Explainable Subgraph Reasoning for Forecasting on Temporal Knowledge Graphs
Authors: Zhen Han
Peng Chen
Yunpu Ma
Volker Tresp
Venue: ICLR 2021 Poster (2021)
Keywords: Temporal knowledge graph
future link prediction
graph neural network
subgraph reasoning.

Abstract: Modeling time-evolving knowledge graphs (KGs) has recently gained increasing interest. Here, graph representation learning has become the dominant paradigm for link prediction on temporal KGs. However, the embedding-based approaches largely operate in a black-box fashion, lacking the ability to interpret their predictions. This paper provides a link forecasting framework that reasons over query-relevant subgraphs of temporal KGs and jointly models the structural dependencies and the temporal dynamics. Especially, we propose a temporal relational attention mechanism and a novel reverse representation update scheme to guide the extraction of an enclosing subgraph around the query. The subgraph is expanded by an iterative sampling of temporal neighbors and by attention propagation. Our approach provides human-understandable evidence explaining the forecast. We evaluate our model on four benchmark temporal knowledge graphs for the link forecasting task. While being more explainable, our model obtains a relative improvement of up to 20 $\%$ on Hits@1 compared to the previous best temporal KG forecasting method. We also conduct a survey with 53 respondents, and the results show that the evidence extracted by the model for link forecasting is aligned with human understanding. 

Published as a conference paper at ICLR 2021
EXPLAINABLE SUBGRAPH REASONING FOR FORE- CASTING ON TEMPORAL KNOWLEDGE GRAPHS
Zhen Han Peng Chen Yunpu Ma Volker Tresp 1.2
"Istiituee of Informatics. LMU Munich 2 CCopportte Technology, Siemens AG 3 Department of Informatics, Technical University of Munich
zhen. han& campus. 1mu. de, peng chen@tum. de cognitive, yunpu@gmaill gom, volker. wrespesiementtee com
ABSTRACT
Modeling time-evolving knowledge graphs (KGs) has recently gained increasing interest. Here, graph representation learning has become the dominant paradigm for link prediction on temporal KGs. However, the embedding based approaches largely operate in a black-box fashion, lacking the ability to interpret their predic- tions. This paper provides a link forecasting framework that reasons over query- relevant subgraphs of temporal KGs and jointly models the structural dependen- cies and the temporal dynamies. Especially, we propose temporal relational at- tention mechanism and novel reverse representation update scheme to guide the extraction of an enclosing subgraph around the query. The subgraph is expanded by an iterative sampling of temporal neighbors and by attention propagation. Our approach provides human-unde undurstdddttt evidence explaining the forecast. We evaluate our model on four benchmark temporal knowledge graphs for the link forecasting task. While being more explainable, model obtains relative im- provement of up to 20 % on Hits@ compared to the previous best temporal KG forecasting method. We also conduct survey with 53 respondents, and the results show that the evidence extracted by the model for link forecasting is aligned with human understanding.
INTRODUCTION
Reasoning, process of inferring new knowledge from available facts, has long been considered an essential topic Al research. Recently, reasoning on knowledge graphs (KG) has gained increasing interest (Das et al. 2017: Ren et al.) 2020 Hildebrandt et al. 2020). A knowledge graph is graph- structured knowledge base that stores factual information in the form triples (s, p. o), e-g., (Alice, livesIn, Toronto). In particular, (subject) and (object) are expressed as nodes and (predicate) as an edge type. Most knowledge graph models assume that the underlying graph is static. However, in the real world, facts and knowledge can change with time. For example, (Alice, livesIn, Toronto) becomes invalid after Alice moves to Vancouver. To accommodate time-evolving multi-relational data, temporal KGs have been introduced (Boschee et al. (015), where temporal fact is represented as a quadruple by extending the static triple with a timestamp / indicating the triple valid at t, i.e. (Barack Obama, visit, India, 2010-1 1-06).
In this work, we focus on forecasting on temporal KGs, where we infer future events based on past events. Forecasting temporal KGs can improve plethora of downstream applications such as decision support in personalized health care and finance. The use cases often require the predic- tions made by the learning models be interpretable, such that predictions. However, current machine learning approaches (Trivedi et al., 2017;; Jin et al., 2019) for temporal KG forecasting operate in black-box fashion, where they design an embedding- based score function to estimate the plausibility of a quadruple. These models cannot clearly show which evidence contributes a prediction and lack explainability to the forecast, making them less suitable for many real-world applications.
can understand and trust the
"quual contribution. Corresponding authors.

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Published as a conference paper at ICLR 2021
Explainable approaches generally be categorized into post-hoc interpretable methods and inte- grated transparent methods (Došilović et al. 2018). Post-hoc interpretable approaches (Montavon et al. 2017 Ying et al., 2019) aim to interpret the results of black-box model, while integrated transparent approaches (Das et al. 2017; Qiu et al. 2019 Wang et al.) 2019) have an explainable internal mechanism. In particular, most integrated transparent (Lin al. 2018 Hildebrandt et al. 2020) approaches for KGs employ path-based methods to derive an explicit reasoning path and demonstrate a transparent reasoning process. The path-based methods focus on finding the answer to a query within a single reasoning chain. However, many complicated queries require multiple supporting reasoning chains rather than just one reasoning path. Recent work (Xu al., 2019] Teru et al. 2019) has shown that reasoning over local subgraphs substantially boosts performance while maintaining interpretability. However, these explainable models cannot be applied to temporal graph-structured data because they do not take time information into account. This work aims to design a transparent forecasting mechanism on temporal KGs that can generate informative expla- nations of the predictions.
In this paper, we propose an explainable reasoning framework for forecasting future links on temporal knowledge graphs, xERTE, which employs sequential reasoning process over local sub- graphs. To answer a query in the form of (subject Eq. predicate Pq. 2, timestamp tq), xERTE starts from the query subject, iteratively samples relevant edges of entities included in the subgraph and propagates attention along the sampled edges. After several rounds of expansion and pruning, the missing object is predicted from entities in the subgraph. Thus, the extracted subgraph can be seen as a concise and compact graphical explanation of the prediction. To guide the subgraph to expand in the direction of the query's ' interest, we propose a temporal relational graph attention (TRGA) mechanism. We pose temporal constraints on passing messages to preserve the causal nature of the temporal data. Specifically, we update the time-dependent hidden representation of an entity e, at a timestamp by attentively aggregating messages from its temporal neighbors that were linked with e prior to I. We call such temporal neighbors as prior neighbors of eq. Additionally, we use an em- bedding module consisting of stationary entity embeddings and functional time encoding, enabling the model to capture both global structural information and temporal dynamics. Besides, we develop novel representation update mechanism to mimic human reasoning behavior. When humans per- form a reasoning process, their perceived profiles of observed entities will update, as new clues are found. Thus, it necessary to ensure that all entities in a subgraph can receive messages from prior neighbors newly added to the subgraph. To this end, the proposed representation update mechanism enables every entity to receive messages from its farthest prior neighbors in the subgraph.
The major contributions of this work are as follows. (1) We develop XERTE, the first explainable model for predicting future links on temporal KGs. The model is based on a temporal relational attention mechanisms that preserves the causal nature of the temporal multi-relational data. (2) Unlike most black-box embedding- vides an interpretable inference graph to emphasize important evidence. (3) The dynamical pruning procedure enables our model to perform reasoning on large-scale temporal knowledge graphs with millions of edges. (4) We apply our model for forecasting future links on four benchmark temporal knowledge graphs. The results show that our method achieves on average a better performance than current state-of-the-as methods, thus providing respondents to evaluate whether the extracted evidence is aligned with human understanding.
models, xERTE visualizes the reasoning process and pro-
baseline. (5) We conduct survey with 53
2 RELATED WORK
Representation learning is an expressive and popular paradigm underlying many KG models. The embedding-basse based approaches for knowledge graphs can generally be categorized into bilinear mod- els (Nickel et al.] 20111: Yang et al., 2014 Ma et al. 2018a), translational models (Bordes et al. 2013 Lv et al. [0188] Sun et al. 2019 Hao et al. 2019), and deep-learning models (Dettmers et al.) 2017 Schlichtkrull et al. 2018). However, the above methods are not able to use rich dynamics available on temporal knowledge graphs. To this end, several studies have been conducted for tem-
poral knowledge graph reasoning (Garcia-Duril et al. 2018 Ma et al. 2018b Jin et al.) 2019 Goel et al. 2019 Lacroix et al. 2020; Han et al. 2020a Zhu et al. 2020). The published approaches are Barelyy black-box, lacking the ability to interpret their predictions. Recently, several explainable
reasoning methods for knowledge graphs have been proposed (Das al. 2017 Xu et al. 2019
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Hildebrandt et al. 2020 Teru et al. 2019). However, the above explainable methods can only deal with static KGs, while our model is designed for interpretable forecasting on temporal KGs.
