Learning with Dual-level Noisy Correspondence for Multi-modal Entity Alignment
Authors: Haobin Li
Yijie Lin
Peng Hu
Mouxing Yang
Xi Peng
Venue: ICLR 2026 Oral (2026)
Keywords: Noisy correspondence; Multi-modal entity alignment.
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Multi-modal entity alignment (MMEA) aims to identify equivalent entities across heterogeneous multi-modal knowledge graphs (MMKGs), where each entity is described by attributes from various modalities. Existing methods typically assume that both intra-entity and inter-graph correspondences are faultless, which is often violated in real-world MMKGs due to the reliance on expert annotations. In this paper, we reveal and study a highly practical yet under-explored problem in MMEA, termed Dual-level Noisy Correspondence (DNC).
DNC refers to misalignments in both intra-entity (entity-attribute) and inter-graph (entity-entity and attribute-attribute) correspondences. To address the DNC problem, we propose a robust MMEA framework termed RULE. RULE first estimates the reliability of both intra-entity and inter-graph correspondences via a dedicated two-fold principle. Leveraging the estimated reliabilities, RULE mitigates the negative impact of intra-entity noise during attribute fusion and prevents overfitting to noisy inter-graph correspondences during inter-graph discrepancy elimination. Beyond the training-time designs, RULE further incorporates a correspondence reasoning module that uncovers the underlying attribute-attribute connection across graphs, guaranteeing more accurate equivalent entity identification. Extensive experiments on five benchmarks verify the effectiveness of our method against DNC compared with seven state-of-the-art methods. Code is available at https://github.com/XLearning-SCU/2026-ICLR-RULE.

Published as a conference paper at ICLR 2026
LEARNING WITH DUAL-LEVEL NOISY CORRESPON- DENCE FOR MULTI-MODAL ENTITY ALIGNMENT
Haobin Li' Yijie Lin' Peng Hu'
Mouxing Yang",
Xi Pengl.2
College Computer Science, Sichuan University, China. National Key Laboratory of Fundamental Algorithms and Models for Engineering Numerical Simulation, Sichuan University, China.
[haobinli.g gm, iin,jjiegm,, penghu.ml, yangmouxing, pengx.gm| @al]]llmaalo
ABSTRACT
Multi-modal entity alignment (MMEA) aims to identify equivalent entities across heterogeneous multi-modal knowledge graphs (MMKGs), where each entity is described by attributes from various modalities. Existing methods typically assume that both intra-entity and inter-grahh correspondences are faultless, which is often violated in real-world MMKGs due the reliance expert annotations. In this paper, we reveal and study highly practical yet under-explored problem in MMEA, termed Dual-level Noisy Correspondence (DNC). DNC refers misalignments in both intra-entity (entity-atriiutte) and inter-graph (entity-entity and attribute- attribute) correspondences. To address the DNC problem, we propose a robust MMEA framework termed RULE. RULE first estimates the reliability of both intra-entity and inter-grap inter-graph correspondences via dedicated two-fold principle. Leveraging the estimated reliabilities, RULE mitigates the negative impact of intra- entity noise during attribute fusion and prevents overfitting to noisy inter-graph correspondences during inter-graph discrepancy elimination. Beyond the training- time designs, RULE further incorporates a correspondence reasoning module that uncovers the underlying titribute-attribute connection across graphs, guaranteeing more accurate equivalent entity identification. Extensive experiments on five benchmarks verify the effectiveness of our method against DNC compared with seven state-of of-ate-fftthearr art methods. Code is available at http://ggtuub.cmm/XXeiiiii SCU/2022-ICIRRRRT..
INTRODUCTION
Multi-Modal Entity Alignment (Liu et al. 2021 Li et al. 2023) (MMEA) aims to identify equivalent entities across different Multi-modal Knowled Graphs (MMKGs) (Liu al. 2019 Zhu al.) 2022), where each entity is associated with attributes of various modalities (e.g., structural triples and images). Due the heterogeneity of attributes from different modalities and graphs from different sources (e.g.. Wikidata (Vrandečié & Krötzsch] 2014) and YAGO (Suchanek et al. (007)). the key challenge of MMEA is learn comprehensive representation for each entity with its respective attributes while eliminating the cross-graph discrepancy. To this end, existing methods usually conduct multi-modal fusion for attributes within the same entity based on the intra-entity correspondences (i.e., entity- attribbee pairs), while performing cross-graph alignment by resorting to the inter-graph correspondences (i.e., entity-entity pairs and autribute-attribus pairs).
