Learning to Sample and Aggregate: Few-shot Reasoning over Temporal Knowledge Graphs
Authors: Ruijie Wang
zheng li
Dachun Sun
Shengzhong Liu
Jinning Li
Bing Yin
Tarek Abdelzaher
Venue: NeurIPS 2022 Accept (2022)
Keywords: Few-shot knowledge graph reasoning
Temporal knowledge graph
Meta learning

Abstract: In this paper, we investigate a realistic but underexplored problem, called few-shot temporal knowledge graph reasoning, that aims to predict future facts for newly emerging entities based on extremely limited observations in evolving graphs. It offers practical value in applications that need to derive instant new knowledge about new entities in temporal knowledge graphs (TKGs) with minimal supervision. The challenges mainly come from the few-shot and time shift properties of new entities. First, the limited observations associated with them are insufficient for training a model from scratch. Second, the potentially dynamic distributions from the initially observable facts to the future facts ask for explicitly modeling the evolving characteristics of new entities. We correspondingly propose a novel Meta Temporal Knowledge Graph Reasoning (MetaTKGR) framework. Unlike prior work that relies on rigid neighborhood aggregation schemes to enhance low-data entity representation, MetaTKGR dynamically adjusts the strategies of sampling and aggregating neighbors from recent facts for new entities, through temporally supervised signals on future facts as instant feedback. Besides, such a meta temporal reasoning procedure goes beyond existing meta-learning paradigms on static knowledge graphs that fail to handle temporal adaptation with large entity variance. We further provide a theoretical analysis and propose a temporal adaptation regularizer to stabilize the meta temporal reasoning over time. Empirically, extensive experiments on three real-world TKGs demonstrate the superiority of MetaTKGR over eight state-of-the-art baselines by a large margin.

Learning to Sample and A Aggregate: Few-shot Reasoning over Temporal Knowledge Graphs
Ruijie Wang', Zheng Li?, Dachun Sun', Shengzhong Liu', Jinning Li',
Bing Yin Tarek Abdelzaher'
University Illinois at Urbana Champaign, II, USA
*Amazon.com Inc, CA, USA (ruijiew2, dsun18, s129, jinning4, zaher) Williniillinn inois.nii....... edu (amzzhe, alexbyinn@amaazn com
Abstract
In this paper, we investigate a realistic but underexplored problem, called few-shot temporal knowledge graph reasoning, that aims to predict future facts for newly emerging entities based on extremely limited observations in evolving graphs. It offers practical value in applications that need to derive instant new knowledge about new entities in temporal knowledge graphs (TKGs) with minimal supervi- sion. The challenges mainly come from the few-shot and time shift properties of new entities. First. the limited observations associated with them are insufficient for training model from scratch. Second, the potentially dynamic distributions from the initially observable facts the future facts ask for explicitly modeling the evolving characteristics of new entities. We correspondingly propose a novel Meta Temporal Knowledge Graph Reasoning (MetaTKGR) framework. Unlike prior work that relies rigid neighborhood aggregation schemes to enhance low-data entity representation, MetaTKGR dynamically adjusts the strategies sampling and aggregating neighbors from recent facts for new entities, through temporally supervised signals on future facts as instant feedback. Besides, such a meta tempo- ral reasoning procedure goes beyond existing meta-learning paradigms knowledge graphs that fail handle temporal adaptation with large entity variance. We further provide theoretical analysis and propose temporal adaptation regu- larizer to stabilize the meta temporal reasoning over time. Empirically, extensive experiments three real-world TKGs demonstrate the superiority of MetaTKGR over state-of-the baselines by a large margin.
static
Introduction
store temporally evolving facts (By fact, we refer a subject entity has a relation with object entity some time, e.g., "Macron" was "elected" as "French president" in "2017"). It has been increasingly used in various knowledge-drive and time-sensitive applications, such as social event forecasting
Temporal Knowledge Graphs (TKGs) --
3
22
55
3S 24 533 question answering 44), and recommendation 770 69 54 Large scale TKGs are hard to obtain due to the time-varying nature of labels the excessive cost of human annotation. As such, automating prediction and reasoning about missing facts over time has attracted more recent interest [47
[0 3 48 20 However, most
prior efforts are limited to reasoning about existing entities but neglecting the commonly observed low-data regime where many new entities emerge with extremely few observations topics evolve over time
events or
This restricts their applicability.
Instead, inspired by the human ability to recognize new concepts from exposure to only very few instances, we propose and solve a practical and challenging few-shot temporal knowledge graph
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

---

reasoning problem that specifically aims to predict future facts for newly emerging entities with a in similar settings simplify the task by
few observed links on TKGs. Existing efforts [ ignoring the emergence of new entities over time and randomly simulating unseen entities on static knowledge graphs. This formulation, originating from few-shot learning in the vision domain [T] 39), fails at capturing the real-world divergence between the distributions of seen and unseen entities. To the best of our knowledge, the generalized few-shot temporal reasoning task, that aims to imitate the fast learning ability of humans, has still not been formally investigated.
The challenges in solving this problem are two-fold: 1) few-shot: the extremely few facts associated with new entities cannot provide sufficient information for representation learning from scratch. 2) time shift: new entities usually exhibit different characteristics in the future, due to the time-evolving nature of TKGs. It leads models to generalize poorly in the future. Unfortunately, prior work fails to overcome these two challenges simultaneously.