3 PRELIMINARIES
Let & and P represent a finite set of entities and predicates, respectively. temporal knowledge graph is a collection of timestamped facts written as quadruples. A quadruple q = (es. Cas 1) represents a timestamped and labeled edge between a subject entity с₃ & and an object entity eo E, where P denotes the edge type (predicate). The temporal knowledge graph forecasting task aims to predict unknown links at future timestamps based on observed past events.
Definition (Temporal KG forecasting). Let F represent the set of all ground-truth quadruples, and let (Eq,Par Pay Cos tq) E F denote the target quadruple. Given query (Eqspq ?, R,4g) derived from the target quadruple and a set of observed prior facts O = {(er,ps, Ps, E Ftt < tg), the temporal KG forecasting task is predict the missing object entity Co. Specifically, all entities in the set & as candidates and rank them by their likelihood to form a true quadruple timestamp 1.0
consider
together with the given
For given query q (eg.Pg.3 ?, 2,tg), we build an inference graph Gif to visualize the reasoning process. Unlike in temporal KGs, where a node represents an entity, each node in Gin is an entity- timestamp pair. The inference graph is directed graph in which a link points from node with an earlier timestamp to a node with a later timestamp.
(Node in Inference Graph and its Temporal Neighborhood). Let ε represent all enti- ties, F denote all ground-truth quadruples. and let represent timestamp. A node in an inference graph Gmg is defined as an entity-limestamp pair = (ei, () E E. We define the set of one-hop prior neighbors of u as Nu=le..) = {(eg.t') [e), Pl,...P.,,s, e,. t') E F A (t' < {)} For simplicity, we denote one-hop prior neighbors as N₂- Similarly,
Definition 2
define the of one-hop posterior neighbors of u as N (=(e),)) {(ej, (ej, Pk. e,, 1) E F A (t' > {)}. We denote them as N for short.
We provide an example in Figure 4 in the appendix to illustrate the inference graph.
4
OUR MODEL
We describe xERTE in a top-down fashion where we provide an overview Section 4.1 and then explain each module from Section to 4.6
4.1 SUBGRAPII REASONING PROCESS
Our model conducts the reasoning process on a dynamically expanded inference graph Gin extracted from the temporal KG. We show toy example in Figure [ Given query q = (eqp Pa, ?, by), we initialize Gif with node v,- = (eg,4) consisting of the query subject and the query time. The inference graph expands by sampling prior neighbors of vg. For For example, suppose that (eg, Pk: pk.,,, e', is a valid quadruple where t' < tg. we add the node = [e,, t') into Ginf and link it with ey where the link is labeled with Pı: and points from Uy V1. We use an embedding module assign each node and predicate included in Ging temporal embedding that is shared across queries. The main goal of the embedding module to let the nodes access query-independent information and get a broad view of the graph structure since the following temporal relational graph attention (TRGA) layer only performs query-dependent message passing locally. Next, we feed the inference graph into the TRGA layer that takes node embeddings and predicate embeddings a query- deeendde representation for each node by passing messages on the small inference graph, and computes query- -eeendeet attention score for each edge. As explained in Section 4.7 propagate the attention of each node to its prior neighbors using the edge attention scores. Then we further expand Gnd by sampling the prior neighbors of the nodes in Gugf The expansion will grow
the input, produces
'Throughout this work, we add reciprocal relations for every quadruple, i.c., we add (c.: e) for every (Cx, P, e., t). Hence, the restriction to predict object entities does not lead to a loss of generality. Prior neighbors linked with e; subject entity, e.g., (ee, Pk. es, t), covered using reciprocal relations.
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Inference sterenccceeepllee 1=2
Subgraph from step =1
Neighborhood Sampling
Attention Propagation Subgraph Pruning of
Embedding Module
TRGA Layer
a
B
Query: (ey Pay 2, [g)
Model Architecture. We take the second inference step (1 2) as an example. Each directed edge points from source node to its prior neighbor. @ denotes nodes that have not been sampled. a means the attention score of node V at the 4 inference step. af., is the attention score of the edge between node and its prior neighbor j at the 1th inference step. Note that all scores are query -eery-deeendeet. For simplicity, we do not show edge labels (predicates) in the figure.
Figure/ I:
rapidly and cover almost all nodes after few steps. To prevent the inference graph from exploding, we reduce the edge amount by pruning the edges that gain less attention. As the expansion and pruning iterate, Ging allocates more and more information from the temporal KG. After running L inference steps, the model selects the entity with the highest attention score in Gug as the prediction of the missing query object, where the inference graph itself serves as graphical explanation.
4.2 NEIGHBORHOOD SAMPLING
We define the set of edges between node (ei, 1) and its prior neighbors N₂ Q.. where Tu Qu is a prior edge of To reduce the complexity, sample subset of prior edges Q. Qu at each inference step. We denote the remaining prior neighbors and posterior neighbors of node
after the sampling as N, and Nr, respectively. Note that there might be multiple edges between node v and its prior neighbor because of multiple predicates. If there is at least one edge that has been sampled between and we add into N... The sampling can be uniform if there is no bias, it can also be temporally biased using a non non-uniform distribution. For instance, we may want to sample more edges closer to the current time point the events that took place long ago may have less impact on the inference. Specifically, we propose three different sampling strategies: (1) Uniform sampling. Each prior edge d. E Q. has the same probability of being selected: P(qx) 1/12al. (2) Time-aware exponentially weighted sampling. We temporally bias the neighborhood sampling using an exponential distribution and assign the probability (g (et, Pky ej, (')) exp(!' - -1)/ (e:.pp.e....... E,
exp(t" - -)) to each prior neighbor, which negatively correlates with
the time difference between node and its prior neighbor (ey.t). Note that t' and t" are prior to t. (3) Time-aware linearly weighted sampling. We use a linear function to bias the sampling. Compared to the second strategy, the quadruples occurred in early stages have higher probability of being sampled. Overall, we have empirically found that the second strategy is most beneficial to our framework and provide a detailed ablation study in Section 5.2
4.3 EMBEDDING
In temporal knowledge graphs, graph structures are longer static, as entities and their links evolve over time. Thus, entity features may change and exhibit temporal patterns. In this work, the embed- ding of an entity E E E at time consists of static low-dimensional vector and functional rep- resentation of time. The time-aware entity embedding is defined as (t) = [ē.l| [t)]" e IR Here, C; E Rds represents the static embedding that captures time-invariant features and global dependencies over the temporal KG. o(-) denotes a time encoding that captures temporal depen- dencies between entities (Xu et al. 2020). We provide more details about (.) in Appendix I denotes the concatenation operator. dy and dr represent the dimensionality of the static embedding and the time embedding, which can be tuned according to the temporal fraction of the given dataset. We also tried the temporal encoding presented in Goel et al. (2019), which has significantly more parameters. But we did not see considerable improvements. Besides, we assume that predicate features do not evolve. Thus, learn stationary embedding vector pı: for each predicate ps-
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4.4 TEMPORAL RELATIONAL GRAPH ATTENTION LAYER
Here, we propose a temporal relational graph attention (TRGA) layer for identifying the relevant evidence in the inference graph related to a given query q. The input the TRGA layer is a set of entity embeddings (t) and predicate embeddings produces a query-dependen attention score for each edge and a new set of hidden representations as its output. Similar to GraphSAGE: (Hamilton et al. 2017) and GAT (Veličković et al. 2017), the TRGA layer performs a local representation aggregation. To avoid misusing future information, we only allow message passing from prior neighbors to posterior neighbors. Specifically, for each node v in the inference graph, the aggregation function fuses the representation of node v and the sampled prior neighbors N₂ to output a aane-wware representation for v. Since entities may play different roles, depending on the predicate they are associated with, incorporate the predicate embeddings in the attention function to exploit relation information. Instead of treating all prior neighbors with equal importance, we take the query information into account and assign varying importance levels each prior neighbor u NN by calculating a query-dependent attention score using
in the given inference graph. The layer
Lou pk)) (h, (h. ( " 1
" obj (h W
IP4 11
(1)
where ei ph) ) is the attention score of the edge (v, Pk. u) regarding the query (egg Pq: ?, k)) Pk corresponds the predicate between node u and node v, Ps: and Py are predicate embeddings. h/-11 denotes the hidden representation of node
the (1 11)th inference step. When / = i.e.,
for the first layer, he = W (t) + b., where v = (e; t). w! sub and W obj are two weight matrices for capturing the dependencies between query features and node features. Then, we compute the normalized attention score a'. Pk) using the softmax function as follows
exp(e (g.
a (g. Pb) = E Ep.ep.. exp( (n (q.Pz))
(2)
where Pow represents the set of labels of edges that connect nodes v and w. Once obtained, aggregate the representations of prior neighbors and weight them using the normalized attention scores, which is written as
Σ Σ
o' (g. (a.Pp) (2).
