Revisit and Outstrip Entity Alignment: A Perspective of Generative Models
Authors: Lingbing Guo
Zhuo Chen
Jiaoyan Chen
Yin Fang
Wen Zhang
Huajun Chen
Venue: ICLR 2024 poster (2024)
Keywords: entity alignment
variational autoencoder
generative models
knowledge graphs
Primary area: generative models

Abstract: Recent embedding-based methods have achieved great successes in exploiting entity alignment from knowledge graph (KG) embeddings of multiple modalities. In this paper, we study embedding-based entity alignment (EEA) from a perspective of generative models. We show that EEA shares similarities with typical generative models and prove the effectiveness of the recently developed generative adversarial network (GAN)-based EEA methods theoretically. We then reveal that their incomplete objective limits the capacity on both entity alignment and entity synthesis (i.e., generating new entities). We mitigate this problem by introducing a generative EEA (GEEA) framework with the proposed mutual variational autoencoder (M-VAE) as the generative model. M-VAE enables entity conversion between KGs and generation of new entities from random noise vectors. We demonstrate the power of GEEA with theoretical analysis and empirical experiments on both entity alignment and entity synthesis tasks. The source code and datasets are available at github.com/zjukg/GEEA.

Published as a conference paper at ICLR 2024
REVISIT AND OUTSTRIP ENTITY ALIGNMENT: A PERSPECTIVE OF GENERATIVE MODELS
Lingbing Guo 1,,3 Zhuo Chen 1,3,3 Jiaoyan Chen', Yin Fang! ,2.3, Wen Zhang 2hang?22.3
Huajun Chen 1.2.3f C.en
'College of Computer Science and Technology. Zhejiang University
ZZhejiang University Ant Group Joint Laboratory Knowledge Graph
3 Allibba--Zhejiang University Joint Reseach Institute of Frontier Technologies
4 Department of Computer Science, The University of Manchester School of Software Technology, Zhejiang University
ABSTRACT
Recent embedding- -bsed methods have achieved great successes in exploiting en- tity alignment from knowledge graph (KG) embeddings multiple modalities. this paper, we study embedding- based entity alignment (EEA) from a perspective of generative models. We show that EEA shares similarities with typical generative models and prove the effectiveness of the recently developed generative adversarial network (GAN)-based EEA methods theoretically. We then reveal that their incom- plete objective limits the capacity on both entity alignment and entity synthesis (i.e.. generating new entities). We mitigate this problem by introducing a genera- tive EEA (GEEA) framework with the proposed mutual variational autoencoder (M-VAE) as the generative model. M- M-V enables entity conversion between KGs and generation of new entities from random noise vectors. We demonstrate the power of GEEA with theoretical analysis and empirical experiments on both entity alignment and entity synthesis tasks. The source code and datasets are available at gittub.com/zjjkg/GGEA.
INTRODUCTION
As one of the most prevalent tasks in the knowledge graph (KG) area, entity alignment (EA) has recently made great progress and developments with the support the embedding techniques (Chen et al., 2017: Sun et al. 2017 Zhang et al. 2019, Chen et al. 2020 Liu et al.) 2021 Chen et al. 2022a b Guo et al. 2022a bj Chen et al. (024). By encoding the relational and other information into low- -iw-dienniooall vectors, the embedding based entity alignment (EEA) methods are friendly for development and deployment, and have achieved tfate-ofthhe-e art performance on many benchmarks.
The objective of EA is to maximize the conditional probability p(y]æz) where x, y are pair of aligned entities belonging to source KG X' and target KG ), respectively. we view x as the input and y the label (and vice versa), the problem
be solved by a discriminative model. To this end, we need an EEA model which comprises an encoder module and a fusion layer (Zhang et al. 2019) Chen et al. 2020: Liu et al. 202T] Chen al. 2022a b. Lin al., 2022) (see Figure D). The encoder module uses different encoders to encode multi-modal information into oowddimesiional embeddings.
The fusion layer then combines these sub-embeddings a joint embedding as the output.
We also need a predictor, as shown in the yellow area in Figure I The predictor is usually independent of the EEA model and parameterized with neural layers (Chen et al. 2017] Guo et al., 2020) or based on the embedding distance (Sun et al. 20177 2018). In either case, it learns the probability pl p()|z) where p(y (z) if the two entities xr y are aligned and otherwise. The difference lies primarily in data augmentation. The existing methods employ different strategies to construct more training data,
"qqual contribution
Correspondence to: (zhang.wen, huajunsir) @zju.edu.cn

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Published as a conference paper at ICLR 2024
Graph
graph
lind tnf
attribute
Attu Eacoder
image
Image Eacoder
p(xb)
Sub-
Juint
Modal
Data
Enewder
Emboediin
Posion
Emboddling
Predictor
Target
Figure 1: Illustration of wwwedding- entity alignment. The modules in the blue area belong to the EEA model, while those the yellow area belong to the predictor.
e.g., negative sampling (Chen et al. 2017: Sun et al. 2017 Wang et al. 2018) and bootstrapping (Snn
al. 2018 Pei al. 2019a Guo al. 2022a).
In fact, entity alignment is not the ultimate aim of many applications. The results of entity alignment
are used enrich each other's KGs, but there are often entities in the source KG that do have aligned counterparts in the target KG, known as dangling entities (Sun et al. 2021 Luo & Yu 2022). For instance, a source entity Star Wars (fil)) may not have a counterpart the target KG, which means we cannot directly enrich the target KG with the information of Star Wars (film) via entity alignment. However, if we can convert entities like Star Wars (film) from the source KG to the target KG, it would save major expenditure of time and effort for many knowledge engineering tasks, such as knowledge integration and fact checking. Hence, we propose conditional entity synthesis to generate entities for the target KG with the entities in the source KG as input. Additionally, generating new entities from random variables may contribute to the fields like Metaverse and video games where the design of virtual characters still relies hand-crafted features and randomized algorithms (Khalifa et al. 2017; Lee et al. 2021). For example, modern video games feature large number of non-player characters (NPCs) with unique backgrounds and relationships, which essential for creating immersive virtual worlds. Designing NPCs is a laborious and complex process, and using the randomized algorithms often yields unrealistic results. By storing the information and relationships of NPCs in a KG, one can leverage even small initial training KG to generate high- quality NPCs with coherent backgrounds and relationships. Therefore, we propose unconditional entity synthesis for generating new entities with random noise vectors as input.
We propose generative EEA (abbr., GEEA) framework with the mutual variational autoencoder (M-VAE) to encode/decode entities between source and target KGs. GEEA is capable of generating concrete features, such as the exact neighborhood or attribute information of a new entity, rather than only the inexplicable embeddings previous works have done (Pei et al. 2019a by Guo et al.) 20226). We introduce the prior reconstruction and post reconstruction to control the generation process. Briefly, the prior reconstruction is used to generate specific features for each modality, while the post reconstruction ensures these different kinds of features belong to the same entity. We conduct experiments to validate the performance of GEEA, where it achieves state-of-the-art performance in entity aligmment and generates high-quality new entities in entity synthesis.
REVISIT EMBEDDING-BASE ENTITY ALIGNMENT
In this section, we revisit embedding- entity alignment by a theoretical analysis of how the generative models contribute to entity alignment learning, and then discuss their limitations.