On one hand, to enhance low-data entity characterization, a diverse range of neighhorhood aggregation schemes that retrieve related information from other entities are explored, such as hard subgraph sampling methods (e.g., vanilla hop-based sampling AM,, random sampling [T6], personalized Pagerank sampling 666
54]. importance sampling (6, etc) and soft sampling via trainable attention 48 20 However, those rigid methods cannot well adapt to the new entities with
mechanisms 47
the Lieevaryiing distributions due to the lack of instant supervision. On the other hand, recent leverage meta-learning to improve unseen entity adaptation. While the setup for unseen entities is simulated by randomly splitting entity sets from static graphs, they fail to handle the more realistic temporal adaptation with large entity variances.
attempts [1 68
18
!
To overcome both the aforementioned challenges, we propose a novel Meta Temporal Knowledge Graph Reasoning (MetaTKGR) framework, where learning the strategies for sampling and aggregating neighbors from recent facts (to enhance the new entities' predictions) can be dynamically adapted from signals of temporal supervision on their future facts as instant feedback. Intuitively, the global knowledge of sampling and aggregating can be extracted as learning to learn ability through such a oettaoppimizztion,, which takes the time-evolving nature of knowledge into consideration, avoiding progressive performance drift over time. Concretely, we formulate this learning strategy to be parameterized by temporal encoder. On the simulated new entities during training phase, starting from the initial few-shot links, the temporal encoder can softly sample and attentively integrate relative and time-aware information from the temporal neighbors, making the strategy learning (neighbor sampling + aggregation) differentiable. The quantitative measurement of how well the current strategy performs can be reflected in the performance on predicting future facts allowing one to automatically adjust the strategy in turn. During the nested loop for meta-optimization, we firstly learn the temporal encoder on recent facts (inner loop), then gradually increase the difficulties by autoregressively adapting it to farther away future facts (outer loop). Furthermore, to better estimate the supervision signal given by future facts in different and unseen distributions, the PAC- AAC-Bayes method [35 to theoretically analyze the temporal adaptation bound on the future facts. This can serve as adaptation regularizer to provide stability and improve the generalization ability of current strategy over time. Empirically, extensive experiments on three real-world TKGs validate the effectiveness of TKGR which significantly outperforms all baselines from static/temporal KG reasoning and few-shot (knowledge) graph learning areas, by up to 11.4% relative gain on average with competitive efficiency. To sum up, our main contributions are three-fold:
adopt
Problem formulation:
We explore a practical few-shot temporal knowledge graph reasoning setting, minimizing the gap with the realistic few-shot learning scenarios for humans;
Novel framework: We propose a novel meta temporal reasoning framework on TKGs, namely MetaTKGR, to address both few-shot and time shift challenges;
Extensive evaluation: the proposed MetaTKGR method demonstrates significant gains in effectiveness on three real-world TKGs over diverse range of state-of-the-ar baselines.
2 Problem Definition
In this section, we formally define the few-shot temporal knowledge graph reasoning task. First of all, a temporal knowledge graph can be defined as follows:
Definition 2.1 (Temporal Knowledge Graph). A temporal knowledge graph can be denoted as G ((e., T, co, })} C ET R x E. x T. where E9 denotes set of entities that appear in time
2

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interval (0. T), R denotes relation set, and T denotes timestamp set. Each temporal link (e., r, Co. t) refers to the fact that a subject entity eg E E9 has a relation r E R with an object entity en E Ed at timestamp I E 'T.
As temporal knowledge graph evolves, new entities continuously emerge, leading to an expansion of the entities set E9 over time. We further define new entities as follows:
Definition 2.2 (New Entities in Temporal Knowledge Graph), Given a time interval T")
(T" > T), entities that join the graph during (T,T") i.e., E E NET (\ denotes setminus), are defined as new entities on time interval (T, (T,T").
Knowledge graph reasoning (KGR) is essentially the problem of predicting missing facts in the partially observed KG. While existing few-shot KGR models simulate unseen entities by randomly selecting from the existing entities, we focus specifically predictions for newly emerging entities over time, which can be formalized as few-shol lemporal knowledge graph reasoning task:
Definition 2.3 (Few-shot Temporal Knowledge Graph Reasoning). Given a temporal knowledge
graph GJ collected no later than T, for each new entity é ET Ed 'T' > T), we assume the first K associated facts are observed: {(ē, ee, t.) or (e,,Ti,,,ti) (.)4 ii=1. The task aims to predict the missing entities in the future facts (e,r, 7, or (?,r,E, é, t) given the relation r E R and specific time t (T,T".. We further assume K is a small number, realistic setting.
3 Learning to Sample And Aggregate with MetaTKGR
In this section, we present a novel framework MetaTKGR to solve the few-shot temporal knowledge graph reasoning problem. We first introduce the basic setup of our learning objective and the overall framework, and then detail the temporal encoder module to represent new entities, followed by introduction of meta temporal reasoning for model training.
3.1 Learning Objective
Suppose we are given a temporal knowledge graph G" = [(c,, r, Co, t)} S ET x R x T collected no later than time T. For each new entity è appearing within later interval (T, T'), aim to predict future links (é, r, e, t) or (e, re,r, ,, happening at timestamp E T'). Towards this goal, we measure correctness of each possible quadruple by a score function s(5 Φ) parameterized by o, and maximize the scores of true quadruples containing any new entities in order to rank them higher than all other false quadruples:
max E En (s(,, e,44 or 2,,,,, where E= ET' LE,
(L)
where P(E) denotes distribution of all new entities, à denotes parameters of model to represent entity/relation into d-dimensional space ha, he, h, E Rd. To represent è into ha via é as aforemen- tioned, the challenges lie in how to enable @ to encode generalized knowledge (how to sample and aggregate temporal neighbors) that can be easily adapted to new and achieve robust performance over time, even for a long time interval )"). We thereby formulate sew-shot temporal knowledge graph reasoning meta-learning problem to extract such knowledge.
