDRA, the first representation learning approach dedicated to disentangling heterogeneous event-level causalities in Temporal Knowledge Graphs, employing counterfactual detection, instrumental variable-guided modules, and evolutionary orthogonal mechanisms to separate non-causality, spurious causality, and dynamic causality, respectively; extensive experiments on five real-world datasets demonstrate HEDRA’s state-of-the-art performance in TKG reasoning.", "questions": "See Weakness", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The manuscript is well-written and structurally coherent. Despite the extensive use of diverse symbols, each is accompanied by a clear and explicit explanation.\n\n2. The paper is grounded in solid theoretical foundations, effectively integrating causal learning theory into the domain of temporal knowledge graphs.\n\n3. The experimental evaluation presented in the paper is comprehensive and rigorous, providing substantial evidence for the effectiveness of the proposed method.", "weaknesses": "1. This manuscript introduces numerous modules, which inevitably leads to increased computational time complexity (as demonstrated in Appendix C.3 and Table 8), potentially limiting the applicability of this approach to larger-scale temporal knowledge graphs.\n\n2. This paper introduces numerous hyperparameters ($\\alpha_{attn}$, $\\beta_{KL}$); however, it lacks corresponding sensitivity analysis. If these parameters are all set to fixed values (0.5), then incorporating such an extensive array of hyperparameters becomes unnecessary.\n\n3. In Table 1, the experimental results on ICEWS18 show a notable decrease in Hits@10 performance despite achieving superior outcomes on other metrics. The underlying reasons for this discrepancy warrant further clarification.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)