2.1 PRELIMINARIES
Entity alignment aims to find the implicitly aligned entity pairs ((x, y) a e X. E J), where X. y denote the source and target entity sets, and (z, y) represents pair of aligned entities referring to the same real-world object. An EEA model M uses a small number of aligned entity pairs S (a.k.a,, seed alignment set) training data infer the remaining alignment pairs T in the testing set. We consider three different modalities: relational graphs Gz, Gy. attributes Ag, Ay. and images I,, Iy. Other types of information can be also given as features for X' and )
Entity Alignment
For instance, the relational graph feature of an entity Star Wars (film) is represented as triplets, such (Star Wars (film), founded by, George Lucas). Similarly, the attribute feature is represented as
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attribute triplets, e.g., (Star Wars (film), title, Star Wars (English)). For the image feature, follow the existing multi-modal EEA works to use a constant pretrained embedding from a vision model as the image feature of Star Wars (film) (Liu et al. 202 Lin et al. 2022). The EEA model M takes the above multi-modal features x = (0z: Oz lay as input, where Ja. dgr, iz denote the relational graph information, attribute information and image information of x; respectively. The output consists of the embeddings for each modality (i.e., sub-embeddings)) and a final output embedding x (i.c., joint embedding) that combines all modalities:
x = M(x) Linear Manear(ConcatMMM(( (gx),
(1)
Linear Concat gz: agy i2:..))
(2)
where Mg. Ma. and M₁ denote the EEA encoders for different modalities (also see Figure [ ga, az. and is denote the embeddings of different modalities. Similarly, we obtain y by y = Myy)
Entity Synthesis We consider two entity synthesis tasks: conditional entity synthesis and uncondi- tional entity synthesis. Conditional entity synthesis aims to generate entities in the target KG with the dangling entities in the source KG as input. Formally, the model takes an entity x: as input and convert it to an entity yz-zy for the target KG. It should also produce the corresponding concrete features, such as neighborhood and attribute information specific to the target KG. On the other hand, the unconditional entity synthesis involves generating new entities in the target KG with random noise variables as input. Formally, the model takes a random noise vector z as input and generate a target entity embedding Yz-ty which is then converted back to concrete features.
For instance, to reconstruct the neighborhood (or attribute) information of Star Wars (film) from its embedding, we leverage decoder module convert the embedding into a probability distribution of all candidate entities (or attributes). As the image features are constant pretrained embeddings, we can use the image corresponding the nearest neighbor of the reconstructed image embedding of Star Wars (film) as the output image.
Generative Models Generative models learn the underlying probability distribution p(z) of the input data x. Take variational autoencoder (VAE) (Kingma & Welling 2013) as an example, the encoding and decoding processes can be defined as:
Encoder(x)
(Encoding)
(3)
μ
Linear, (h) + Linear, (h) e
(Reparamcterizatioon Trick)
(4)
X = Decoder(z)
(Decoding),
(5)
where h is the hidden output. VAE uses the reparameterization trick to rewrite h as coefficients μl, in deterministic function of a noise variable e (N(e; 0, enable back poock-rpppgation... Xx-zz denotes that this reconstructed entity embedding is with as input and for x. VAE generates new entities by sampling a noise vector and converting it to x.
2.2 EEA BENEFITS FROM THE GENERATIVE OBJECTIVES
Let X ~ y be two entities sampled from the entity sets X. V) respectively. The main target of EEA is to learn a predictor that estimates the conditional probability po (xly) (and reversely Po (y (x)), where 0 represents the parameter set. For simplicity, assume that the reverse function po (y (x)
shares the same parameter set with po (x y)
Now, suppose that one wants to learn generative model for generating entity embeddings:
/ po po(y|x)dd (y)
logp(x) log p(x)
(6)
log p(x,
Ee (x)
+ DKL (po(lxx) p(y[x)),
Po (y xx)
where the left-hand side of Equation is the evidence lower bound (ELBO) Kingma & Welling 2013), and the right-hand side is the Kullback-Leibler (KL) divergence (Kullback & Leibler 1951) between our parameterized distribution Po (x())) (i.e., the predictor) and the true distribution p(y x).
In typical generative learning, pay (x) is intractable because y is a noise variable sampled from a normal distribution, and thus p(y) x) is unknown. However, in EEA, we can obtain few samples by
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using the training set, which leads classical negative sampling loss (Sun et al. 2019
2017
Cao et al.
Zhang et al. 22019; Chen et al. 2020 Guo et al. 2020 Sun et al. 2020a
Liu et al.
2021
Chen
al. 2022a b Guo et al. 2022a Lin et al. 2022):
Lus =
Log(pe(y'les p(y' xx)) +
Σ jiyt
log (po (y" xx) - p(y" |x )))]
(8)
Nus
where (y', x²) denotes pair of aligned entities in the training data. The randomly sampled entity y regarded as the negative entity. i, j are the entity IDs. Nus is the normalization constant. Here, Las is formulated as cross-entropy loss with the label p(y" (xx) defined as:
0, if i
ply² xx)
[1
otherwise
Given that EEA typically only a small number of aligned entity pairs for training, the observation of p (x) may be subject to bias and limitations. To alleviate this problem, the recent GAN-based methods (Pei al. 9a b Guo et al. 2022b) propose leveraging entities outside the training set for unsupervised learning. The common idea behind these methods is to make the entity embeddings from different KGs indiscriminative a discriminator, such that the underlying aligned entities shall be encoded in the same way and have similar embeddings. To formally prove this idea, we dissect the ELBO in Equation
(7) as follows:
E p log p(x,y)] ()(()
px log po (x - (po((x))))) ply))
(10)
The complete derivation in this section can be found in Appendix A. Therefore, we have:
l(g) = Exp(yix) log (og
DKL (po (po (ylx) p(y)) + DKL p(y|x)
(11)
roconstruction term
distribution matching term
prediction matching
The first term aims to reconstruct the original embedding x based on generated from x, which has not been studied in existing discriminative EEA methods (Guo et al. 2020 Liu et al. et al. (022). The second term enforces the distribution of y conditioned on x to match the prior distribution y. which has been investigated by the GAN-based EEA methods (Pei al.) 201 b Guo et al. 2022b). The third term represents the main objective of EEA (as described in Equation 8 where the target p(y|x) is partially observed).
2021 Lin
Note that, p(x) is irrelevant to our parameter set 0 and can be treated as constant during optimization. Consequently, maximizing the ELBO (i.e., maximizing the first term and minimizing the second term) will result in minimizing the third term:
Proposition 1. Maximizing the reconstruction term and/or minimizing the distribution matching term subsequently minimizes the EEA prediction matching term.
The primary objective of EEA is to minimize the prediction matching term. Proposition D provides theoretical evidence that the generative objectives naturally contribute to the minimization of the EEA objective, thereby enhancing overall performance.
2.3 THE LIMITATIONS OF GAN BASED EEA METHODS
The GAN-based EEA methods leverage discriminator discriminate the entities from KG against those from another KG. Supposed that x, are embeddings produced by an EEA model M, sampled from the source KG and the target KG, respectively. The GAN-based methods train discriminator 'D to distinguish x from (and vice versa), with the following objective:
argmax x.y.