MEN, PEEPoN
We combine the hidden representation hg) of node v with the aggregated neighborhood repre- sentation h² and feed them into a fully connected layer with LeakyReLU activation function a()). as shown below
(2) - (Whh (4) + - hh) bb))),
(4)
where h, denotes the representation of node v at the Ith inference step. and y is a hyperparameter. Further, we use the same layer to update the relation embeddings, which is of the form Pk WAP W + bj.- Thus, the relations are projected to the same embedding space as nodes and can be utilized in the next inference step.
4.5 ATTENTION PROPAGATION AND SUBGRAPH PRUNING
After having the edges' attention scores in the inference graph, we compute the attention score of of node regarding query q at the 1th inference step follows:
d
>>>
Σ
a (g. 1
(5)
NEA, P.EPuc
Thus, we propagate the attention of each node to its prior neighbors. As stated in Definition 2 each node in inference graph is an antiy-timestamp pair. To assign each entity unique attention score, we aggregate the attention scores of nodes whose entity is the same:
d de.. = g(ob/g (((e) = =e:), for E Vayn
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where d=..g denotes the attention score of entity cs. Ven is the set of nodes in inference graph Gig.. u(e) represents the entity included in node v, and g(-) represents score aggregation function. We try two score aggregation functions g()), i... summation and mean. We conduct an ablation study and find that the summation aggregation performs better. To demonstrate which evidence is important for the reasoning process, we assign each edge in the inference graph a contribution score. Specifically, the contribution score of edge (u. Pk: u) is defined Cra(q. Pa) a'... (g. Ph pa)ak.. where node u is a prior neighbor of node v associated with the predicate Pa- We prune the inference graph at each inference step and keep the edges with K largest contribution scores. We set the attention score of entities, which the inference graph does not include, to zero Finally, we rank all entity candidates according to their attention scores and choose the entity with the highest score as our prediction.
4.6 REVERSE REPRESENTATION UPDATE MECHANISM
When humans perform a reasoning process, the perceived profile of an entity during the inference may change as new evidence joins the reasoning process. For example, we want to predict the profitability of company A. We knew that A has the largest market portion, which gives us a high expectation about A's profitability. However, new evidence shows that conglomerate B enters this market as a strong competitor. Although the new evidence is not directly related to A, it indicates that there will be high competition between A and B, which lowers our expectation about A's prof- itability. To mimic human reasoning behavior, we should ensure that all existing nodes in inference graph Gin can receive messages from nodes newly added Guy. However, since Gir expands once at each inference step, it might include I-hop neighbors of the query subject the 1th step. The vanilla solution is to iterate the message passing / times at the 1 inference step, which means that we need to run the message passing (1 + -) L times in total, for L inference steps. To avoid the quadratic increase of message passing iterations, we propose a novel reverse representation update mechanism. Recall that, avoid violating temporal constraints, we use prior neighbors to update nodes' representations. And at each inference step, we expand Gin by adding prior neighbors of each node in Gig. For example, assuming that we are at the fourth inference step, for a node that has been added at the second step, we only need to aggregate messages from nodes added at the third and fourth steps. Hence, we can update the representations of nodes in reverse order as they have been added in Gmy. Specifically, at the (th inference step, we first update the representations of nodes added at the (1 1)th inference step, then the nodes added (1 2)th and so forth until O. as shown in Algorithm| iin the appendix. In this way, we compute messages along each edge in Gin only once and ensure that every node can receive messages from its farthest prior neighbor.
4.7 LEARNING
We split quadruples of temporal KG into train, validation, and test sets by timestamps, ensuring (timestamps of training (timesstm of validation (tiess(tssss of test set). We use the binary cross-entropy as the loss function, which is defined as
diig
L
Σ ELEE
yeu.g log( Σejecter o
) + (1- ye..a) log(1 log(1 Ee, Egins deggg
VEQ
7
where gins represents the set of entities in the inference graph of the query yer.g represents the binary label that indicates whether e; is the answer for q, and Q denotes the set of training quadruples. a denotes the attention score of e; at the final inference step. We list all model parameters in Table _ in the appendix. Particularly, we jointly learn the embeddings and other model parameters by end-to-end training.
5 EXPERIMENTS
5.1 DATASETS AND BASELINES
Integrated Crisis Early Warning System (ICEWS) (Boschee et al. 2015) and YAGO (Mahdisoltani ct al.) 2013) have established themselves in the research community as benchmark datasets of tem- poral KGs. The ICEWS dataset contains information about political events with time annotations,

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Published as a conference paper at ICLR 2021
e.g., (Barack Obama, visit, Malaysia, 2014-02-19). We evaluate model on three subsets of the ICEWS dataset, i.e., ICEWS14, ICEWS18, and ICEWS05-15, that contain event facts in 2014, 2018, and the facts from 2005 to 2015, respectively. The YAGO dataset is a temporal knowledge base that fuses information from Wikipedia with the English WordNet dataset (Miller 1995). Fol- lowing the experimental settings of HyTE (Dasgupta al.) 2018), we subset and only deal with year level granularity by dropping the month and date information. We compare our approach and baseline methods by performing the link prediction task on the ICEWS14, ICEWSI8, ICEWS0515, and YAGO datasets. The statistics of the datasets are provided in Appendix g
We compare XERTE with benchmark temporal KG and static KG reasoning models. From the temporal KG reasoning models, we compare our model with several state-of-the-ar methods, in- cluding TTransE (Leblay & Chekol 2018). TA-DistMult/TA TransEE (García-Durán et al.. 2018). DE- et al. 2019),. INTCCompEx (Lacroix et al. 2020). CyGNet(ZZu et al. al.[22000, and RE-Net (Jin et (2T22009). From the static KG reasoning models, we choose TransE. (Bordes et al.) 2013).
DistMult (Yang et al. 2014), and ComplEx (Trouillon et al. 2016).
5.2
EXPERIMENTAL RESULTS AND ABLATION STUDY
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21.51
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Table Results of future link prediction on four datasets. Compared metries are time-aware filtered MRR (%) and Hits@ 1/3/10 (%). The best results among all models are in bold.
Comparison results Table 1 summarizes the time-aware filtered results of the link prediction task on the ICEWS and YAGO " The time-aware filtering scheme only filters out triples that are genuine at the query time while the filtering scheme applied in prior work (Jin et al. 2019 Zhu et al.] 2020) filters all triples that occurred in history. A detailed explanation is provided in Appendix D Overall, xERTE outperforms all baseline models on ICEWS14/05 155118 in MRR and Hits@ T while being more interpretable. Compared to the strongest baseline RE-Neet, XERTE obtains a relative improvement of 5.60% and 15.15% in MRR and Hits@I 11 which are averaged on
Especially, XERTE achieves more gains in Hits @ I than in Hits @ 10. It confirms the assumption that subgraph reasoning helps XERTE make a sharp prediction by exploiting local structures. On the YAGO dataset, xERTE achieves comparable results with RE-Net in terms of MRR and Hits 1/3. To assess the importance of each component, we conduct several ablation studies and show their results in the following.
Representation update analysis We train model without the reverse representation update mechanism to investigate how this mechanism contributes to our model. Since the reverse repre- sentation update ensures that each node can receive messages from all its prior neighbors in the inference graph, we expect this mechanism could help nodes mine available information. This up- date mechanism should be especially important for nodes that only have been involved in a small number of events. Since the historical information of such nodes is quite limited, it is very chal- lenging to forecast their future behavior. In Figure 2a and 2b we show the metrics of Hits I and Hits @ 10 against the number of nodes in the inference graph. It can be observed the model with the reverse update mechanism performs better in general. In particular, this update mechanism signif- icantly improves the performance if the query subject only has small number of neighbors in the subgraph, which meets our expectation.