3.2 MetaTKGR Framework
Figure D shows the MetaTKGR framework. To be more formal, each task corresponds to each new entity ē over distribution p(E), and the links can be represented as a chronological sequence {(E, ris ei, (;) or (es, rı, E, 4.)44 E (T,T",, S ly if < ", where N₂ denotes total number of links associated to ē. Then we divide them into support set Sa = ((ē, ((,,r,, rs, 44,44 or (ei, ri, ē, ) and query set Q: = {(ē, ri, e,, e,,t,) t.) or (c,,r,, ē, b=)k+ where K denotes the amount of initially observable facts of ē.
During the meta-training phase, we simulate a set of new entities from existing entity set by assuming there are only few-shot links of these entities (support set Sa). The model first fine-tunes parameters on Sa (inner loop), and then minimizes the predictive loss on corresponding query set Qa using the updated parameters dz (outer loop). It optimizes the global sampling and aggregation strategy as
3

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Inner Optimiztiinn
Outer Optimization
parameter
é P(E)
Al. (4) Mog (t2) a (G.) Neighbor Senture
Temporal Neighbors
Ran Fere Hany
Re Deaatoonie Aop
Time: OCC- tx)
A (t.)
Temporal adappation by Fi. (%)
Endity: A2
(E)
by Eq. IsL
Fine-tung-
Query set
Ciler 2
g)
function
(33, 1S
Query sot Q
(i
New entiyy shat
Stop by stop
Query set Q
21 C."
(2
(a) Temporal KG with new entity
(b) Temporal Encoder f
Meta Temporal Reasoning
An overview of MetaTKGR framework. (a) Task illustration; (b) Temporal encoder pa- rameterized by Φ samples and aggregates information from temporal neighbors; (c) Meta temporal reasoning adopts bi-level optiizationn to learn é. In the inner optimization: MetaTKGR initializes entity-specific parameters from global parameters via step (1), and fine-tunes them on support set via step (2) to optimize entity-specific parameters; In the outer optimization, MetaTKGR optimizes global parameters on query set via step (3) to learn good and robust global parameters.
Figure 1:
generalized knowledge (i.e., learning to learn ability) by this bi-level optimization, as this procedure mimics the normal machine learning and inference process. For simplicity, to represent new entity along time, we denote for the temporal encoder parameterized by Φg. L(f Sg) as model predictive loss on Sg. Model-agnostic meta-lcarning (MAML) [[]] can be utilized to fulfill this goal as follows:
arg min Ee))tt) [C[S 2e)], where de o- Sz)
(2)
06
where 1y
denotes inner-loop learning rate. However, this training strategy cannot guarantee good generalization ability over time (challenge 2), as they assume identical distributions between S; and Qz, contradicting the facts that new entities are highly evolving over time on TKGs. To coherently resolve the two challenges, we advance the existing few-shot KG reasoning works by proposing:
Temporal encoder, which learns the time-aware representation of each new entity à by sampling and aggregating information from TKG neighbors on continuous domain.
Meta temporal reasoning, which learns an optimal sampling and aggregating parameters via bi-level optimization (inner optimization and outer optimization). The learned parameters can be easily adapted new entities and maintain temporal robustness.
3.3 Temporal Encoder
On temporal knowledge graphs, entities are evolving over time. The temporal en- coder fo is to embed each entity into low-dimensional latent space each time: ha(t) E Rd, where it can model the temporal pattern of along time. By doing so, it resolves the scarcity issues caused by few-shot links to some ex- tent. Towards this goal, f first samples temporal neighbors from TKGs, then at- tentively aggregates information from the temporal neighbors of each entity, which takes neighbor feature, relation feature and time feature into account.
Algorithm 1: Temporal Neighbor Sampler.
Input: New entity é, temporal knowledge graph G", current
timestamp f, neighhor budget b, time bound At. Output: Temporal Neighbor (t).).
Initialize Queue <- è, Ne((t) + ():
while [Na(t)] < and Queue is not empty do
e + -uueuedeqqueue():
for each (e,, Co, in G do
and >> tmar At then if e, Add (e., 1) to NG((), Add e, to Queue;
if Co = e and > tmaz - At then Add (fo, r, f) to (2(t), Add e, to Queue;
To better represent few-shot entities, wider range of neighbors should be considered, as the close neighbors around the new entities are usually insufficient. Conventionally, stacking several graph neural networks (GNNs)-basee layers can integrate information from multi-hop neighbors 41 In few-shot cases, such layer-by-layer procedure faces difficulties. For one thing, the limited one-hop neighbors can dominate the aggregation process, as the information of multi-hop neighbors is all propagated from them to the target entity. Also, the size of neighbors grows exponentially with the increase of GNN layers, as they collect all neighbors in each hop without strategic selection,

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causing severe efficiency issues. Instead, our temporal encoder first samples multi-hop neighbors via doundoondedd feaudhh-irst-searchh algorithm, then aggregates information directly from the sampled neighbors in an attentive manner. As summarized in Algorithm D at each time, it selectively samples up to multi-hop temporal neighbors (a(() which have interactions within recent time range At. Given the temporal neighbor (t( for each new entity, temporal encoder fo represents new entity as ha (t) at time
de.e, (L. (b))(())))
(t) =0
Σ
(3)
(cL.PE))ENN(())
where 1 denotes the layer number, (..) denotes the activation function ReLU, ag,e, denotes the attention weight of entity to new entity é, and W is the trainable transformation matrix. To aggregate from history, 0a,e, is supposed to be aware of entity feature, time delay and topology feature induced by relations. Thus, we design oz, as follows:
exp(ge.e)
(EENNN exp(qa.e,)' Qe.c. (h! [b,, | (t))-
where qa,e; measures the pairwise importance by considering the entity embedding, relation embed- ding and time embedding, a E IR 4d is the shared parameter in the attention mechanism. Following M we adopt random Fourier features as time encoding (Ai) to reflect the time difference.