Exax log D (M, + Ey-y log D (MM)
(Generator)
(12)
+ argmax
Exex log (M + Eyny log(1 - D. (M
(Discriminator)
(13)
Here, the EEA model M takes entities x, input and produces the output embeddings y. respectively. is the discriminator that learns to predict whether the input variable is from the target distribution. 1a the parameter sets of M, DD respectively.
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It is important to note that both (z) and y My( do not follow fixed distribution (e.g..
a normal distribution). They are learnable vectors during training, which is significantly different from the objective of a typical GAN, where variables like x (e.g., image) and (e.g., sampled from a normal distribution) have deterministic distributions. Consequently, the generator in Equation (12) can be overly strong, allowing y to be consistently mapped to plausible positions to deceive D.
Therefore, one major issue with the existing GAN-based methods is mode collapse (Srivastava et al. 2017; Pei al. 2019b Guo al. 2022b). Mode collapse often occurs when the generator (i.e., the EEA model in our case) over-optimizes for the discriminator. The generator may find some outputs appear most plausible to the discriminator and consistently produces those outputs. This is harmful for EEA as irrelevant entities are encouraged to have similar embeddings. We argue that mode collapse is more likely to occur in the existing GAN-based EFA methods, which is why they often use very small weight (e.g., 0.001 or less) to optimize the generator against the discriminator (Pei Guo al. 20226p.
al. 2019b
Another limitation of the existing GAN-based methods is their inability to generate new entities. The generated target entity embedding Yz-sy cannot be converted back to the native concrete features, such as the neighborhood {& y .... or attributes {a' a² ........
3 GENERATIVE EMBEDDING-BASH ENTITY ALIGNMENT
3.1 MUTUAL VARIATIONAL AUTOENCODER
In many generative tasks, such as image synthesis, the conditional variable (e.g., a textual description) and the input variable (e.g., image) differ in modality. However, in our case, they are entities from different KGs. Therefore, we propose mutual variational autoencoder (M- VAE) for efficient generation of new entities. One of the most important characteristics of M-VAE lies in the variety of the encode-decode process. It has four different flows:
The first two flows used for self-supervised learning, i.e., reconstructing the input variables:
X 22-+2 VAE(x), Yy-y 2y-r VAE(y), Var, Vy, X, E
(14)
We use the subscript z-z denote the flow is from x to z, and similarly for g->g. Zz-rxa Zy-ty are the latent variables (as defined in Equation 4 of the two flows, respectively. In EEA, the majority of alignment pairs are unknown, but all information of the entities is known. Thus, these two flows provide abundant examples to train GEEA in a self-supervised fashion.
The latter two flows are used for supervised learning, i.e., reconstructing the mutual target variables:
Ya-yy by VAE(x), Xy-ra Zy VAE(y). Y(,,y) E.
(15)
is worth noting that we always share the parameters of VAEs across all flows. We wish the rich experience gained from reconstructing the input variables (Equation (14)) can be flexibly conveyed to reconstructing the mutual target (Equation (15).
3.2 DISTRIBUTION MATCHI
The existing GAN-based methods directly minimize the KL divergence (Kullback & Leibler 1951)
between two embedding distributions, resulting in the verroppimizzttinn generator and incapability of generating new entities. In this paper, we propose to draw support from the latent noise variable
to avoid these two issues. The distribution match loss is defined as follows:
Lus =
p(z²)))) ))+ + DKL. (p).()zzy=)))p((
(16)
where p(zz-a)) denotes the distribution of Ze-oar and p(z") denotes the target normal distribution. We do not optimize the distributions of Zy-ty. Zy-+z in the latter two flows, because they are sampled from seed alignment set S, a (likely) biased and small training set.
Minimizing Lus can be regarded aligning the entity embeddings from respective KGs to fixed normal distribution. We provide a formal proof that the entity embedding distributions of two KGs will be aligned although do not implicitly minmmzze DKI( p(y)):
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Variational Autoeneoder
Prior Reconstruction
graph
Ennoder
Deooder
Dicader
0.0.0.0.....
artribute
VAE Eneader
VAR Deoaler
Amrian Decnder
00,0.99.. O)
(0,1. A......0
imsage
VAE Ennaker
VAE Deosler
lingee Decnder
00.28,0, 04.0..0..... 07
(0.3, 0.5.
Prediction Match
Distribution Match
Post Reconstruction
POYK)
8x-y
4g
Peston Exper
pCHb)
milti gaussian
X---y
CaTtL origenson loss
inivinte cach palrnniie ELL diveggnce
ausuniee the post--a diffrencce
Figure 2: The workflow of GEEA. Top: different sub- VA-E process different sub-embeddings, and the respective decoders convert the sub-embeddings back to concrete features. Bottom-leftt the entity aligmment prediction loss is retained. Bottom- center: the latent variables of sub- VAEs are used for distribution matching. Bottom-right: The reconstructed sub-embeddings are feed into the fusion layer the EEA model produce the reconstructed joint embedding for post reconstruction.
Proposition 2. Let z", Zz--2, Zy-ty be the normal distribution, and the latent variable distribu- tions w.r.t. X' and y. respectively. Jointly minimizing the KL divergence Dku(p(zz-za) p(z)), (Ru(p(Zz (ayp(yypp "o))))p))((""" will contribute to minimizing DrI(ppxx),p(S)
DkL(p(x), DKL (KL(p(Zo-=))ppzz + (KL(p(zy-g)
(17)
Proof. Please see Appendix A.2
3.3 PRIOR RECONSTRUCTION
The prior reconstruction aims to reconstruct the sub-embedding each modality and recover the original concrete feature from the sub-embedding. Take the relational graph information of flow x + y as an example, we first employ a sub- VAE to process the input sub-embedding:
gx+ty z (gE)
(18)
where VAE, denotes the variational autoencoder for relational graph information. ga is the graph embedding of æ, and Ez-y is the reconstructed graph embedding for y based on x. zi-oy is the corresponding latent variable. To recover the original features (i.e., the neighborhood information of y), we consider prediction loss defined as:
Ege.p = 9y log Decoder, (gx=H)) + (1 - gy) log( (1 Decoddr,(g.--))
(19)
Here, Cg.-.y is binary cross-entropy (BCE) loss. We employ decoder Decoder, to convert the reconstructed sub-embedding gx-,y to probability estimation regarding the neighborhood of y.
3.4 POST RECONSTRUCTION
We propose post reconstruction ensure the reconstructed features of different modalities belong to the same entity. We re-input the reconstructed sub-embeddings (gz-ty ag-ty: to the fusion layer (defined in the EEA model M) to obtain reconstructed joint embedding Yz--y- We then employs mean square error (MSE) loss to match the reconstructed joint embedding with the original one:
Yr-ty Fusion( (go-ny a sy.......)) ....);;;
V(a,y) E
(20)
Cy- = MSE(y NoGradien(())) V(z,y) E
(21)
where Cu-oy denotes the post reconstruction loss for the reconstructed joint embedding Yz-t- Fusion represents the fusion layer in M, and MSE the mean square error. We use the copy value of the original joint embedding NoGradient(y) to avoid y inversely match Yz-zg-

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Table 1: Entity alignment results on DBP15K datasets, without surface information and iterative strategy. t: higher is better; ): lower is better. Average of 5 runs, the same below.