Despite significant efforts in intra-entity attribute fusion (Chen et al. 2023al Huang al. 2024a) and inter-graph discrepancy elimination (Xu al., 2023) Guo et al. 2021), existing MMBA methods heavily rely the assumption of faultless intra-entity entity and inter- gree- correspondences. However, as shown in Fig. aa). the assumption is daunting and even impossible to satisfy, leading to the Noisy Correspondence (NC) problem dual levels. On the requires expert knowledge, it is inevitable to wrongly associate some entities with irrelevant attributes, resulting in intra-entity NC. For instance, image of "Elvis Tsui" is incorrectly associated with entity "Jason Momoa" because of the visual resemblance. On the other hand, due to the inherent complexities in attribute and entity association, accurately associating all the giter-graphh entities and
hand, the MMKG construction
"Corresponding author.

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Published as a conference paper at ICLR 2026
Exhrty Antribute
Inter-grapph Infrt-eshity Carr.
Inter-graph NC
Query Entity
low
high
Intro-enhiyy NC
Cristions Rondido
Mexico
Cristions Ronaido
260
florcce
Mccoos
E45 Tout
Mill Seitth
Mr. Mrs. Smith
100
Cseeningl Simller
g
Inherestly
(a) Dual-level Noisy Correspondences
(b) Observations
(c) Misidentification at Test Time
Figure I: (a) Dual-level Noisy Correspondence occurs in both intra-entity level (i.e., entity-attribute pairs such as ((") and the gater-graph level (i.e., entity-entity Rx) or attribute-attribute pairs (x.)) ). (b) Observations: On the one hand, both vanilla adaptive fusion (AF) and concatenation (Concat) tend to integrate erroneous attributes and thus degrade performance. while our method achieves reliable fusion against intergrrahh NC. On the other hand, existing methods suffer in cross- graph alignment when encountering inter-graph NC, whereas our method boosts performance by mitigating the negative impact of intra-entity NC. (c) Misidentification at Test Time: Seemingly similar attribute pairs may prevent the query entity from being associated with its equivalent entity. For instance, the implicit connection between the football player "Cristiano Ronaldo" and his home country are often overlooked, resulting in misidentification during entity alignment.
their corresponding attributes is impractical, leading to inter-graph NC. For example, movie entity "Mr. & Mrs. Smith" is mistakenly associated with real-life couple "Will Smith and Mrs. Smith". According to the statistics in Appendix B real-world benchmarks always contain numerous NC (e.g.. over 50% in ICEWS benchmarks). As shown in Fig. [b), NC would not only undermine the fusion of within-entie entity attributes but also mislead the inter- graph alignment, both of which significantly degrade the performance.
Based on the above observations, we reveal new problem for MMEA, termed Dual-level Noisy Correspondence (DNC). To conquer the DNC problem, we propose novel method, dubbed dually RobUst LEarning (RULE), for achieving robust MMEA against DNC. Specifically, RULE first estimates the reliability of both the intra-entity and inter-graph correspondences by resorting to dedicatedly-dessineee two-fold principle and then divides the entity-attribute, entity-entity, and results, surribute-attribut pairs into different groups. Based on the estimated reliabilities and division
RULE alleviates the negative impact of intra-entity NC during intra-entity attribute fusion, while preventing the model from overfitting the inter-graph NC during inter-graph discrepancy elimination. Beyond the training-time designs, RULE further incorporates a novel correspondence reasoning module to enhance the test-time robustness. In brief, this module performs deep reasoning to uncover the underlying attribute-attribute connections across graphs, thus preventing seemingly dissimilar but inherently identical attributes from being neglected (as shown in Fig. [c) and guaranteeing more accurate equivalent entity identification during inference.
In summary, the major contributions and novelties of this work are given as follows.
We reveal and study a novel and practical problem in MMEA, termed Dual-level Noisy Corre- spondence (DNC). In brief, DNC refers to the noisy correspondence rooted in the intra-entity (entity-attribur pairs and inter-graph (entity-entity, stribute-attribute pairs. We empirically demonstrate that DNC not only undermines multi-modas attribute fusion but also misleads the inter-graph alignment, leading to significant performance degradation for existing MMEA methods.