We found that CyGNet does not perform subject prediction in its evaluation code and does not report time-aware filtered results. The performance significantly drops after fixing the code. *Code and datasets are available hups://github.co wwwwo//meemoooeeeeaaaemaam
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Figure 2: Ablation Study. Unlike in Table that reports results the whole test set, here filter out test quadruples that contain unseen entities. (a)-(b) We compare the model with/without the re- verse representation update in terms of raw Hits @ 1(%) and Hits @ 10(%) ICEWS14, respectively. (c) Temporal embedding analysis on YAGO. We refer the model without temporal embeddings as BARTE-Static (d) Attention
aggregation function analysis Hits@ 1/3/10((%) ()). (e) Inference time (seconds) on the test set of ICEWS14 regarding different in-
ICEWS14 14: MRR (%) and
ference step settings L (1,2,3,4) 4). (f) Raw MRR(%) ICEWS14 regarding different inference step settings L.
Time-aware representation analysis and node attention aggregation To verify the importance of the time embedding, evaluate the performance of model without time encoding. As shown in Figure 2c removing the time-dependent part from entity representations sacrifices the model's per- formance significantly. Recall that each node in inference graph Goff associated with timestamp, the same entity might appear in several nodes in Guy with different timestamps. To get unified attention score for each entity, we aggregate the attention scores nodes whose entity is the same. Figure 2d shows that the summation aggregator brings a considerable gain ICEWS14.
Sampling analysis We run experiments with different sampling strategies proposed in Section To assess the necessity of the time-aware weighted sampling, we propose deterministic version of the time-aware weighted sampling, where we chronologically sort the prior edges of node in terms of their timestamps and select the last N edges to build the subset 2.. The experimental results are provided in Table in the appendix. We find that the sampling strategy on model's performance. Sampling strategies that bias towards recent quadruples perform better. Specifically, the exponentially time-weighted strategy performs better than the linear time-weighted strategy and the deterministic last-N-edges strategy.
a considerable influence
Time cost analysis The time cost of xERTE is affected not only by the scale of a dataset but also by the number of inference steps I.. Thus, we run experiments of inference time and predictive power regarding different settings of L. and show the results in Figures (2c and 2i We see that the model achieves the best performance with L goes up. To make the computation more efficient, we develop series of segment operations for subgraph reasoning. Please see Appendix G for more details.
while the training time significantly increases as
5.3 GRAPHICAL EXPLANATION AND HUMAN EVALUATION
The extracted inference graph provides a graphical explanation for model's prediction. As intro- duced in 4.7 assign each edge in the inference graph contribution score. Thus, users trace back the important evidence that the prediction mainly depends on. We study query chosen from the test set, where predict whom will Catherine Ashton visit Nov. 2014 and show the final
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Matuomnd Ber 30101164
John 11--1-30
Cabrnet Council of Welster Aodion ore (Unted Stateo) 3014-11-47
Oprass Intent spae nagotial
Connult
Host& viex Host viait
Capreso intent to regotiate
segotiate
Heaf&
Chaaa 181--1144
Mano
11-43
La
MOSE VIST
Chics 11-11
Catariis TITTETIIO
Moot 'fird location
1HL-1142 Jn
Ior-
stattrnent
Exprese HOSpE negotatee
Expross negetiote
Express Intant TO or repotiate
Chima 19-31
Oman 2014-11-00
Make octipeltcc comment Chasa 11
11-8
Makio optiiiitte commrnnt
Motammed 2814-1--3
Make optientti comment
Maka atatirmend
Malia optivieiic
Figure 3: The inference graph for the query (Catherine Ashton, Make visit, ?, 2014-11-09) from ICEWS14. The biggest cyan node represents the object predicted by xERTE. The cyan node with the entity Catherine Ashton and the timestamp 2014-11-000 represents the given query subject and the query timestamp. The node size indicates the value of the node attention score. Also, the edges' color indicates the contribution score of the edge, where darkness increases the contribution score goes up. The entity at an arrow's tail, the predicate on the arrow, the entity and the timestamp at the arrow's head build a true quadruple.
inference graph in Figure 3 In this case, the model's prediction is Oman. And (Catherine Ashton, express intent to meet or negotiate, Oman, 2014-11-04) is the most important evidence to support this answer.
To assess whether the evidence is informative for users in an objective setting, we conduct a survey where respondents evaluate the relevance of the extracted evidence to the prediction. More con- cretely, we set up an online quiz consisting of 7 rounds. Each round is centered around a query sampled from the test set of ICEWS14/ICESSO answer, we present the human respondents with two pieces of evidence in the inference graph with high contribution scores and two pieces of evidence with low contribution scores order. Specifically, each evidence is based on chronological reasoning path that connects the query subject with an object candidate. For example, given a query (police, arrest, ?. 2014-1 1--222))), an extracted clue is that police made statements to lawyers on 2014- then lawyers were criticized by citizens on 2014-12-10 10. In each round, we set up three questions to ask the participants to choose the most relevant evidence, the most irrelevant evidence, and sort the pieces of evidence according to their relevance. Then we rank the evidence according to the contribution scores computed by our model and check whether the relevance order classified by the respondents matches that estimated by our models. We surveyed 53 participants, and the average accuracy of all questions is 70.5%. Moreover, based on majority vote, 18 out of 21 questions were answered correctly, indicating that the extracted inference graphs are informative, and the model is aligned with human intuition. The complete survey and detailed evaluation are reported in Appendix H
Along with the query and the ground-truth
randomized
CONCLUSION
We proposed an explainable reasoning approach for forecasting links on temporal knowledge graphs. The model extracts a guery-ddpendeet subgraph from a given temporal KG and performs an attention propagation process to reason on Extensive experiments on four benchmark datasets demonstrate the effectiveness of our method. We conducted a survey about the evidence included in the extracted subgraph. The results indicate that the evidence is informative for humans.

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APPENDIX
Figure The inference graph for the query (co, (eo.Pr; ?, ()). The entity an ar- row's tail, the predicate on the arrow, the entity and the timestamp at the arrow's head build a true quadruple. Specifically, the true quadruples this graph are as follows: {(eo, (eeo.Pi,eii ei,t), (co, P2, t2, (Co, Pa t2), (eo, e2,t2) Note that t3 is posterior to to, 11,2.
Algorithm Reverse Representation Update at the th Inference Step
Input: Inference graph Gmy, nodes in the inference graph V, nodes that have been added into Gin at the 1hh inference step V., sampled prior neighbors Nr. hidden representation at the (L-1)th step b entity embeddings e,, weight matrices W... W obj' and W K. query = (Eg, Pq: ?, tq), sub.
update ratio 7.
Output: Hidden representations h at the thh inference step, Vo E V.
1: for
I,... 0 do
2: for V do
3: for u E N₂ do
4:
chulg, Pk))
WL
sub
(h!- (1lpk///4111 Pg
WL (h4 oby
P& ( P.):
5:
a (1.pk))) EwEn, EpsePow (1:pe))
exple (R.Pz))
6:
end for
7:
h/ EnEN, Eo.ep.. (h -
8:
(g) a (W/(hht- (g) + 7) (4) + b
9:
end for
10:
end for
Return h/, Yu V.
Parameter
Symbol
static entity embeddings frequencies and phase shift of time encoding predicate embeddings weight matrices TRGA
é;
w, Φ
P
W
W
W!
sub?
b obj'
bias vector of TRGA weight matrix and bias of node embeddings
W b
Table 2: Model parameters.
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Sampling Strategies
MRR
Hits@1
Hits@3
Hits@ 10
Uniform
36.26
27.66
41.39
53,96
Time-aware exponentially weighted
41.56
32.49
47.27
59.63
Time-aware linearly weighted
38.21
29.25
43.77
56.07
Last-N-edges
39.84
31.31
45.04
57.40
Table 3: Comparison between model variants with different sampling strategies on ICEWS14: raw MRR (%) and Hits@ 1/3/10 (%). In this ablation study, we filter out test triples that contain unseen entities.