DBP15K DBP15KmaN
DBP15Ka.m
DBP15KTE
Models
Hits If
Hits@ 101
MRRT
1T
Hits 10r
MRR1
Hisse1
Hits@107
MRRT
MUGNN Cão al
2019
.944
844
.611
.501
857
.611
.495
.870
621
(Sin
539
docentKL Ubo ml
2020
389
.819
.672
.596
819
.678
.602
.842
689
Lin
.662
.683
923
MSNEX Cien of
20224
.01
830
6844
.535
.715
.617
.543
.011
630
MCLEA
715
9223
788
.115
9009
785
.711
.909
782
20226
796
7112
GREA
.761
.946
.827
.755
.953
.877
.776
.62
844
Table 2: Results on FB15K-DBISH and FBI5KYYAG015K datasets.
EYA
JESEA
(M)
FBISK-DBISK
FBISK-YAGOLSK
Training time (s)
Hisd011
His@ 101
MRRT
Hivelt
Hisvl 101
MRRT
EVA MSNEA
10.2/1.467.6
.199
448
.283
.153
361
.224
11,57755.2
433
MCLEA
13.2/285
.295
.582
.393
.254
484
.332
Egoch
GEEANALL GEEA
11,2/217.3
.322
.602
.177
.20
.13
.352
Figure 3: MRR results on
13,9/252.4
.298
.313
FBDBI5K w.r.t. epochs.
3.5
IMPLEMENTATION DETAILS
example to illustrate the workflow of GEEA. First, the sub-embeddings outputted by M are used as input for sub-VAEs (top-left). Then, the reconstructed sub-embeddings are passed to respective decoders predict the concrete features of different modalities (top-right). The conventional entity alignment prediction loss is also retained in GEEA (bottom-left). The latent variables outputted by dab- are further used to match the predefined normal distribution (bottom- center). The reconstructed sub-embeddings are fed into the fusion layer to obtain reconstructed joint embedding, which is used to match the true joint embedding for post reconstruction (bottom-righh).. The final training loss is defined as:
We take Figure
C
Σ JEF
Σ (g.
Lm
C post reconstraction
Lidd. +
Lys
(22)
mE (g.a.,.... distribution matching term
prodiction matching term
prior reconstraction
reconstruction term
where F= - available modalities. For details, please refer Appendix B
f 2, + y, x y.y x} is the set of all flows, and (g. a, i..) is the set of all
EXPERIMENTS
4.1 SETTINGS
We used the multi-modal EEA benchmarks (DBP15K (Sun et al. 2017). FBISK-DB15K and 1115KYYAG115 (Chen al. 2020) as datasets, excluding surface information (i.e., the textual
label information) to prevent data leakage (Sun et al. 2020b Chen et al. (2022b). The baselines MUGNN (Cao al. 2019) AliNet (Sun al. (2200a) and decentRL (Guo et al. 2020) are methods tailored to relational graphs, while EVA (Liu et al. 2021). MSNEA (Chen et al. 2022a) and
MCLEA (Lin al. (022) are state-of-the-an multi-modal EEA methods. We chose MCLEA (Lin
et al. 2022) as the EEA model of GEEA and NeoEA (Guo et al. (022b) in the main experiments.
The results of using other models (e.g., EVA and MSNEA) can found in Appendix
C
The neural
layers and input/hidden/output dimensions were kept identical for fair comparison.
4.2 ENTITY ALIGNMENT RESULTS
The entity alignment results on DBPISK are shown in Tables [ The multi-modal methods signifi- cantly outperformed the single-modal methods, demonstrating the strength of leveraging different
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Table Entity synthesis results on five datasets. PRE (x10- RE (x (x10-2) denote the reconstruc- tion errors for prior concrete features and output embeddings, respectively.
Models
DBP15Kkssx
DBP15KIsEN
DBP15Krs.EN
FD15K: DB15K
FBISK YAGOISK
PREE
RC1
FDD
PRE]
REL
FIDI
PRE]
RE]
FID.
PRE]
REI
[TD]
PRE
REJ
RIDI
MCI decader
8.104
4.218
7.640
5.441
N/A
10:578
5.965
18.504
inf
NIA
20.997
inf
N/A
decader
0.737
0.205
1821
0.542
0.329
2,184
0.689
3,083
10.564
11,254
10.495
9.645
9,982
16.180
Sub- VAEs+ decuder
0.701
0.246
1,920
0.531
0.291
2,483
0.514
0.663
2.694
3.557
15.389
4.340
2,424
5.576
5,503
GEEA
0.438
0.184
0.935
0.385
0.195
1.871
0.451
0.121
2.422
3,141
6.851
3,069
1,730
2,039
3,903
1.0
1.0
0018
0.4
GLEA
MCLEA
0,651
0.787
0.K
0,890
0%
Hitsg
0.6
0.5
Tinsee
8.6
01515
0,699
0,764
0.6
0.450
0,555
0.582
0.326
0.2
0:230
0
9.2
GEEA
MCLEA
0.2
0.251
GEEA
MCLEA
0.0
0.169
0.0
0.0
1065
50%
50%
25%
50%
50%
20%
50%5
Ratio
Figure 4: Entity alignment results on FBDBI5K, w.r.t. ratios of training alignment. resources. Remarkably, our GEEA achieved new state-of-the-ar performance on all three datasets across all metrics. The superior performance empirically verified the correlations between the gener- ative objectives and EEA objective. In Table 2 we compared the performance of the multi-modal methods on FBI5K-DB15K and FB15K- YAGOI5K, where GEEA remained the best- best-performing method. Nevertheless, we observe that GEEA had more parameters compared with others, as it used VAES and decoders to decode the embeddings back to concrete features. To probe the effectiveness of GEEA, we reduced the number of neurons to construct GREASMALL and it still outperformed others with a significant margin.
In Figure 3
we plotted the MRR results w.r.t training epochs on FBDBISK, where MCLEA and GEEA learned much faster than the methods with fewer parameters (i.e., EVA and MSNEA), In Figure further compared the performance of these two perf-rrrn methods under different ratios of training alignment. We can observe that our GEEA achieved consistent better performance than MCLEA across various settings and metries. The performance gap more significantly when there were fewer training entity alignments (S 30%). For instance, GEEA surpassed the second-best method by 36.1% 1% % in Hits @1 when only 10% aligned entity pairs were used for training.
In summary, the primary weakness of GEEA is its higher parameter count compared to existing methods. However, we demonstrated that a compact version of GEEA still outperformed the baselines in Table This suggests that its potential weakness is manageable. Additionally, GEEA excelled in utilizing training data, achieving greater performance gains with less available training data.
4.3 ENTITY SYNTHESIS RESULTS
We conducted entity synthesis experiments by modifying the EEA benchmarks. We randomly selected 30% of the source entities in the testing alignment set as dangling entities, and removed the information of their counterpart entities during training. The goal was reconstruct the information of their counterpart entities. We evaluated the performance using several metrics: the prior reconstruction error (PRE) for concrete features, the reconstruction error (RE) for the sub-embeddings, and Frechet inception distance (FID) for unconditional synthesis (Heusel et al. 2017). FID is a popular metric for evaluating generative models by measuring the feature distance between real and generated samples.