3.4 Meta Temporal Reasoning
Let (t) denote the representations new entity E produced by f with layers. For each quadruple (2, t). we employ translation- score function [2] measure the correctness: s(ē, r, e, t; Φ) = - [bh + h, (t)l.. We first fine-tune fa on support set Sş for entity-specifi parameters fau. and then optimize training loss query set Qa to learn the global parameters shared by all entities. To calculate the predictive loss, since each set only contains positive quadruples, we perform negative sampling (2) update MetaTKGR by training it to rank positive quadruples higher than negative ones. Specifically, taking the support set S: of entity é as an example, we construct a negative set S {(ē,r, r, e .) or (e , ē, t)} by replace the ground truth entity e with a corrupted entity e We then use empirical hinge loss on the given set as follows:
S()
Σ
Σ
max (7 s(cs, eo,
eo, t) + r,,,,
(5)
(ex-Fveo.tEESe (ca.5st, ES
where 7 > is margin value distinguish positive and negative quadruples.
Inner optimization: For each task corresponding new entity ē p(E), we first adapt the global parameter à for each new entity by minimizing the predictive loss on the support set Sg:
Algorithm 2: MetaTKGR: Meta-training.
Input: Temporal knowledge graph G" C x T, randomly initialized ø.
Output: Learned global parameter ạ).
Simulate new entity set & from E.:
=== Sc(fo.Sa) 0s
Train model parameter ø from many-shot entities g E; Construct S: and Q: for each new entity é, where Qa = (o( ,.2,,...,,0 while á not converge do
(6)
(M) ,
....
where is the inner loop learning rate. By 6 we simulate the adaption for new entities. Updating from an opti- mal global parameter o, the model is fine-tuned into entity-specific for new entities. Thus, it is crucial to design a meta-learning strategy to learn op- timal global parameter ó with a robust generalization ability over time.
for each time interval m do
# Outer optimization:
for each new entity do
# Inner optimization:
Calculate L(fo. S2) on Sa by Eq. 5
Perform adaptation by Eq. to update de;
Calculate Ż(fez (())) by Eq.
Calculate temporal adaptation regularizer by Eq.
Update ((m) by Eq. 9
Outer optimization:
Since new enti-
o (m)
ties evolve over time, it not only Q but also each part of O₂ that follows
different distributions. Thus. instead of optimizing the meta-leamer on the whole query set Qs at
5

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once by Eq. 2 we first adapt entity-specific parameters og to recent facts, then gradually increase the difficulties by autoregressively adapting it to farther away future facts. Through this process, we are able to guide and stablize the training of global parameters via a temporal signal. Specifically, we split the time span of query sets into M time intervals, where each new entity has sequence of query set corresponding to different time intervals Q2 = = (22) , o 1 J. We first adapt and optimize de for each new entity on o for ((1) encoding global knowledge for predictions in the 1-st time interval. Then we gradually adapt each Φa fine-tuned from last time interval on farther away intervals until ef (M) is learned, which maintain temporal robustness from time interval 1 to M.
We then diseuss how to measure the feedback (predictive loss) from each adaptation. To simulate real scenarios, we assume query sets to follow different and unseen distributions. Taking adaptation from m-th time interval to m + 1-th time interval as example, we view p(((())) as prior parameter distribution and aim to learn the posterior parameter distribution g(s)(m+1) conditioning on query set in + 1-th interval. The unseen query set distribution in + 1-th interval prevent to estimate (()(m+1)) by either using unbiased empirical loss or Bayes rules. To resolve this, we instead adopt the PAC-Bayes method [35]. which allows one learn a parameter posterior that fits the observations without knowing the observations distribution. We propose the following theorem to relate real predictive loss in new time interval with its empirical verson:
Theorem 3.1 (PAC-Bayes Generalization Bound on Temporal Adaptation). Let D(m++)) =
Useê 2 2 (m++1) denote all query sets in m + 1-th time interval of all new entities from &. For any ō E (0, 1) and learned parameter distribution p plafmm) in last time interval, with probubility at least 1 on D(m+1);
(LL (p(((mm)))) + log 2/D(m+1)
[D(m+1)
L(falm), Dim+tl) S L(fam)), D(m+t)) +
) denotes real predictive loss on new time interval with new and unknown data distribution, L( D(m+t)) denote the empirical version of the loss, and (-I--) is the Kullback-Leible divergence.
where [(fatms, D(m+1))= = Explt) [CLF
Readers can refer to Appendix A. for proof. Thus, using Theorem 3.1 we can adapt (f()) to m + 1 time interval and estimate the feedback (predictive loss) for our meta-learning framework via the following temporal adaptation regularizer.