A RELATED WORK
A.1 KNOWLEDGE GRAPII MODELS
Representation learning is an expressive and popular paradigm underlying many KG models. The key idea is to embed entities and relations into a low-dimensional vector space. The embedding- based approaches for knowledge graphs can generally be categorized into bilinear models (Nickel al. 2011 Balažević et al. 2019), translational models (Bordes et al. 2013 Sun et al. 2019), and deep-learning models (Dettmers et al., 2017 Schlichtkrull et al.) 2018)_ Besides, several studies (Hao et al., 2019 Lv al. 2018 Ma et al., (017)) explore the ontology of entity types and relation types and utilize type-based semantic similarity to produce better knowledge embeddings. However, the above methods lack the ability to use rich temporal dynamics available on temporal knowledge graphs. To this end, several studies have been conducted for link prediction on temporal knowledge graphs (Leblay & Chekol 2018 García-Durán et al. 2018 Ma et al., 201 8b) Dasgupta et al. 2018
Trivedi et al.) 2017 Jin et al.) 2019 Goel et al. 2019; Lacroix et al. 2020). Ma et al. (2018b) developed extensions static knowle knowledge graph models by adding timestamp embeddings to their score functions. Besides, Garcia- Durán et al. (2018) suggested straight forward extension of some existing static knowledge graph models that utilize a recurrent neural network (RNN) to encode predicates with temporal tokens derived from given timestamps. Also, HyTE (Dasgupta al. 2018) embeds time information in the entity-relation space by arranging a temporal hyperplane to each timestamp. However, these models cannot generalize to unseen timestamps because they only learn embeddings for observed timestamps. Additionally, the methods are largely black-box, lacking the ability to interpret their predictions while our main focus to employ an integrated transparency mechanism for achieving human-undersenn understandable results.
A.2 EXPLAINABLE REASONING ON KNOWLEDGE GRAPHS
Recently, several explainable reasoning methods for knowledge graphs have been proposed (Das ctt al.) 2017 Xu et al., 2019; Hildebrandt et al.) 2020) Das et al. (2017) proposed a reinforcement learning- based path searching approach display the query subject and predicate to the agents and let them perform a policy guided walk to the correct object entity. The reasoning paths produced by the agents can explain the prediction results to some extent. Also, [iidebrandd et al. (2020) framed the link prediction task as debate game between two reinforcement learning agents that extract evidence from knowledge graphs and allow users understand the decision made by the agents. Besides, and more related to our work, Xu et al. (2019) models sequential reasoning process by dynamically constructing an input-dependent subgraph. The difference here is that these explainable methods can only deal with static KGs, while our model is designed for forecasting on temporal KGs.
B WORKFLOW
We show the workflow of the subgraph reasoning process in Figure The model conducts the reasoning process on a dynamically expanding inference graph Guy extracted from the temporal KG. interpretable graphical explanation about the final prediction. Given a query q = (c,, pa. 2, tg), we initialize the inference graph with the query entity e, and define the tuple of (eqs f.y) the first node in the inference graph (Figure 5a). The inference graph expands by
This inference graph gives
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(a) Initialization.
(b) Expansion.
(c) Pruning.
(d) New Expansion.
Figure 5: Inference step by step illustration. Node attention scores are attached to the nodes. Gray nodes are removed by the pruning procedure.
sample neighbors that have been linked with Eg prior to lg. as shown in Figure 5b The expansion would go rapidly that covers almost all nodes after few steps. To prevent the inference graph from exploding. we constrain the number of edge by pruning the edges that are less related to the query (Figure 5cp Here, we propose query-dependent temporal relational attention mechanism in Section 4.4 to identify the nodes' importance in the inference graph for query and aggregate information from nodes' local neighbors. Next, we sample the prior neighbors of the remaining nodes in the inference graph to expand it further, as shown in Figure 5d As this process iterates, the inference graph incrementally gains more and more information from the temporal KG. After running L inference steps, the model selects the entity with the highest attention score in Gig as the prediction of the missing query object, where the inference graph itself serves as graphical explanation.
2
C DATASET STATISTICS
Dataset
Ntrain
Noulid
Ntest
Nent
Nyel
Niimestamp
Time granularity
ICEWS14
63685
13823
13222
7128
230
365
day
ICEWS18
373018
45995
49545
23033
256
304
day
ICEWS0515
322958
69224
69147
10488
251
4017
day
YAGO
51205
10973
10973
10038
10
194
year
Table 4: Dataset Statistics
Dataset
|
E E
EEr-vaa
|E]
ICEWS14
6180
86.7
6710
7128
ICEWS18
21085
91.5
21995
23033
ICEWS0515
8853
84.4
9792
10488
YAGO
7904
78.7
9008
10038
Table 5: Unseen entities (new emerging entities) in the validation set and set. |1trl denotes the number of entities in the training set, vatl+vatl represents the number of entities in the training set and validation set, [g] denotes the number of entities in the whole dataset.
We provide the statistics of datasets in Table Since we split each dataset into subsets by times- tamps, ensuring (timestamps of training set) (timestamps of validation set) < (timestamps of test set), a considerable amount entities in test sets is unseen. We report the number of entities each subset in T
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D EVALUATION PROTOCOL
For each quadruple q = (e., p, Co. t) in the test set Grest. create two queries: (e and (eo, Po..p_. ?,,), where p 11 denotes the reciprocal relation of p. For each query. the model ranks all entities Eii in the final inference graph according to their attention scores. If the ground truth entity does not appear in the final subgraph, Let Ve. and Vn, represent the rank for es and e, of the two queries respectively. We evaluate our model using standard metrics across the link prediction literature: mean reciprocal rank (MRR): 2- Egggner (p-s + V.. and Hitskt(k- E (1,3, 10)): the percentage of times that the true entity candidate appears in the top k of the ranked candidates.
set its rank as |8| (the number of entities in the dataset).
In this paper, we consider two different filtering settings. The first one following the ranking technique described in [ordde et al. (2013), where we remove from the list of corrupted triples all the triples that appear either in the training, validation, or test set. We name static filtering. Trivedi al. (2017), 7), Jin et al. (0119), and MadZZhuee et al. (2020) this filtering setting for reporting their results on temporal KG forecasting. However, this filtering setting is not appropriate for evaluating the link prediction on temporal KGs. For example, there is a test quadruple (Barack Obama, visit, India, 2015-01-25), and we perform the object prediction (Barack Obama, visit, ?, 2015-01-25). We have observed the quadruple (Barack Obama, visit. Germany, 2013-01-18) in the training set. According to the static filtering, (Barack Obama, visit, Germany) will be considered as genuine triple at the timestamp 2015-01-25 and will be filtered out because the triple (Barack Obama, visit, Germany) appears in the training set in the quadruple (Barack Obama, visit, Germany, 2015-01-18). However, the triple (Barack Obama, visit, Germany) only temporally valid on 2013-01-18 but not on 2015-01-25. Therefore, we apply another filtering scheme, which is more appropriate for the link forecasting task on temporal KGs. We name time-aware filtering. In this case, we only filter out the triples that are genuine the timestamp of the query. In other words, if the triple (Barack Obama, visit, Germany) does not appear at the query time of 2015-01-22 the quadruple (Barack Obama, visit, Germany, 2015-01-25 -12) is considered corrupted and will be filtered out. We report the time-aware filtered results of baselines and our model in Table
E IMPLEMENTATION
We implement our model and all baselines in PyTorch (Paszke et al.) 2019). We tune hyperparam-
eters of our model using grid search. We set the learning rate to be 0.0002, the batch size to be 128, the inference step L to be 3. Please see the source code for detailed hyperparameter settings. We implement TTranSE, TA- PA-TransE/TA-DistMuus et al., 2019). We use the released code to implement DE-SimplEE TNTComplEX We use the binary cross-entropy loss to train these baselines and optimize hyperparameters accord- ing to MRR on the validation set. Besides, we use the datasets augmented with reciprucal relations to train all baseline models.
and RE-Net based on the code provided in (Jin
1 and CyGNe
F REVERSE REPRESENTATION UPDATE MECHANISM FOR SUBGRAPH REASONING
In this section, explain an additional reason why we have to update node representations along edges selected in previous inference steps. We show our intuition by simple query in Figure two inference steps. For simplicity, we do not apply the pruning procedure here. First, we check the equations without updating node representations along previously selected edges. hţ denotes the
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hidden representation of node i at the 1t inference step.
First inference step:
ho s(h h1. h2. hg)
h f(h))
h2 S(b))
h f(b
Second inference step:
hg = f(h): h): h2, h2)
f(b): (hl), ((b)
hf f(h). ha. bz)
h2 f(h,, h/. h2)
h [bb3 hb)
Note that h is updated with hf. hgg h& and has nothing to do with h hb. h.. h hgg i.e. two-hop neighbors. In comparison, if we update the node representations along previously selected edges, the update in second layer changes to:
Second inference step part a: hī s(((h)))
hg f(f(h!)
h f(((g))
h f(((D)))
h = f(F(h))
Second inference step part b:
h = f(h), h2 h2)
h s(bg. ba h2)
h f(h). by)
Second inference step part e:
h Shb ; hy h h
Thus, the node 1~3 receive messages from their one-hop prior neighbors, i.c. h (h], hz). Then they pass the information to the query subject (node 0), i.e., hj = s(hj. h h2 h2)
G SEGMENT OPERATIONS
The degree of entities in temporal KGs, i.e., ICEWS, varies from thousands to a single digit. Thus, the size of inference graphs of each query also different. To optimize the batch training, we define an array to record all nodes in inference graphs for batch of queries. Each node is represented by tuple of (inference graph index, entity index, timestamp, node index). The node index is the unique index to distinguish the same node in different inference graphs.