We implemented several baselines for comparison and present the results in Table MCLEA with the decoders performed worst and could not generate new entities unconditionally. Using Sub-VAEs to process different modalities performed better than using one VAE to process all modalities. However, the VAES in SAb-VAES could not support each other, and sometimes they failed to reconstruct the embeddings (e.g., the RE results on FB F515KDDB 15K). By contrast, significantly outperformed these baselines. We also noticed that the results on FB 1BB1K-DBB51 and FB15K-YAGE YAGO15K were worse than those on DBP15K. This could be due to the larger heterogeneity between two KGs compared to the heterogeneity between two languages of the same KG.
GEEA consistently and
We present some generated samples of GEEA conditioned on the source dangling entities in Table 4 GEEA not only generated samples with the exact information that existed in the target KG, but also completed the target entities with highly reliable predictions. For example, the entity Star Wars (fil)
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Table 4: Entity synthesis samples from the FB15K-DB15K dataset. The boldfaced denotes the exactly matched entry, while the underlined denotes the potentially true entry.
Source
Tagst
GBEA Daiu
Enite
Image
Enage
Neigleochood
Ataibbuee
Imagee
Neigiborhood
Artiibte
Century Fox.
Willow
WARF
WARS
Wan: The
Inditld Onitertttgtoode
(RISkcaa)
Geonge Harison
Klass Vooemamn. Jeft Lyrne, Pop music
The Resilzs, Guite, Rock mustc.
Ninhilasc datehDatc,
YotreYoussturteee active Yeorstaeee..... indhid
The Hand, Ringo Stare Klun Voeemann. Jef JefTaanne, Rock music
The Beaties
active VenreStarr
deaththaie Nirthihute.
artive Year Yior.
deati Nethheer
baiehe netwoett
Table Ablation study results on DBPISKZHEN.
Prodiction Match
Distribution Match
Prior Reconstraction
Post Reconstruction
Entity Aligoment
Eutity Synthosis RE.
Hits@ 1
Hitsd 101
MRR
PRE.
FIDJ
.04.
.186
.015
0.717
0.305
2.149
202
0.551
0.195
.766
.930
.813
inf
0.267
11488
750
0.701
0.246
1,920
target KG only had three basic attributes in the target KG, but GEEA predicted that it may also have the attributes like indbid and initial release data.
4.4 ABLATION STUDY
We conducted ablation studies to verify the effectiveness of each module GEEA. In Table we can observe that the best results were achieved by the complete GEEA, and removing any module resulted in performance loss. Interestingly, GEEA still worked even if we did not employ an EEA loss (the 2nd row) in the entity alignment experiment. It captured alignment information without the explicit optimization of the entity alignment objective through contrastive loss, which is an indispensable module in previous EEA methods. This observation further validates the effectiveness of GEEA.
RELATED WORKS
Embedding basedd Entity Alignment Most pioneer works focus on modeling the relational graph information. They can be divided into triplet-based (Sun et al., 2017 Pei et al. 2019a) and GNN- based (Wang al.) 2018 Guo al. 2020). Recent methods explore multi-modal KG embedding for EEA (Zhang et al. 2019 Chen et al. 2022b Lin et al.) 2022). Although GEEA is designed multi-modal EEA, it differs by focusing on objective optimization rather than specific models. GAN-based methods (Pei et al. 22019a Guo et al. (202bb) are closely related to GEEA but distinct, as GEEA prioritizes the reconstruction process, while the existing methods focus on processing relational graph information for EEA.
Variational Autoencoder We draw the inspiration from various excellent works, e.g., VAEs, flow- based models, GANs, and diffusion models that have achieved state-of-the-an performance in many fields (Heusel et al., 2017 Kong et al. 2020 Mittal et al., 2021 Nichol & Dhariwal 2021 Ho et al.) 2020 Rombach et al.) 2022). Furthermore, recent studies (Hoogeboom al. 2022, Li et al. 2022) find that these generative models can be used in controllable text generation. To the best of our knowledge, GEEA the first method capable of generating new entities with concrete features. The design of M-VAE, prior and post reconstruction also differs from existing generative models and may offer insights for other domains.
CONCLUSION
This paper presents a theoretical analysis of how generative models can enhance EEA learning and introduces GEEA to address the limitations of existing GAN-based methods. Experiments demonstrate that GEEA achieves state-of-the-ar performance in entity alignment and entity synthesis tasks. Future work will focus designing multi-modal encoders enhance generative ability.

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ACKNOWLEDGMENT
We would like to thank all anonymous reviewers for their insightful and invaluable com- ments. This work is funded by National Natural Science Foundation of China (NS- RCD::B05//NFCCU99027//SY)) 186624)) Zhejiang Provincial Natural Science Foundation of China (No.LGG22F03001), Fundamental Research Funds for the Central Universities (226-2023- 00138), and the EPSRC project ConCur (EP/V050869/1).
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A PROOFS OF THINGS
A.1 THE COMPLETE PROOF OF PROPOSITION
Proof. Let x. X, y/ y be two entities sampled from the entity sets X, V, respectively. The main larget of EEA is to learn a predictor that estimates the conditional probability pe (xly) (and reversely poly x)), where 0 represents the parameter set. For simplicity, we assume that the reverse function po(y)x) shares the same parameter set with po (x
Now, suppose that one wants to learn a generative model for generating entity embeddings:
log p(x) log p(x) / po po(ylx)dy
(23)
/ po(ylxx logp(x)dy
(24)
Epo(y loooy/>))logptee p(x)
(25)
log y(xx,))
(x) (x)
(26)
p(y|x)
p(x, )po (y (x)
( (x)
log
(27)
p(y /x po (y x)
y(x,y)
log Poly x)
(y)()) (c)
log
+ px)
(28)
Py ix)
p(y(x)
p(x, y)
(y (x)
log
+ (volxx) (|)(())))
(29)
po
xx)
where the left-hand side of Equation 7 is the evidence lower bound (ELBO) Kingma & Welling
2013), and the right-hand side is the KL divergence (Kullback & Leibler 1951) between our
parameterized distribution (y (x) (i.e., the predictor) and the true distribution ply(x).
The recent GAN-based methods (Pei et al. 2019a b Guo et al., 2022b) propose leverage the entities out of training set for unsupervised learning. Their common idea is to make the entity embeddings from different KGs indiscriminative to a discriminator, and the underlying aligned entities shall be encoded in the same way and have similar embeddings. To formally prove this idea, we dissect the ELBO in Equation ( as follows:
p(x. y) Ey)(y)x) log ()(y(x)
po (x(x)))p(y)
(x((x)))) log
(30)
(y(y)x)
1xg])(x(y)] + ppo(ri))) [og p(y)
Exo())
(31)
po (o(x))
(xo()
logpo(xly)] DKL(Po(y(x)) ply))
(32)
Therefore, we have:
log p(x) Epo xx) log px(())
DKL (po (y(x)) p(y)) DKL p(ylx))
(33)
reconstructio term
distribution matching term
prediction matching term
The first term aims to reconstruct the original embedding x based on generated from x, which has not been studied by the existing discriminative EEA methods (Guo al. 2020 Liu et al. 202T] x to match the prior
Lin et al.) 2022). The second term imposes the distribution y conditioned distribution of y. which has been investigated by the GaN-based EEA methods (Pei et al. 2019a] b)
Guo et al. 2022b). The third term is the main objective of EEA (i.e., Equation (8) with the target p(y x) being only partially observed).
Note that, p(x) is irrelevant to parameter set 0 and thus can be regarded constant during optimization. Therefore, maximizing the ELBO (i.c., maximizing the first term and minimizing the second term) will result in minimizing the third term, concluding the proof.