KTT (g((( (lmp + log [D(+t))
R(fa(mo D(mmt)) & Lifatto, Dim+t)) +
(8)
2|D(m++)] -1
Remark. To interpret the temporal adaptation regularizer R(farm) ((m+1)), it can be viewed as a combination of empirical risk on the query set in the new time interval as well as a regularizer of parameter distribution across time intervals in form of KL--dvergeene. The regularizer along time domain can guarantee that global knowledge is trained by predictive losses from all time intervals without overfitting in specific time interval. Thus, we can improve the generalization ability of our meta-learner over time by the following update step by step, from m m M:
HR (Raaat)); (() D(m)1)
(m+
(m())
where (00) can be obtained by training on existing entities. The meta-training phase of MetaTKGR is summarized in Algorithm 2 During meta-test phase, given new entity é, we can first fine-tune 6 on few-shot links, and then utilize for to represent é for future predictions.
4 Experiments
Datasets. We evaluate the proposed MetaTKGR framework on three public TKGs, where YAGO 34 and WIKI (22) stores time-varying facts and ICEWS18 3 is event-centrie. They are collected from different time ranges and have different time units, which can validate our framework in the context of various types of evolution. Notably, most new entities appear with few-shot validating the practical value of our proposed setting. Table | shows the detailed statistics. We report detailed dataset descriptions as well as entity links distribution in the Appendix A.2

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Table 2: The results of 3-shot temporal knowledge graph reasoning. Average results on independent runs are reported. * indicates the statistically significant improvements over the best baseline, with p-value smaller than 0.001. We report standard deviation in Appendix A.5
YAGO
WIKI
ICEWSIN
Models
MRR
H61
H68
Hot 10
MRR
H61
H63
He:10
MRR
H61
He3
Ho:
Transk:
0:223
0.15%
0.242
0.300
0.161
0.111
0.171
0.236
0.058
0,052
0.062
0.558
TransR
0.165
0.259
0.183
0.188
0.245
0.062
0.073
RotatE:
0.241
0.182
0.278
0.409
0.232
0.171
0.223
0.284
0.078
0.074
0.082
0.128
RE-NET
0.261
0.210
0.298
0.410
0.261
0.210
0.251
0.331
0.232
0.139
0.241
0.309
RE-GUN
0.226
0.307
0.277
0.225
0.262
0.344
0.142
0.238
LAN
0.230
0.154
0.247
0.352
0.185
0.155
0.201
0.287
0.207
0.119
0.234
0.321
I-GEN
0.303
0.238
0.323
0.420
0.221
0.179
0.229
0.264
0.212
0.120
0:251
0.346
T-GEN
0.293
0.218
0.310
0.391
0.234
0.185
0,222
0.271
0.169
0.122
0.181
0.265
MeNaDyGNN
0,350
0,270
0.379
0.511
0.309
0.238
0,309
0.459
0.307
0.216
0.309
0.469
NetaTKGR
0,370
0.303
0.416*
0,558
0,329
0.253
0,335
0.489
0.335
0.249
0.340
0,527
Gains (%)
5.68
12.21
9.80
9.19
6.26
6.38
8.47
6.35
9.11
14.85
9.89
12.4
Table 3: The results of I-shot and 2-shot experiment. We report complete results in Appendix A.5
YAGO
WIKI
ICEWS18
Models
I-shol
2-shol
I-shol
2-shol
1-shol
2-shol
MRR
1@:1
MRR
18
MRR
16 10
MRR
HG:1
MRR
11
MRR
18 10
Transk
0,183
0.268
0.193
0.304
0.144
0.186
0.146
0.215
0.049
0.077
0.058
0.086
TransR
0.189
0.270
0.198
0.160
0.183
0.160
0.225
0.080
0.060
RotatE:
0.315
0.280
0,210
0.359
0.175
0,190
0,261
0.268
0.068
0.098
0,070
0.091
RE-NET
0.221
0.304
0.233
0.390
0.212
0.259
0.239
0.294
0.185
0.250
0.200
0.341
RE-GUN
0.320
0.223
0.250
0.347
0.310
0.247
0.205
LAN
0.196
0.269
0.200
0.310
0.174
0.275
0,162
0.273
0.170
0.301
0.188
0.317
I-GEN
0.238
0.521
0.237
0.402
0.181
0.241
0.223
0.287
0.199
0.520
0.177
0.337
T-GEN
0,247
0.331
0,260
0.379
0.202
0.245
0,240
0.319
0.131
0.262
0,161
0,259
MetaDyGNN
0,269
0.396
0,316
0.196
0.241
0.371
0.271
0.390
0,219
0.120
0,269
0.141
NetaTKGB
0.294
0,428
0.356*
0.526
0,277
0.419
0.30
0.441
0.295
0.496*
0.301
0.500
Gains (%)
8.04
12.69
6.14
14.64
12.93
14.04
13.20
18:45
17,87
11.47
13.39
Table 1: Dataset statistics.