To achieve robust MMEA against the DNC problem, we propose novel method termed RULE, which estimates the reliability of both the intra-entity and inter-graph correspondences with a dedicatedly-designee two-fold principle and accordingly mitigates the negative impact of DNC during the multi-modal attribute fusion and inter- -eer- alignment processes.
During inference, RULE employs a novel correspondence reasoning module to uncover inherently- identical attributes and accordingly achieve more precise gross-graph equivalent entity identifi- cation. To the best of our knowledge, this could be one of the first methods to enhance test-time robustness for the MMEA task.
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2 METHOD
In this section, we introduce the proposed RULE for tackling the DNC problem. In Section 2.1 we
present the formal definition of the MMEA task and the DNC problem. In Section 2.2 we aboaate
on the two-fold principle for the reliability estimation and pair division. In Section 2.3 2.4 we
introduce the robust attribute fusion and robust discrepancy elimination modules. Section 2.5 we
design test-time correspondence reasoning module to uncover underlying connections between inter-graph attributes, facilitating the equivalent entity identification.
2.1 PROBLEM FORMULATION
Given two heterogeneous multi-modal knowledge graphs (MMKGs), denoted as G fær, [=:""' - and n {āj, )M Im=1)y - where 2; and ă, are entities in 9 and 9, re- spectively. Each entity x; E associated with M attribut-speccficc attributes {-:th ) m==1 such as structured triples, textual descriptions, and images.
Within single graph, the association between an entity and its attributes captured by antity-atrribute pairs (I,, x²"", h,"),, where hT" E {0, 1 is binary indicator, hT" indicates the valid intru-entity correspondence, and hm denotes no correspondence between x; and a." Across graphs, inter- gruph correspondences govern the alignment of both the entity-entity pairs and attribute-attribe pairs. To be specific, the entity-entity pair is represented by (z,, J Mty)). where the correspondence Bky 1 if z; and žn refer to the same real-world concepts, and 1/r 0 otherwise. Similarly, the attribute-attribnn pair is denoted by (x"", .77 U.g where the correspondence vy = 1 i.f. both "er",""
attributes linked correct entities (i.e., hT & hy 1) and the corresponding entities in; and Σ, are aligned (i.e., Mij = 1). In other words, once the inter-gr onter-graph entities are associated, their corresponding attributes could be treated as matched.
Given query entity x; E G. the goal of multi-modal entity alignment is to identify its equivalent entity Ty from the other & such that Vi = 1. To this end, existing approaches typically follow a two-stage pipeline: intra-entity attribute fusion: for each entity I,, attribute representations are first extracted using attributesppecific encoders 2." = (I""'";), and then aggregated to form a unified entity representation 2;; ii) inter-graph discrepancy elimination: based on the fused entity representations 2; and Zj. contrastive learning (Chen et al. (220)) is employed to mitigate the inter-graph discrepancy. However, in practice, this pipeline assumes that both the intra-entity correspondences (i.e., entity- attribute hm))) ) and inter-graph correspondences (i.e., entity-entity yii and attribute-attribute v are perfectly labeled. However, due to annotation errors, such an assumption is often violated, leading to the DNC challenge. As discussed in Introduction, the DNC problem would undermine the inter inter-graph and intra-entity learning, leading to remarkable performance degradation.
2.2 RELIABILITY ESTIMATION AND PAIR DIVISION
To facilitate robust inter-graph discrepancy elimination and intra-entity attribute fusion, we first estimate the reliability of both the intra-entity and inter-graph correspondences by resorting two-fold principle, i.e., uncertainty and consensus. Without loss of generality, in the following, we take the graph entity-entity correspondence as showcase to elaborate on the process of correspondence reliability estimation. For a given entity 2;, the reliability w; between I; and its associated counterpart ž. (yi = is estimated using the following principle:
:i = (1 - us) + c1(1 (1 7),
where 7 is the balanced hyper-parameter (fixed as 0.5 for simplicity, see Appendix 1. for more choices), n, and e denote the uncertainty and consensus for the correspondence and will be detailed in the following sections.