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A.2 PROOF OF PROPOSITION
2
Proof. We first have a look on the right hand:
(KI,(((Z=-a)) p(z²)) + Dri. (p(y(p(z
(34)
Ideally, all the variables zy- Zy- and z follow the Gaussian distributions with Pa- My PC* and az-zz Ty-sy. a² mean and variance, respectively.
Luckily, we can use the following equation to calculate the KI. divergence between two Gaussian distributions conveniently:
(RL(((E)). log 02 of + (11 - -22)²
+
(35)
σ1
20
2
and rewrite Equation 34) as:
DKL(p(Zz-H p(zz)) + DKL (p(zy-sy)
(36)
0¹ o² xx + (Ma-1z 1=))
1
0
+ og +
(Hyyy - -2²)²
=(lg
+ (log
(37)
2(0x))2
2
8y-v
2(0*)32
N + (Mz - 12)1
+ o go (-4yy) 11")2
=(log
+ log
-)-1 -1
(38)
2(0²)2
2(0*)2
x-+x
0¹
0¹
2Z + (#a-1z 11 + o + (1yrg - 11")2
=(log
log
(39)
2(
02-22
Take n²' ~N 0, a² = I) into the above equation, we will have:
DKL (p(2)- p(z²)) )) +
(40)
log xx-x 7 y- + / 102 + oy + 1o + pgyoo) -1
(41)
Similarly, the left hand can be expanded as:
(au((p(z=)), = log Jy-U Lo + (M My
(42)
xx-
20 4-t
2
Thus, the difference between the left hand and the right hand can be computed:
(KL(((Z=-z),p(EZ" + (pLzp(zy)g)) p((=))))))p('()) p(z")) - DKL (p(Z=s))) p(Zg-u))
(43)
=- log azzzzaypp + 3 x-0 + +0z + 12200 + ( -
(44)
- (log Jy-y + 2 2z + (pr-rx Myy
(45)
20
2
-(- log 0 Or-nn log 04-0 )
(46)
xx-
2 + (Ho- - My ) + (-1+ 1
+ ( 10
+ toy + 2 + (1
2
(47)
202 2
1
= = 2log O4+t
(48)
2
0 -2o + 0 v-
+ 2 12 o + py
0-
1 kg + 2p 21 yy by
202 kーンy
(49)
1
--2 vytyy 2
(50)
(og 1)0 + (13 + 112 ( 1) o 2p
(51)
20 2
+ (mZ-2 + +12 + -
)
10
- 1) +
و 2pz
= = --2log Oytty 2
(52)
20
-
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As optimize zy-y - z², i.e., minimize DKL (p(zy+y))))) p(z))), we will have:
log vU+y + 0, 6zyo - -00, 0, Pz P2-z2y-2 + 0, oy + 1, and consequently:
(53)
(KL(p(Zz-z)) p(z')) DKL (p(Z - DKL (p(x p(Zyy>y) 0,
(54)
Similarly, as we optimize Zz-tz + zz, i.e, minimize DKL (p(z - p(zz (2)) we will have:
DKL(P(Ze-o)) p(z*)) + DLL (p(z)-u),
DKL (pl (p(2) , p(zz+z)) - 0
(55)
Therefore, jointly minimizing (p 2 (Zz-+z()) x p(z")) and DEL (pl (Zy p(z))) will subsequently
minimizing DKL (p(z-<=))) .(Zz and DKL (p(Zz-u)), p (zx=x)) )), and finally aligning the distri-
butions between x and y. concluding the proof.
B IMPLEMENTATION DETAILS
B.1 DECODING EMBEDDINGS BACK TO CONCRETE FEATURES
All decoders used decode the reconstructed embeddings the concrete features comprise several hidden layers and an output layer. Specifically, each hidden layer has a linear layer with layer norm and ReI.U/Tanh activations. The output layer is different for different modalities. For the relational graph and attribute information, their concrete features are organized in the form of multi- classification labels. For example, the relational graph information gi for an entity æ; represented by:
9: = 1,
1, ........... 0)²,
[g.| = |
(56)
where 9i has | elements with 1 indicating the connection and 0 otherwise. Therefore, the output layer transforms the hidden output to the concrete feature prediction with a matrix W, E IR x where is the output dimension of the final hidden layer.
The image concrete features are actually the pretrained embeddings rather than pixel data, as we use the existing EEA models for embedding entities. Therefore, we replaced the binary cross-entropy loss with MSE loss to train GEEA to recover this pretrained embedding.
B.2 IMPLEMENTING A GEEA
We implement GEEA with PyTorch and run the main experiments on a RTX 4090. We illustrate the training procedure of GEEA outlined in Algorithm [ We first initialize all trainable variables and the get the mini-bateh data of supervised flows x + y. > x and unsupervised flows x + æ. y y, respectively.
For the supervised flows, we iterate the batched data and calculate the prediction matching loss which also used in most existing works. Then, calculate the distribution matching, prior reconstruction and post reconstruction losses and sum them for later joint optimization.
For the unsupervised flows, first process the raw feature with M and VAE to obtain the embeddings and reconstructed embeddings. Then we estimate the distribution matching loss with the embedding sets input (Equation (16), after which calculate the prior and post reconstruction loss for each x and each
Finally, we sum all the losses produced with all flows, and minimize them until the performance on the valid dataset does not improve.
The overall hyper-parameter settings in the main experiments are presented in Table 6
C ADDITIONAL EXPERIMENTS
C.I DATASETS
We present the statistics of entity alignment and entity synthesis datasets in Table To construct an entity synthesis dataset, first sample 30% of entity alignments from the testing set of the original
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Algorithm I Generative Einbedding-basee Entity Alignment
1: Input: The entity sets , ) the multi-mode information 9, A, I ... the EEA model M, and
M-VAE VAE;
2: Randomly initialize all parameters;
3: repeat
4: Baup +- {Z, (zz,))((z,)) ~ S); I1 get a batch of supervised training data
5: Bunsup < (2. ~ X y): get a batch of unsupervised training data
6: for v) Bup do
7:
x,y - M(z)
obtain embeddings and sub-embeddings
8:
Yz-ty1 Xy- VAE(x), VAE(y); // obtain the reconstructed mutual embeddings
9:
Calculate the prediction matching loss following Equation (8)
Calculate the prior reconstruction loss following Equation
11:
Calculate the post reconstruction loss following Equation 20
end for
13:
Ny--yl (ar, y) Buusap) < (VAE(M())), VAE(M(y)) E Bumsup) ): // obtain the
reconstructed self embeddings
14:
Calculate the distribution matching loss following Equation (16
15:
Calculate the prior reconstruction loss following Equation (19
16:
Calculate the post reconstruction loss following Equation 20
17:
Jointly minimize all losses;
18:
until the performance does not improve.
Table 6: Hyper-parameter settings the main experiments. PM,DM, PrioR, PostR denote prediction matching, distribution matching, prior reconstruction, and post reconstruction, respectively.