Note that the inference graphs of two queries may overlap, which means they have the same nodes in their inference graphs. But the query-dependent node representations would be distinct in differ- ent inference graphs. To avoid mixing information across different queries, we need to make sure that tensor operations can be applied separately to nodes in different inference graphs. Instead of iterating through each inference graph, we develop a series segment operations based on matrix multiplication. The segment operations significantly improve time efficiency and reduce the time cost. We report the improvement of time efficiency on ICEWS14 in Table b Additionally, we list two examples of segment operations in the following.
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1
1
2
0
8
3
6
Figure 6: A simple example with two inference steps for illustrating reverse node representation update schema. The graph is initialized with the green node. In the first step (the left figure), orange nodes are sampled; and in the second step (the right figure), blue nodes are sampled. Each directed edge points from source node to its prior neighbor.
Computations
Time Cost using Iterator
Time Cost using Segment Operation
Aggregation of Node Score Aggregation of Entity Score
11.75s
0.004s
3.62s
0.026s
Softmax
1.56s
0.017s
Node Score Normalization
0.000738s
0.000047s
Table 6: Reduction time cost for batch on ICEWS14
Segment Sum Given vector R and another vector E Rd that indicates the segment index of each element in x, segment sum operator returns the summation for each segment. For example, have
[3, 1, 5)"" and [0, 0, 1]" which means the first two element of x belong to the 9th segment and the last elements belongs to the first segment. The segment sum operator returns [4, 5) as the output. It is realized by creating sparse matrix Y E Raxd where denotes the number of segments. We set 1 in positions {s][i, i), Vi E {O...., d}} of and pad other positions with zeros. Finally, multiply Y with x to get the sum of each segment.
Segment Softmax
The standard softmax function o :RRK +
R is defined as:
o (z): exp (z;
exp(2;)
The segment softmax function has two inputs: R contains elements to normalize and s R K denotes the segment index of each element. It is then defined as:
exp (Z:)
(z), EjE(HN== exp (23)
where s; denotes the segment that 2; is in.
The segment softmax function can be calculated by the following steps:
1. We apply the exponential function each element of and then apply the segment operator to get a denominator vector d. We need broadcast d such that aligns with z, which means dii the summation of segment s(i).
2. We apply element-wise division between d and z.
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11%
12%
32%
30%
47%
68%
Some College but No Degree Bachelor's Degree
Male Female
Under 20
23-40 Over
Master's Degree
Doctoral Degree
(a) Gender distribution.
(b) Age distribution.
(c) Education level.
Figure 7: Information about the respondent population.
H SURVEY
In this section, provide the online survey (see Section 5.3 in the main body) and the evaluation statistics based on 53 respondents. To avoid biasing the respondents, we did not inform them about the type of our project. Further, all questions are permuted random.
We set up the quiz consisting of 7 rounds. In each round, we sample a query from the test set of ICEWSI 4/CEE400SS Along with the query and the ground-truth object, we present the users with two pieces of evidence extracted from the inference graph with high contribution scores and two pieces of evidence with low contribution scores randomized order. The respondents are supposed to judge the relevance of the evidence to the query in two levels, namely relevant or less relevant. There are three questions in each round that ask the participants to give the most relevant evidence, the most irrelevant evidence, and rank the four pieces of evidence according their relevance. The answer to the first question is classified as correct a participant gives one the two statements with high contribution scores the most relevant evidence. Similarly, the answer to the second question classified as correct if the participant gives one of the two statements with low contribution scores the most irrelevant evidence. For the relevance ranking task, the answer is right if the participant ranks the two statements with high contribution scores higher than the two statements with low contribution scores.
H.1 POPULATION
We provide the information about gender, age, and education level of the respondents in Figure
H.2 AI QUIZ
You will participate in a quiz consisting of eight rounds. Each round is centered around an interna- tional event. Along with the event, we also show you four reasons that explain why the given event happened. While some evidence may be informative and explain the occurrence of this event, oth- may irrelevant to this event. Your task is to find the most relevant evidence and most irrelevant evidence, and then sort all four evidence according to their relevance. Don't worry if you feel that you cannot make informed decision: Guessing is part of this game!
Additional Remarks: Please don't look for external information (e.g., Google, Wikipedia) or talk to other respondents about the quiz. But you are allowed to dictionary if you need vocabulary clarifications.
Example
Given an event, please rank the followed evidence according to the relevance to the given event. Especially, please select the most relevant reason, the most irrelevant reason, and rank the relevance from high to low.
Event: French government made an optimistic comment about China 2014-11-24
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A. First, 2014-11-20, South Africa engaged in diplomatic cooperation with Morocco. Later, on 2014-11-21, a representative of the Morocco government met a representative of the French government.
B. First, on 2014-11-18, the Chinese government engaged in negotiation with the Iranian govern- ment. Later, on 2014-11-21, representative of the French government met representative of the Chinese government.
C. On 2014-11-23, the French hosted a visit by Abdel Fattah Al-Sisi.
D. A representative of the French government met a representative of the Chinese government on 2014-11-21.
Correct answer
Most relevant: D
Most irrelevant: A
Relevance ranking: DBCA
Tasks
Event: On 2014-12-17, the UN Security Council accused South Sudan.
A. South Africa engaged in diplomatic cooperation with South Sudan 2014-12-11.
B. First, on 2014-11-17, Uhuru Muigai Kenyatta accused UN Security Council. Later, on 2014-11- 26, the UN Security Council provided military protection to South Sudan.
C. On 2014-12-16, UN Security Council threatened South Sudan with sanctions.
D. South Sudan hosted the visit of John Kerry on 2014-12-16.
Most relevant: Most irrelevant:
Relevance ranking:
2. Event: Indonesia police arrested and retained Indonesia citizen at 2014-12-28.
A. The Indonesia police claimed that an attorney denounced the citizen on 2014-12-10.
B. Zaini Abdullah endorsed the Indonesia citizen on 2014-12-25.
C. The Indonesia police made an optimistic comment on the citizen on 2014-12-14.
D. The Indonesia police investigated the citizen on 2014-12-08.
Most relevant:
Most irrelevant: Relevance ranking:
3. Event: A citizen from Greece protested violently against the police of Greece on 2014-11-17.
A. The Greek head of government accused the political party "Coalition of the Radical Left" on 2014-05-25.
B. Greek police refused to surrender the Greek head of government on 2014-10-15
C. Greek citizens gathered support on behalf of John Kerry on 2014-11-17.
D. Greek police arrested and detained another Greek police officer 2014 11-4.
Most relevant:
Most irrelevant:
Relevance ranking:
4. Event: Raál Castro signed formal agreement with Barack Obama on 2014-12-17
A. First, on 2009-01-28, Dmitry A. Medvedev made statements to Barack Obama. Later, on 2009- 01-30, Raúl Castro negotiated with Dmitry A. Medvedev.
B. Raúl Castro visited Angola on 2009-07-22.
C. Raál Castro hosted visit of Evo Morales 201 1-09-19.
D. First, on 1D08-11-05. Evo Morales hosted a visit of Barack Obama. Later, on 1-09-99- Raúl Castro appeal for de-escalation of military engagement Evo Morales.
Most relevant:
Most irrelevant:
Relevance ranking:
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Published as a conference paper at ICLR 2021
5. Event: The head of the government of Ukraine considered make a policy option with Angela Merkel on 2015-07-10.
A. First, 2014-07-04, the armed rebel in Ukraine used unconventional violence to the military of Ukraine. Later, on 2014-07-10, the head of government of Ukraine made statements to the armed rebel in Ukraine.
B. The head of the government Ukraine expressed intent to meet with Angela Merkel on 2014- 10-30.
C. First, on 2014-07-04, the armed rebel Ukraine used unconventional violence to the military of Ukraine. Later, on 2014-07-19, the head of government of Ukraine made statements to the armed rebel in Ukraine.
D. The head of the government of Ukraine consulted with Angela Merkel 2015-06-06.
Most relevant: Most irrelevant:
Relevance ranking:
6. Event:
On 2014-08-09, Ukraine police arrested member of the Ukraine military.