Baselines. We compare nine state-of-the-ard
baselines from four related areas: 1) TransE 2
Datasets
# Entities
Relutions
Quadruples
Time Unit
2) TransR 33 3) RotatE [46]: Translation
YAGO
10,623
10
201,090
year
distance based embedding methods for static knowledge graphs; 4) RE-NET 100 5) RE-
WIKI
12,554
24
669.935
year
ICEWS18
23,033
256
281,205
day
GCN BI: Temporal knowledge graph embedding methods; 6) LAN [52]: 7) I-GEN M: 8)
T-GEN [] Few-shot methods static knowledge graph; MeMetaDGNN [65] A meta-learning
framework for few-shot link prediction on homogeneous graphs. We describe the baselines in detail in Appendix A.3
Experimental Setup. Given the temporal knowledge graph, we first split the time duration into four with a ratio of 0.4:0.25:0.1 1:0.25 chronologically, then we collect the entities that firstly appear in sagpoounn/mmetttrriinnnnnnnn traaiininn/mmta-aaaiaaiiioonnnni validation//mtta-tes entity set. We train our model on background set as initialization and simulate few-shot tasks meta-traine meta-training set. To construct few-shot tasks, we assume the first K = 1, 3 quadruples of new entities are known and report the performance of the remaining quadruples in the future. For fair comparison, we keep the dimension of all embeddings as 128, and utilize pre- pre-trained 1-shot TransE embeddings for initialization for models if applicable. We report detailed experimental setup, especially of MetaTKGR, in the Appendix A..4
each period as
Evaluation Protocol and Metrics. For each prediction (ě,r, ?, or (?, r, ē, t), we use ranking scheme to evaluate the performance. Specifically, we rank all entities at the missing position in quadruples, and adopt mean reciprocal rank (MRR) and Hits at ( 10) (H@ /1,3, 10)) as evaluation metrics. It is worth noting that we measure the ranks in filtered setting, where we filter other true quadruples existing in datasets, following 33 46
Main Results. Table and Table rreport overall result for K = 3 and K = 1, few-shot experiments respectively. On average, MetaTKGR achieves 11.4% relative improvement over best baseline model, demonstrating the superiority of MetaTKCR in modeling new entity evolution in low-data regime. Baselines (TransE, TransR, RotatE, RE-NET) that do not optimize for new entities perform poorly on all datasets, although they are trained on both existing entities and new entities with few-shot links. LAN, J-GEN, T-GEN also produce unsatisfying results, despite the fact that they propose special designs to represent new entities. Note that they have worse performance in some cases than RE-NET that does not optimize for new entities, as they ignore the temporal information and perform poorly in future predictions. Compared with MeNaDyGNN, MetaTKGR shows consistently better performance,
7

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because our temporal encoder can handle multi nulti-relational graphs in low-data regimes better, and our temporal meta-learning framework can produce more robust predictions.
Performance of Predic- tion over Time. Next, we study the performance of MetaTKGR over time. Figure 2 shows the per- formance comparisons of 3-shot predictions over different timestamps on the YAGO and ICEWSI8 datasets, measured by filtered H@10 metrics. MetaTKGR consistently beats all strong baselines. Although the compared baselines can optimize newly emerging entities, they perform poorly in wide time intervals because they largely ignore the temporal information and the distribution discrepancy caused by evolution. We notice that the relative gains of our model get more significant with increasing time steps. illustrates that our temporal meta-learning framework can improve the generalization ability over time. Performance on ICEWS11 18 fluctuates more severely. This is expected since the evolution of ICEWS18 is not stable due to the much shorter time unit (day).
0.6
0.5
I:DEN
T-GEN MesaDyCNN
T-GEN
MataTiia
0.2
25 40 50
Time Unit: Year
Timee
Day
Figure 2: Performance YAGO (left) and ICEWS18 (right) over time.
K_shot
K_shot 2
Khot
0.6
Hit@10
0.5
Ablations Fine-tuning Static Meta-Learning
MetaTKGR w/o Reg MetaTKGR
YAGO
WIKI
ICEWS18
YAGO
WIKI
ICEWS18
YAGO
WIKI
ICEWS18
Dataset
Dataset
Dataset
Figure 3: Ablation Studies, evaluated by filtered Hit@10.
Ablation Study. We evaluate performance improvements brought by the temporal meta-learning framework by following ablations: 1) Fine-Tuning is trained on existing entities without using any meta-learning strategy, and then fine-tuned on new entities; 2) Static Meta-Learning utilizes conven- tional MAML to train models; 3) MetaTKGR w/o Regularizer meta-trains model parameters on each time interval step by step, without explicitly optimizing the témporal adaptation regularizer. Figure 3 reports the results measured by filtered H 10. We conclude that modeling the distribution discrepancy caused by the temporal evolution and optimizing the temporal adaptation regularizer can improve the performance in the future prediction. Also, simply fine-tuning the model parameters new entities leads to poor results, as during background phase, the model does not extract generalized knowledge that can be easily adapted new entities.
5.375
Meta TKGR
I-Shot (Training)
3-Shot (Training)
MelaDyyGM
Test
MRR
H@l
H@10
MRR
HØl
H@ 10
3.325
1-S
0.294
0.240
0.428
0.281
0.242
0.403
g 0,300
3-8
0.354
0.297
0.540
0.370
0.303
0.558
6:275
RE NET
R-S
5-8
0.358
0.377
0.360
0.304
0.542
0.569
0.377
0.389
0.369
0.316
0.591
0.570
8.200
TransE
LAN
50
100
150
200
250
300
Table 4: Cross-shot results on YAGO.
Triking Time (mir)
Figure 4: MRR over training time.