Tatneh
Pepoch
hashssio
VAE lagres
Auniiss 1t3c
optiniier
despect ralc
Lioaporebol
Bow veteati (36389813))
J01 WEREbh:
lidies si0ce
laane
sic
doceder
D8P:5R
200
2,500
0031
Adar
0.5
2,500
[... 5
[L L.DSLLL1
300 300)
300
1300, 1000)
5001
E.J.A.3
300
(044)
FSISK- LIBKI
Adb
115
2.501
B.L.5.1
11000200200
320
(300.990 1901]
FSESK- VAALDSI
0081
1.41
11000
Ade
015
2.501
1.1.5.5
20000000
300
[3000 1130]
Table 7: Statistics of the datasets.
Aligament Tist Aligsments
Fmity Synthesis
Entitios
Relations
Altributes
Imagess
Known Tex Alignments
Unknown Test Aligensents
10,500
1,323
7,173
14.125
DDP15Kaas
10,500
10,500
7,350
7,350
3,150
3
19,750
19,814
1,153
1.299
6,056
5,830
13,741
12.730
DRPI5K
10,500
7,350
3,150
19,661
903
4,547
14.174
10,500
7,350
3,150
19,993
1,208
6,422
13858
FB1SK DBISK
10,500
7,350
3,150
14,951
12,842
1,345
279
12,837
FBISK-YAGOISK
6,272
1,345
13.444
entity alignment dataset. Then, view the source entities in sampled entities pairs the dangling entities, and make their target entities unseen during training. To this end, we remove all types of information referred to these target entities from the training set.
C.2 SINGLE-MODAL GEEA
We first remove the image encoder from multi-modal EEA models. The results shown in Table [] Notably, our GEEA without the image encoder still achieves state-of-the-art performance on several metrics, such @its 10.
Then, we conducted new experiments on the OpenEA 100K (Sun et al.
2020b). Although OpenEA
100K does not have multi-moda version, it is still interesting to explore the performance of GEEA with single-modal EEA models on it, similar to NeoEA (Guo et al. 2022b). We conducted experiments following the NeoEA and present the results in Table 12 It is clear that method can
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Table 8: Entity alignment results of GEEA with different EEA models on DBPI5K datasets.
DBPISKau
DBP1SKWEN
DBP1SKmu
His@ 11
Hixe 107
MRR
Hite8 11
His@@ 101
MRR.
Hic 11
Hiss 101
MRR
EVA
Lin or 2021
480
.100
.762
.773
9988
757
683
-925
767
GEE
.715
.794
.707
.955
.791
.277
.940
817
MSNEA Chen el 2022a
601
830
684
535
775
617
543
801
GREA W/ NEA
.443
.822
.732
.59
.21
.671
.966
.53
.72
MCLEA
Lin al. 2022
.715
788
715
9099
785
311
909
782
GEEA MCLEA
.761
.933
Table More entity synthesis samples from different dataset. The first two rows are from FB15K-
YAGO15K; the middle two rows are from DBP15 the last two rows are from DBP15KFR.
Haage
Negil
Image
Prigl Regeerilllla
Laiedd de New le Sunalaae
Unbad Birbaaer
Iesiaaa Cuados
Cuaads la
Valaa Pralits
was suredDallenn wedliwky wilecten
Nox fae anddl Ye Dhenee
Lake tit Wuterrill Belc ger
Hinptier Auggls
Lad pesiiiatiios
Flakary the Chis albari talluaa
The Eza Enlietenn Capefor albans
mane ar wrepke Nesitear
Mick wuse
Peliciia la His Mwc.Phoiee
gotoo clili
Peldec Derros
kemiin Palker Confeorindes Hulyy
prolake laggaais Maack pilli
positiii las
Bally Istaad Ii fimm.
Naaadda Natvooa baakh fres. To Warh.
Bah typ tall
Table 10: Some false samples from FB15K- YAGO15K.
Suuce
Taget
GEEA Ougun
Harrry
Imrage
trrge
Natghbuttzed
Attritune
Irroge
Naighbuthood
Caniz-Auze
Receath
(alm)
Laamaze Fiatheme
Hago Weaking
Lideas Michel Drirs Bomsatt
Unided Seats, Tomes
United States, Nicasgan Revolatios Assorad (alm)
Neao.
(ilm)
Armiid Schwaneenageer
significantly enhance the performance of SEA (Pii et al. 2019a), which can be attributed to the more stringent objectives analyzed in Section
C.3 GEEA ON DANGLING ENTITY DETECTION
The methods for detecting dangling entities (Sun et al. 2021) can be categorized into three groups: (1) Nearest Neighbor Classifier (NNC), which trains classifier to determine whether a source entity lacks counterpart entity in the target KG; (2) Margin-based Ranking (MR), which learns margin value A. If the embedding distance between a source entity and its nearest neighbor in the target KG exceeds A, this source entity is considered dangling entity: (3) Background Ranking (BR), which regards the dangling entities as background and randomly pushes them away from aligned entities.
All three types of dangling detection methods heavily rely the quality of entity embeddings. Therefore, if the proposed GEEA learns better embeddings for entity alignment, is expected to contribute the detection of dangling entities. To verify this idea, we conducted experiments new datasets, following [1]. We used the same parameter settings and employed MTransE (Chen et al. 2017) as the backbone model. The results are presented in Table 13 Clearly, incorporating GEEA led to significant performance improvements in dangling entity detection across all three datasets. The performance gains were particularly notable in terms precision and F1 metrics.
C.4 GEEA WITH DIFFERENT EEA MODELS
We also investigated the performance of GEEA with different EEA models. As shown in Table X GEEA significantly improved all the baseline models all metries and datasets. Remarkably, the
16

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Published as a conference paper at ICLR 2024
Table 11: Detailed entity alignment results on DBP15K datasets, without surface information and iterative strategy.
DBPI5Kama
DBP15Ka.xx
DBP15KpRaN
Models
Hi 17
Hits 101
MRR
Hita 11
Hiss 10"
MRR
Hits 11
Hits
MRR
EVA Lin et al.
2021
.80
910
.762
.673
.908
.757
.683
.923
.767
MSNEA
2022a
.011
830
684
.355
.775
.617
.53
.001
.60
MCLEA (Lin et 2022
715
923
.888
.15
.009
785
.711
9099
.782
MCLEA W/S image
658
9155
.662
.904
740
.902
.747
.755
.827
.962
.844
GEEA w/o image
.709
929
.782
.708
935
.784
.117
.946
776
Table 12: Single-modal entity alignment results OpenEA 100K datasets.
EN-FR
EN-DE
DBPedia-WikiDen
DBPedia-Yage
Models
Hits@111
MRRT
Hits
MRRT
Hits@1
MRRT
Hitx
MRR
SEA Pei et
2019
.225
314
.411
.411
.211
.388
.490
.578
NvoLXTSEE Goo
.254
.651
GEEA (SEA)
.269
.355
.377
.459
.349
.466
.597
.685
performance of EVA with GEEA some datasets like DBPI5KFREE were even better than that of the original MCLEA.
C.5 RESULTS WITH DIFFERENT ALIGNMENT RATIOS ON ALL DATASETS
We present the results with different alignment ratios on all datasets Figure which demonstrate
the same conclusion as in Figure
C.6 MORE ENTITY SYNTHESIS SAMPLES
We illustrate more entity synthesis samples in Table and some false samples in Table I0 The main reason for less accurate synthesis results is the lack of information. For example, in the FB15K- YAGO15K datasets, the YAGO KG has only different attributes. Also, as some entities do not have image features, the EEA models configured to initialize the pretrained image embeddings with random vectors. To mitigate this problem, we plan to design new benchmarks and new EEA models directly process and generate the raw data in future work.