A. First, on 2014-07-23, a member of Ukraine parliament consulted the head of the Ukraine govern- ment. Later, 2014-07-24, the head of government made statement to the Ukraine police.
B. First, on 2014-06-25, the military of Ukraine used violence to an armed rebel that occurred in Ukraine. Later, 2014-07-10, the armed rebel used violence to the Ukraine police.
C. First, on 2005-02-20, the military of Ukraine made a statement to the head of the government of Ukraine. Later, 2005-07-18, the head of government of Ukraine appealed for change in leadership of the Ukraine police.
D. On 2014-07-31, the head of the Ukraine government praised the Ukraine police.
Most relevant:
Most irrelevant:
Relevance ranking:
7. Event: The Office of Business Affairs of Bahrain negotiated with the Labor and Employment Ministry of Bahrain on 2015-07-16.
A. First, 2014-07-27, the undersecretary of Bahrain made statements to the Labor and Employ- ment Ministry of Bahrain. Later, on 0015-01-21, an officer of Business Affairs Bahrain signed a formal agreement with the undersecretary of Bahrain.
B. On 2012-11-2, the office of Business Affairs of Bahrain expressed intent to provide policy support to the employees in Bahrain.
C. First, on 2006-11-01, the employees in Bahrain made statements with the special Rapporteurs of the United Nation. Later, on 2011-05-11, the office of Business Affairs of Bahrain reduced relations with the employees in Bahrain.
D. representative of the Labor and Employment Ministry of Bahrain consulted with representa- tive of the Office of Business Affairs of Bahrain on 2014-01-31.
Most relevant:
Most irrelevant:
Relevance ranking:
H.3 GROUND TRUTH ANSWERS
Question 1:
Most relevant: B/C
Most irrelevant: A/D
Relevance ranking: BCADBCDNCEAD/CEDA
Question 2:
Most relevant: A/D
Most irrelevant: B/C Relevance ranking: ADBC/ADCBBDABC/DACB
Question 3:
Most relevant: B/D
Most irrelevant: A/C
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Published as a conference paper at ICLR 2021
Relevance ranking: BDAC/BDCAIDBAC/DCCA
Question
Most relevant: A/D
Most irrelevant: B/C
Relevance ranking:
ADBC/ADCCIIDBCIDACB
Question 5:
Most relevant: B/D
Most irrelevant: A/C BDACCBDDCWDDBCCDBCCA
Relevance ranking:
Question
Most relevant: B/C.
Most irrelevant: A/D Relevance ranking: BCADIBCDAGCBADICDDA
Question 7:
Most relevant: A/D
Most irrelevant: B/C
Relevance ranking: ADBC/ADDCBDDBC/DACB
H.4 EVALUATION
The evaluation results of respondents are shown in Figure
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Figure 8: The accuracy of the survey questions.
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Published as a conference paper at ICLR 2021
I ADDITIONAL ANALYSIS OF TIME-AWARE ENTITY REPRESENTATIONS
We use a generic time encoding Xu et al. 2020 defined as (1) Vilcos(urt +
$1)...... cos(wat + Qa)] to generate the time-varintt part of entity representations (please Sec- tion for more details). Time-aware representations have considerable influence on the temporal attention mechanism. To make our point, we conduct case study and extract the edges' attention scores from the final inference graph. Specifically, we study the attention scores of the interactions between military and student different timestamps terms of the query (student, criticize, Nov. 17, 2014). We list the results of the model with time encoding in Table and the results of the model without time encoding Table X
As shown in Table 7 by means of the time-encoding, quadruples that even have the same subject, predicate, and object have different attention scores. Specifically, quadruples that occurred recently tend to have higher attention scores. This makes our model more interpretable and effective. For example, given three quadruples {counttr A, accuse, country B, (1). (country A, express intent to negotiate with, country B, tg), (country A, cooperate with, country B. tz)}. country A probably has a good relationship with at t if (f1 < t2 < b3 < t) holds. However, there would be a strained relationship between A and B if > h 12 (x) holds. Thus, can that the time information is crucial to the reasoning, and attention values should be time-dependent. In comparison, Table shows that the triple (military, use conventional military force, student) has randomly different attention scores at different timestamps, which is less interpretable.
Subject
Object
Predicate
Timestamp
Attention Score
Military
Student
Use conventional military force
Jan. 17, 2014
0.0123
Military
Student
Use conventional military force
May 22, 2014
0.0186
Military
Student
Use conventional military force
Aug. 18. 2014
0.0235
Military
Student
Use unconventional violence (reciprocal relation)
Aug. 25, 2014
0.0348
Table 7: Attention scores of the interactions between military and student different timestamps (with time encoding).
Subject
Object
Predicate
Timestamp
Attention Score
Military
Student
conventional military force
Jan. 17. 2014
0.0152
Military
Student
Use conventional military force
May 22, 2014
0.0122
Military
Student
conventional military force
Aug.
0.0159
Military
Student
Use unconventional violence (reciprecal relation)
Aug. 25, 2014
0.0021
Table 8: Attention scores of the interactions between military and student at different timestamps
(without time encoding).
24


Reviews:
[{"review_id": "sQg8zdTlXo", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "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": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper addresses the problem of link forecasting in temporal knowledge graphs with special emphasis on generating explainable predictions. The explainability component of their work involves producing a subgraph of the knowledge graph (called the inference graph) that serves as a context of the query being asked, and on which the prediction decision was based. \n\nThe inference graph is generated by sampling a subset of prior edges in the L-hop neighborhood of the query node. The authors try different sampling schemes to select a subset of edges. They then use a GNN aggregation scheme to produce a time-away representation of each node. This representation is generated by taking into account the “relevance” of nodes and edges to the query by employing a relational attention mechanism. Each node is then given a plausibility score, and the node with highest plausibility score is selected to be the answer to the query.  \n\nThe authors run experiments on standard temporal datasets and have appropriate ablation studies. They compare their work to existing methods, and their experiments show that their model performs significantly better than state of the art.\nLink forecasting in temporal knowledge graphs is an important problem that arises in many real-life applications, and being able to explain these predictions is equally important. The model proposed by the authors contain the right components for tackling the problem: subgraph sampling based on time, attention mechanism based on the role of a given entity in the query, message passing to learn from neighborhood information for each node, ...etc. \n\nThe writing of the paper however is hard to follow; notation is sometimes incomplete or undefined, mathematical formulations are often unnecessarily complex. The pieces were described in a somewhat topsy-turvy order and It was difficult putting together all the pieces of the algorithm. Some further details below:\n- Page 3, paragraph 3: what is tKG? There is possibly a missing word in the sentence before-last of the paragraph “with v_q to .”\n\n- In Definition 2, the definition of N_v and \\bar{N_v} is hard to follow, even though the concept is simple. Consider saying it in plain words first, then state the definition of N_v without the union operator (by using an “or” in the conditional)\n\n- There is a lot of repetition in the text. E.g. mention of “sampling the neighbors” a few times in the text until you encounter it in Section 4.5. Perhaps discuss sampling first?)\n\n- In Equation 2 (and elsewhere), what is P_{vw}?\n\n- Section 4.3 was hard to follow. The motivation for computing representations in a reverse manner seems to stem only from computational considerations, but it is not clear whether this reverse update mechanism produces the same representation as the standard “forward” update would. The section in the appendix on the topic did not shed more light to this process. \n\n- In the same paragraph, the sentence starting with “Since we only feed…” is confusing:  is the current inference step m or l ?\nSection 4.6: It would be less confusing to put the definition of a_e_i^l before that of a_v^l. Also, at which point is this “plausibility score” computed?\n\n- There is a lot happening in Figure 1 but the figure is not referenced from the text. Why are there two identical modules? Perhaps more explanation would be helpful. \n\nOverall, the paper has a lot of promise and the work conducted looks solid. The authors are encouraged to make another attempt at making their work clearer and understandable.\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "logkY-LQ8RL", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": 3, "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": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "In Appendix I.1 it says \"We are machine learning scientists from the University of Munich...\", which violates the rule of anonymity. Please let me know if I should continue on reviewing this paper. Thanks!", "extra_scores": {}, "extra_text": {}}, {"review_id": "gG2h5CFUbj", "reviewer": "AnonReviewer5", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "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": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "**Summary:** This paper proposes xERTE, a comprehensive set of strategies (i.e. a temporal relational attention mechanism and a human-mimic representation update scheme, temporal neighborhood sampling and pruning, etc.) for link forecasting in temporal knowledge graphs (tKGs). Experiments on real-world tKGs show significant improvements and better explainability on KG forecasting. \n\n**Reason to accept:**\n(1) Well motivated problem formation and clear definition. (2) Well illustrated model architecture and model details of major components and technical details, the reverse representation update is particularly interesting; (3) Extensive experiments on multiple tKG datasets are conducted. Insights, ablation studies on model variants, and case studies are also provided.