2.2.1 UNCERTAINTY MODELING
For given entity, uncertainty in this work refers whether its correspondence is trustworthy not, which could serve as the principle to identify NC. According to the Dempster-Shafes Theory (Shafer) 1992). uncertainty could be quantified by evidence, which measures how the data support the
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Multi-modal Encoders
Reliability Estimation and Pair Division
Robust Intro-entity Attribute Fusion
Uncertainty Modeling
C
Struc
Evidence
Ralasiity
Uncortsinty
Conseraus
Σ
Entoy
Computing Ayppoia m
+
Imagee
Uncertainty Volue
Rebust Inter Inter-graph Discrapency Elim.
Pair Division
*+x
O
Se
80
Conaeaz
Relissiity
Consenous Modeling
Multi-modal Encoders
s4 (siy
1)
Correspendence Reasoning
MMKG
D
Sr
Roxza1
Srep
Belichitt
AttiPaaee
MMKG
Multi-modol
Encoders
Uncertority
MILLI
Figure 2: Overview of our method RULE. Given two MMKGs g and ف. RULE first projects the entity attributes into shared latent space and computes coss-graph attribute similarities. These similarities are used to estimate the reliability of inter-graph correspondences and categorize cross- graph pairs into three subsets: Sc, St, and Sy. Subsequently, the robust intra-entity attribute fusion module and robust inter-graph discrepancy climination are employed to mitigate the impact of both intr--entity and inter-graph noisy correspondences. Beyond training-tinn robustness, test-time correspondence reasoning module uncovers latent attribute-atribute connections across graphs, enabling more accurate equivalent entity identification during inference.
association between query and candidate. Specifically, the more evidences the entity accumulates, the lower uncertainty embraces. Formally, evidence of the entity pairs (æ,, R2) is defined as
(2) Σ denotes the dot product between the entity representation and žj. is the temperature, and the evidence vector for x; is e; = [ea;; e22; ... ; :
eij exp (tanh (su//T)),
where 8ij
Following Subjective Logic (Sensoy et al. 2018), associate the evidence vector with the parameters of the Dirichlet distribution a; = a.l ..2.-.. , where 0iş- = eig +.
Definition 1. Uncertainty, For given entity vi the uncertainty and the corresponding belief mass are defined as
N and buj- = Cjj Oij
U1 Q
(3)
Q Q
where Qi E; (et + +1 Σ₁ 0i and u, + Σ by 1.
The Qi denotes the Dirichlet distribution strength, and the belief mass assignment b, [br big: .. ;b, i.e., subjective opinion, corresponds to the Dirichlet distribution with param- eters a,, Such a formulation encourages the mismatched entity-entity pairs to yield limited evidence, as the given entity fails associate with any entity in the other MMKG, resulting in high uncertainty.
2.2.2 CONSENSUS MODELING
Although the formulated uncertainty would help to identify noisy correspondence, we observe that low uncertainty does not necessarily indicate a correct correspondence. Formally, Theorem 1. A low uncertainty u, does not necessarily imply that the highest belief is assigned to the annotated correspondence yı i.e.,
2; with low u, + arg max b, arg max y::
(4)
The Proof is placed Appendix F Here, y: [ya B:2: V. is a one-hot vector indicating the inter-graph entity-entity correspondence of entity Such theorem highlights that uncertainty insufficient to determine whether the belief is concentrated on the annotated correspondence. Therefore, propose the consensus principle follows.
Definition 2. Consensus. For a given entity I; the consensus defined as
G max(0, 8, y:).
(5)
where 8; = [8:1, S:2, Sin] denotes the similarity vector, max(0,.) ensures the consensus is non-negative.
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Intuitively, low consensus e; indicates that the given correspondence is unreliable, thus serving as another principle to identify noisy correspondence. However, during inference, the annotated correspondence y; in Eq. | is unavailable. To remedy this, propose estimate the correct correspondence through a greedy strategy based on marginal contribution. Here, we begin with a definition of marginal contribution.
Definition 3. For a given enfity Vi, the marginal contribution of its m-th altribute is defined as
A =((T U {mm) - v(T),
(6)
where v()) indicates the value function, x III {m} denotes a subset и of attributes excluding the m-th one, II is the complete set of available attributes.
In the implementation, we define the value function as v(x) max (1H 5t and v(n U {m]) max ( Ejenu(m) 8!): where denotes the number of attributes. Inspired by Shannon's principle that "the essence of information is to eliminate uncertainty", we expect that the informative attributes would contribute to establishing reliable correspondence for the antiib- pairs. Thus,
Assumption 1. For given entity 24, if x: is correctly associated with 24, then A 2 0. Conversely, x.TT is irrelevant Fú, then A O.