17

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Published as a conference paper at ICLR 2024
Table 13: Dangling entity detection results on DBP2.0.
DBP B.
DBP E.
DBP 2.0mREN
Models
Precision
Recallf
Precisionf
Recallf
Precisiont
Recallf
F11
NNC Sun al.
2021
.491
459
.47
.53
GREA J
.617
.509
.588
.637
.460
.534
.479
.449
.464
MR (Sun et
2021
-702
.740
.799
.708
.482
.575
.544
GEEA (MK)
.793
.709
.749
.812
.714
.760
.508
.594
.548
BR (Sun al.
2021
.811
.728
.767
.816
.733
.772
.539
.686
.604
GEEA [BK)
.821
.724
.769
.833
.735
.781
.549
.694
.613
DB15K- FBB-KK1KK
0.5
GEEA
MCLEA
0.787
HiNo
0.8
R.515
Ou661
6.796
0.784
03052
0,918
MRR
0.5
0.450
0,620
0.637
0.556
0.7M0
0.4
0.236
0.409
0.
0.326
GEEAA
0.251
GEEA
0.8
0.169
0.0
0.0
10%%
30%
10% Ratio
40%
50%
10%
20%
V9% Ratio
10%
80%
10%
70%
50%
80%
Ratio
DB15K- WHISKYYAGOSKK
0.8
MCLEA GEIA
0.733
0.8
0,59D
0,808
0.5
0L790
Hls@l1
Hiva
494
0,545
0.205
0.324
MRR
0.395
0,512
0.4
201
0.4
00.4
0.286
0,391
0.254
GEEA
GEEA
0.0
0.0
10%
70%
50%
40%
50%
10%
70%
59% Ratio
10%
80%
10%
70%
11%6 Ratio
50%
805
Ratio
Hitg8
0.8
0,005
0.715
0:816
0.757
0.923
Hivg10
0.8
00335
0.903
0.913
0.881
0:923
0.965
0.987
0.991
MRR
0.5
0.691
03857
0321
0.643
0.4
MCCEA GEEA
MCLEA
GEEA
0.0
0.0
10%6
20%
30%
5055
50%
10%
20%
30%
50%
90%
10%
20%
3055
50%
80%
Ratio
Ratio
Ratio
0.925
0.923
079
0.8
0.588
700
0.754
0.8
0.874
0.488
0.951
08%
0.676
0.937
Hitsq
0.677
0.715
HiNe:
MRR
0.546
MCLEA
MCLLA
MCLEA GEEA
0.2
-G--GEEA
022
10%6
25%
50%
50%
50%
10%
20%
30%
50%
90%
10%
20%
305 Ratio
50%
80%
Ratio
Ratio
1.0
0.820
1.905
0.855
0.913
0.958
0 199
0
1.0
0,005
0.796
0,906
0.711
0.802
HiNs8110
MRR
0.665
0.551
MCLEA S.A.A.
MCLEA CEEA
MCLFA
0.2
0.2
GEEA
20%
3055 Ratio
50%
Ratio
Ratso
Figure 5: Entity alignment results on all datasets, w.r.t. ratios of training alignment.
18


Reviews:
[{"review_id": "Ug9ks02fFe", "reviewer": "Reviewer_gcSh", "summary": "The authors introduce the entity synthesis task and propose an M-VAE model that can convert entity embeddings back to the native concrete features. They also propose prior reconstruction loss and post-reconstruction loss to control the generation process. Empirical results show that entity synthesis has a positive effect on entity alignment.", "questions": "GEEA is a general method, but all experiments are completed in multi-modal settings. In a single-modal scenario, will GEEA still be competitive?\nThe time and memory overhead of GEEA should be reported. \nThe number of entities in each data set is 15k. Can GEEA be run on larger datasets(such as 100k)?\nAdditionally, there are some other problems:\nThere are two \"right hand\" in the above line of Eq.43, one of them should be \"left hand\".\nThe weight of prediction matching loss is not included in Table 6.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. Through theoretical analysis from the perspective of generative models, the authors point out that generative objectives contribute to the optimization of EEA models.\n2. A generative EEA framework is proposed. By introducing reconstruction loss and distribution matching loss, GEEA further improves the performance of previous EEA models.", "weaknesses": "The author needs to briefly introduce the metrics of alignment prediction. Is it consistent with the EEA model used in GEEA?\n\nThe proposed M-VAE model is a generative model, but there are no other generative models compared to baseline models. It's better to compare with some GAN-based models like NeoEA(\"Understanding and improving knowledge graph embedding for entity alignment.\" International Conference on Machine Learning. PMLR, 2022.)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Q5l1S6AWXg", "reviewer": "Reviewer_ALxa", "summary": "This paper studies the task of entity alignment. The authors introduce a generative EEA framework, leveraging the mutual variational autoencoder (M-VAE) to facilitate the encoding and decoding of entities between source and target KGs. A series of experiments have been executed to ascertain the efficacy of the GEEA, and the results affirm the prowess of the model.", "questions": "- Could you elaborate on what constitutes the multi-modal information within the knowledge graph (KG) area?\n- What types of attribute information are being referred to in this context?\n- How would you define \"sub-embeddings\" in the framework?\n- What does $\\mathcal{L}_{mf}$ represent within the paper?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The experiments showcased provide evidence of the efficacy of the GEEA model.", "weaknesses": "- The paper would benefit from enhanced clarity. Several concepts are mentioned without a clear definition, leading to potential confusion for readers. See the questions listed below for specifics. \n- The objective of prior reconstruction could be made more comprehensible. There's ambiguity regarding the priors of features in different sub-embeddings. Specifically, when dealing with images, how does one retrieve its original, tangible feature?\n- The paper could provide a more extensive set of experiments to offer insights into the rationale behind the design of individual components.\n\n- Eq. (19)  is missing a right parenthesis.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "MLtqFLqK1Q", "reviewer": "Reviewer_sPPq", "summary": "This paper presents a M-VAE based generative approach for embedding-based entity alignment. This paper theoretically justified the plausibility of formulating the problem as a generative task that is akin to what recent GAN-based EA approach has done. Specifically, for the problem with dangling entities, different from prvious work that has focused on detecting such dangling points, this work proposes a novel solution of entity synthesis. Experiments are done on common datasets shared by most prior works on this topic, with fair comparison ensured (by removing entity names, which has been violated by some prior works).", "questions": "Please see weaknesses above.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "The contributions of this paper are from multiple perspectives. The plausibility of a generative formulation of the problem is theoretically justified. For the recently proposed dangling entity problem, a novel solution of entity synthesis is proposed to fulfill the missing targets in the target-side KG. Evaluation has covered the traditional setting of close-space entity alignment to show the effectiveness from that perspective, and a new, plausible setting is proposed for entity synthesis to show the effectiveness from this new angle of solution. The presented method and experiments look sound.", "weaknesses": "While the proposed entity synthesis approach leads to an essentially different solution to dangling entities from the previous dangling detection approaches, I wonder if the proposed approach can still can contribute to (and be compared with) dangling detection.  \nThere is one detail that I might have missed: in the close-space EA setting without considering dangling entities, is there any technique of constrained generation/decoding that ensure the generation to fall into the candidate space?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)