\n\n**Reason to reject:**\nModel complexity analysis and inference time. Clarity and some details about experiments and sampling techniques.\n\n**Comments & Questions:**\n(1) The approach is technically sound. One concern is about model complexity and inference time. The workflow of xERTE seems complicated with multiple attention calculations and representation updates and it would be better to provide the inference time for query (regarding different steps) to show the scalability and whether it is applicable for large-scale tKG.\n \n(2)  Several questions regarding the experiments need clarification: \n(i) Is $l$ (step number) or $L$ explicitly given in the paper or manually set up? What is the number of steps for inference in the test set? Also, what is the difference between the expansion step and the inference step? \n(ii) How do you make predictions by static KG embedding models by “compressing temporal knowledge graphs into a static, cumulative graph by ignoring the time information”? \n(iii) What does “raw MRR/Hits@k” score mean? Does it refer to the raw/filtered settings? If so, why not use filtered evaluation, which seems more reasonable? (iv) The performance of TcomplEx, which is claimed as one baseline, is not reported. \n(v) Why are the performance of TA-TransE and T-TransE even worse than static TransE? It was not the case using similar datasets in [4].\n(vi) How are all entity embeddings (l=0) and predicated embeddings initialized? Are entity embeddings from 4.4 Dynamic embeddings?  Are all dimension parameters explicitly listed in the paper? \n\n(3) The uniform and time-sensitive sampling are fairly reasonable. However, many KGs (including YAGO used in this paper) have given ontology with specific entity types, domain and range for the edges, which are helpful for KG inference [1,2,3]. Why choose timestamp-weighted sampling instead of sampling by relations or entity types which also significantly limit the subgraph size and are intended to pick high-related relations and important entities. \n\n(4) Can xERTE apply to an inductive setting, in which new entities are emerging as tKG develops as a commonly observed case? A related concern is how the facts in these datasets are split into train/validation/test? \n\n(5) As one major contribution to explainability, it is suggested to provide analysis about justification on temporal model capability. One possible way to do so is to provide how the representation of one node evolves during the inference graph. \n\n(6) In Section 4.4, what are stationary embeddings and time-variant embeddings? Do we assume both are given in the dataset or trained? What is the contribution here to adopt dynamic embeddings?\n\n**Minor issues:**\n(1) Almost all figures are not quite visible and the text in the subfigures needs to be enlarged.\n(2) Page 3, Inference Graph, Line 7: Incomplete sentence.\n\n**References: **\n[1] Ma, S, et al. \"Transt: Type-based multiple embedding representations for knowledge graph completion.\" ECML, 2017.\n[2] Lv, X., et al. \"Differentiating Concepts and Instances for Knowledge Graph Embedding.\" Proceedings of the 2018 Conference on EMNLP. 2018.\n[3] Hao, J., et al. \"Universal representation learning of knowledge bases by jointly embedding instances and ontological concepts.\" KDD, 2019.\n[4] Garcia-Duran, Alberto, Sebastijan Dumančić, and Mathias Niepert. \"Learning Sequence Encoders for Temporal Knowledge Graph Completion.\" EMNLP, 2018.\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "WmtHhe19-_9", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "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": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "\n**[UPDATE, 30 Nov]: Rating raised after reading the authors rebuttal.**\n\nThe paper presents a knowledge graph embedding model that learns latent representation of a temporal knowledge graph to predict unseen events.\n\nThe problem addressed in the paper is relevant for the community, and the angle proposed by the authors is interesting, i.e. tackling learning from temporal graphs with an eye to interpretability.\n\nThe paper is well structured, although some sections lack clarity and at times makes reading difficult (e.g. 4.3). \n\nRelated work is comprehensive and gives a good coverage of recent temporal KGE works.\n\nThe choices made in the architecture (which is grounded on the so-called “inference graph”) seem reasonable. \n\nIt is worth mentioning that is the first KGE paper I see that includes a user evaluation survey. Given the narrative emphasises explainability, this is certainly appreciated. \n\nExperiments use agreed-upon datasets and evaluation protocol.\n\nNevertheless, there are some shortcomings. I have some doubts and questions for the authors:\n\n1. Why not replacing Table 1 with Table 7 (appendix)? Reporting raw metrics in the main paper is less meaningful that the time-aware filtered settings.\n2. Baselines: experiments in table 1 do not include recent SOTA-level models such as DE-Simple [Goel 2020] and TNTComplex [Lacroix 2020] - this despite both works are present in the bibliography. Given that xERTE claims to beat SOTA, I believe it is necessary to add those two models in the experiments to make sure SOTA is beaten, in particular using the time-aware filtered settings (Table 7, appendix).\n3. The paper does not include experiments on training time. It will be interesting to empirically validate claims of scalability. Training time is a deal breaker for time-aware models, so reporting figures would really add value to the work.\n4. The reverse representation update mechanism in 4.3 lacks clarity. Could you please re-phrase and provide a bit more clarity? I fail to see how what described “mimics human behaviour”.\n5. In a note on page 3 you say reciprocal triples are added. How does this impact training time, given that in practice you double the size of the training set?\n6. In 4.1, how is the number of expansion sets L chosen? Is that an hyperparameter? In that case, it would have been interesting to see some experiments of predictive power and training time.\n7. What is the role of the \\gamma hyperparameter in 4.2? Have you provided some experiments to show what happens with ranges of different values?\n8. Have you run ablation studies on the attention mechanism? (i.e. turning it on/off).\n9. How is the time encoding \\Phi defined (4.4)? Could you please clarify?\n10. Unfortunately, the human evaluation is dismissed in the appendix. While I appreciate the effort of running a user survey,  the summary proposed in 5.3 lacks clarity and this piece of your work would deserve more prominence.\n11. Human evaluation: I have doubts on using only 7 questions in the questionnaire. I wonder how meaningful results are. Besides, the questionnaire does not compare against a baseline, so it is hard to tell if the users are really satisfied with the content of the inference graph.\n12. Human evaluation: could you add some details on the population? (i.e. the 53 users) \n\nMinor comments:\n- figures 2,3 are too small.\n- content of user survey description in I.1 may partially break anonymity.", "extra_scores": {}, "extra_text": {}}, {"review_id": "QR_Lc81-s-l", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "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": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "\nAuthors have presented a method to forecast future links on temporal knowledge graphs (KGs). They use attention mechanisms to extract a query-dependent subgraph. According to the authors, this extracted subgraph provides a graphical explanation of the prediction. Authors have performed an ablation study to denote the effect of different components (e.g., updating the representation of nodes, time encoding, sampling strategy) in their method. They have tested the performance of their approach on 3 datasets and have shown that their approach outperforms other baselines in terms of Hits and MRR.\n\nAlthough the method proposed in this work outperforms other baselines, the novelty and contribution of this work is still not completely clear to me. Major contributions are listed in the last paragraph; however,  I believe some of them are derived with straightforward changes to previous works. As an example, authors have mentioned they have provided the \"first\" explainable model based on attention mechanisms for temporal KGs.\n\nAs far as I have understood, by \"explainability\" authors mean providing the graphical explanation or in other words, providing relevant arguments in the extracted subgraph. The most relevant paper to this line of work is by Xu et al. 2019 which is also cited by authors. Authors explicitly mention that the work by Xu et al. deals with static KGs whereas their method works with temporal KGs as well. To me, the base of both approaches are the same since Xu et al. 2019 also models a reasoning process by constructing a sub-graph and I believe this issue is limiting the novelty of this work. It would be great if authors can show an example in which the work by Xu et al. does not provide a proper explainability while their approach does.\n\nI also recommend that authors define the metrics they have used (i.e., Hits and MRR) either in footnotes or the supplementary material.\n\nThe writing of the paper could be improved. Examples are but not limited to:\n- Page 3, 2nd paragraph, \"with $v_q$ to$\n- Page 5, 1st paragraph, \"we need pass messages\"\n- Page 5, 1st paragraph, \"$(l − m)$-aeay\"\n- Page 5, 1st paragraph,  \"at l-th inference step\"\n- Page 6, 1st paragraph, \"an unique\"\n", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper has received 4 positive reviews all supporting the acceptance of the paper. The authors have provided a strong rebuttal and have addressed the reviewers' concerns. Please make sure to include all reviewer feedbacks in the camera-ready version. 
Decision: Accept (Poster)