Cross-shot Learning. In reality, new entities are usually associated with various numbers of facts initially. Thus, the robustness of models on different numbers of shots during testing phase is critical. To simulate such scenario, we evaluate MetaTKGR by varying the number of shots including 1-, 3-, 5-, and random-shot (R-S: between 1 and 5) during meta-training and meta-test test phases. Table reports the cross-shot learning results. As expected, with the increase of observable shots during testing phase, the performance becomes better. The differences in the number of shots used for training do not significantly affect the results, demonstrating that MetaTKGR trained with fixed number of shots performs robustly under the various number of shots during testing.
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Efficiency Analysis. We train MetaTKGR and baseline models from scratch on both existing entities and new entities and compare the training time, for the 3-shot experiment on YAGO. Figure D shows that MetaTKGR significantly outperforms baseline models with reasonable training time. Compared with slow temporal models RE-NET, MetaDyGNN for knowledge graph reasoning. MetaTKGR is more efficient because 1) our temporal encoder can learn temporal entity embeddings via sampled temporal neighbors at each continuous timestamp without using RNNs; 2) our temporal neighborhood sampler can prevent the size of multi-hop neighbors from increasing exponentially.
5 Related Work
Few-shot Learning on Knowledge Graph. To alleviate data scarcity, various advanced techniques have emerged, such as transfer learning 37
25
semi-supervised learning [5I, domain adaptation [50
27 28 26 and few-shot learning (FSL.)
56
57
Few-shot learning aims at learning generalized
knowledge from existing tasks to extract transferable priors for new tasks with few labeled samples.
including metric learning based approaches [50
45 and meta-learning based approaches [1] 39
12 [29] For knowledge graph reasoning, the success of few-shot learning has facilitated learning 36 respectively.
the representations of scarce entities [15 In this paper, we are primarily interested in works to represent entities with few-shot facts, as relation set is relatively stable along time [0] Given new entity linked with few-shot facts, the neighborhood aggregator used in graph neural networks (GNNs) reduces the inductive bias via structural knowledge [21 16
[2
3
|I and scarce relations (68 58
[1 computes the representations of few-shot entities by further extend it by utilizing attention mechanisms. However, those models are usually trained on both many-shot and few-shot entities, ending up being suboptimal for few-shot entities. To address it, a recent work [] explores how to to effectively adapt global knowledge for few-shot knowledge reasoning. Deep graph learning has been attracting enormous interest recently 12]6
GNN-based neighboring aggregation scheme. [52
4 36
mate-train the neighborhood aggregator
61
63
64
62
60 23
More broadly on graphs, Meta- 4 G-Meta |[ and MetaDyGNN 65
are proposed to utilize meta-learning for link prediction across multiple graphs, on static/temporal homogeneous graphs. However, most works are designed for few-shot learning on static (knowledge) graphs. How to aggregate neighbors considering time factors and optimize for long-term performance are unsolved. MetaDyGNN (65) is recent framework combining MAML with TGAT g
on temporal
homogeneous graph. But it did not consider distribution difference between few-shot facts and future facts caused by the evolution of new entities either, leading to increasingly poor performance over time, especially on temporal knowledge graphs with more complicated structures.
Temporal Knowledge Graph Reasoning. Temporal knowledge graphs (TKGs) store time-varying facts in the real-world. Temporal knowledge graph reasoning aims to predict missing facts at a certain time in the future. It is mostly formulated as measuring the correctness of factual samples
13, Compared with static KG reasoning tasks [1)]. the main challenge lies in how to incorporate time information into the representation process. Several embedding- based methods have been proposed. They encode time-dependent information of entities and relations by decoupling embeddings into static component and time-varying component [59 [4] utilizing recurrent neural networks (RNNs) to adaptively learn or learning a sequence of evolving However, all of the existing
and negative samples by specially designed score functions [ 33
the dynamic evolution from historical fact sequence 220
57
representations from discrete knowledge graph snapshots 1r 2
20
temporal KG reasoning models aim to extrapolate future facts among existing entities, and how to predict future facts specifically for new emerging entities is largely under-explored.
6 Conclusion
We study realistic but underexplored few-shot temporal knowledge graph reasoning problem, which aims at predicting future facts for newly emerging entities with few facts. To this end, we propose novel Meta Temporal Knowledge Graph Reasoning framework MetaTKGR. It meta-learns the global knowledge of sampling and aggregating temporal neighbors, which can be adapted quickly to new entities for future prediction. Such procedure is gradually guided by the performance on predicting future facts, from near time intervals to far away ones. We further theoretically analyze and propose a temporal adaptation regularizer to stabilize and generalize the learned knowledge on future tasks. We empirically validate the effectiveness of MKR on three real-world temporal knowledge graphs, on which the proposed framework significantly outperforms an extensive set of SOTA basclines.

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Acknowledgments and Disclosure of Funding
The authors would like to thank Tianshi Wang. Yuchen Yan, Jialu Wang for their helpful comments and discussion. The authors would also like to thank the anonymous reviewers of NeurIPS for valuable comments and suggestions. Research reported in this paper was sponsored in part by DARPA award HR001 1 CO165, DARPA award HR001 12290105, Basic Research Office award HQ003421 10002, and the Army Research Laboratory under Cooperative Agreement W911NF-17-20196
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14


Reviews:
[{"review_id": "hj9zBUChOA_", "reviewer": "Reviewer_oR3L", "summary": "This paper aims to predict future facts about *newly emerging entities in temporal knowledge graphs (TKGs)* using few-shot learning. The authors demonstrated the challenge of predicting facts in temporal knowledge graphs as opposed to static knowledge graphs; temporal graphs evolve over time, making reasoning tasks (such as linking prediction) more complex. These entities pose several challenges, such as few-shot relationships and time-shifting, where characteristics may change over time. Furthermore, the previous works address this task by ignoring the emergence of new entities over time and randomly simulating unseen entities on static knowledge graphs. \nIn this regard, the authors propose **MetaTKGR**, a meta-learning framework for reasoning over temporal knowledge graphs. Here, the meta-learning technique is employed to dynamically learn the strategies for sampling and aggregating neighbours in TKGs. \nThe authors conducted experiments on three public datasets to verify the significance of their approach. The main contributions of this paper are two-fold: I) the authors presented a formal formulation for few-shot temporal graph reasoning. II) The authors proposed a meta-learning framework for solving this problem. In the following, I list my detailed comments on the points raised in the paper. ", "questions": "- There is no clear indication if the future facts to be predicted are predefined based on the entity type?\n- How the quadruples of entities are split: into support and query sets randomly? In which ratio, Is it a hyper-parameter? \n- Line 284, it's unclear how the proposed approach outperforms all baselines with the same ratio of 11.4% (relative). Given that the baselines are different in structure and methodology, it's expected to perform differently and show different results. \n- Line 271, It's unclear why the authors split the time duration into four periods. Does this need to be clarified? Is it suitable for all datasets? \n* The approach presented in [1] is comparable to this paper and employed the same datasets in the experiments. It makes sense to benchmark the performance against it also as a baseline.\n\n* Line 353 and 354, the authors discuss some related works designed for reasoning tasks for static/temporal homogeneous graphs. However, most of these approaches are designed for few-shot learning on a static knowledge graph. Some recent methods [1,2,3] have been developed for temporal knowledge graphs reasoning and are not discussed in the related work section to give readers an overview of other techniques.\n\n[1] https://dl.acm.org/doi/abs/10.1145/3404835.3462963 \n\n[2] https://dl.acm.org/doi/pdf/10.1145/3488560.3498451 \n\n[3] https://ieeexplore.ieee.org/abstract/document/9712786 \n", "limitations": "Yes\n", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "* The paper is well-written, and almost parts are easy to follow. The authors described the research problem in detail and clarified the motivation behind their approach.\n* The problem statement is formally defined with mathematical explanations. The authors formulate clearly the problem of fact reasoning of new entities in temporal knowledge graphs, given challenges: few known facts and time-shift, which makes it easier for the readers to understand it very well. \n* This paper presents an interesting research problem, specifically for time-sensitive applications, and is relevant to the NeurIPS conference. \n* The authors conducted several experiments on different datasets, including different time periods:\n   * A detailed description of the experimental setting is provided to reproduce the results. \n   * The experimental results demonstrated the significance of the proposed approach. The results are reported on five independent runs, with a significance test p-value < 0.001.  \n   * Further, the authors analysed the experimental results from a theoretical perspective.\n", "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": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "W6N8OJjOYxU", "reviewer": "Reviewer_KWLf", "summary": "This paper investigated a novel problem, few-shot temporal knowledge graph reasoning, that aims to predict future facts for newly emerging entities based on limited observations in evolving graphs. To address this problem, the paper proposed a novel framework, namely MetaTKGR, which aims to extract the global knowledge of sampling and aggregating temporal neighbors, which can be adapted to new entities for future prediction. The experiment results on three real-world temporal knowledge graphs are promising.", "questions": "1. Where is the error bar in Section 4 of the main paper?", "limitations": "No.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The paper is well-written and easy to follow.\n2. The motivation is clear and interesting.\n3. The experimental results and discussion are thorough.\n\nWeaknesses:\n1. It is a little hard to understand how the MetaTKGR can address the two challenges, few-shot and time shift. Maybe adding some specific examples for visualization is helpful.\n", "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": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "2Hh904Kc4cO", "reviewer": "Reviewer_NqGR", "summary": "This paper mainly works on knowledge graph reasoning with temporal shift, which is an underexplored problem in real-world setting where the new entities will evolve over time. The challenges mainly lie in few-shot and time shift perspective. In order to solve this problem, this paper proposes a MetaTKGR framework, which can adjust the strategy of sampling and aggregating neighbors from recent facts for the new entities. The paper uses theoretical analysis to provide PAC generalization bound to prove its learnability. \n\nThe empirical results shown in the paper indicate strong performance across the board. Under 1-shot and 2/3-shot cases, the model is able to achieve consistent performance gain over different embedding-based KGR models.1", "questions": "N/A", "limitations": "The compared baseline models are all embedding-based knowledge graph reasoning models, it's not clear whether the proposed method could be used for path-based reasoning models. The path-based reasoning models can normally provide better explainability while achieving better results.", "rating": 6, "confidence": 2, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength:\n\n1. This paper discovers a novel problem of knowledge graph reasoning over temporal shift.\n2. This paper proposes MetaTKGR accompanied with theoretical analysis.\n3. The empirical results are strong.\n\n\nWeakness:\n\n1. The propose method is a bit hard to follow, consisting a total of (5) steps indicated in Figure 2. It would be great to associate the figure with different subsections to help readers follow the logic more closely. ", "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": "", "extra_scores": {"ethics_review_area": ["I don’t know"]}, "extra_text": {}}]

Author rebuttal:

Decision: Accept