Assumption D provides feasible way to estimate the correct correspondence. Specifically, incor- porating attributes until the marginal contribution no longer improves, and the established subset would help to indicate a reliable correspondence. To implement this, we adopt the following greedy
strategy,
="
np U {m E (IT mo) o( U {m}) - v((o) > 0)
(7)
where Tu denotes the initial subset with |To - +1 when M Appendix F3 With the selected subset π², the estimated correspondence is finally given as y; one-hot (arg max( (. Emer. )) where one-hot denotes the vector conversion.
See more details in
2.2.3 PAIR DIVISION
With the formulated uncertainty and consensus, we could further identify the inter-graph NC. Specifically, we propose divide the inter-graph pairs with zij into three portions: noisy portion with high uncertainty Sy = {I; 2, u > Bu}. noisy portion with low consensus S = (x,, øy u, < Bu and c < }.] and clean portion Se = (x,, By ug S By and e; 2 B.). The thresholds B, and Be are determined in a self-adaptive manner via
(8) where u TP = max U4 TTP min and 33 indicates the threshold hyperparameter. Here, STP = (il arg max( = arg max (y:)) denotes the set of true positive pairs. With the above pair division, the inter-graph pairs could be divided into Sy, Sj. and Sc, which are further used for inter-graph discrepancy elimination.
B, min 1-3)), B), 3e max(3, PPP).
2.3 ROBUST INTER-GRAPE DISCREPANCY ELIMINATION
With the established reliability and pair division results, could obtain three subsets: Su, Sr. and Sc. Since the pairs in Sy exhibit high uncertainty, they are considered as unreliable and are excluded from the discrepancy elimination. As discussed in Section 2.2.2 inter-graph pairs with low consensus do not necessarily indicate correct matches, thus the pairs in S cannot be regarded as reliable. Accordingly, we propose novel Dually Robust Learning (DRL) that employs tailored strategies for the three subsets, thereby achieving robustness against inter-graph noisy correspondence. Formally, the overall objective defined as
L L=LDR + XL
(9)
where CDR and Lre denotes the dually robust loss and regularization loss, À denotes the trade-off parameter. Specificallyy, the dually robust loss and regularization loss are given by,
M
M
CDR= = LoR(a,, 0+)+
LDR(O. )TT), LReg = Reg (a,, 9:)+
CReg(a)) m "TT) (10)
m=l
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where aj" and D," are the Dirichlet parameter and refined correspondence for x!" More specifically, for the given entity 2i, the dually robust loss defined as
LD ú.) = (i & Sv) / |b.. - p.lll D(p: (x)) dp.,
(11)
where D(p; (x) denotes the density function of the Dirichlet distribution over the query probability p. = [p- P:2. P.al. and I(() indicates an indicator function evaluating to i.f. the condition is satisfied. The refined correspondence ÿ. is defined as follows.
ÿ. = y::
if E Sc C.y: + (1 - c,) Softmax(s:), if E S₁
(12)
Such behavior enhances robustness against inter- graph noisy correspondences for the following reasons. On the one hand, the upper bound of query probability is proportional to Qi (Theorem 2 thus preventing over-optimization when the accumulate Qi is limited. On the other hand, excluding high-uncertainty correspondences in Sy and refining the low-consensus correspondences in S, would prevent erroneous optimization caused by NC.
Although the proposed dually robust loss in Eq. 11 could encourage higher evidence for inter-graph pairs with reliable correspondence, is unable to guarantee that unassociated inter-graph pairs generate limited evidence. To achieve this, a Dallback-Leibler (KL) divergence term is adopted to penalize the evidence of the unassociated inter-graph pairs, i.e.,
EReg(a; 9.) KL D (p, ā;) D| 1)]
(13)
where 1 E R is N N-dimensional vector of ones, ā; = ū. + (1 g.) c a, denotes the Dirichlet parameters which help to penalize the evidence of unassociated correspondence, r(-) and (-)) are the gamma and digamma function, respectively.
2.4 ROBUST INTRA-ENTITY ATTRIBUTE FUSION
As discussed in Section 2.1 inter-graph attribute associations emerge as the by-product of establishing antity-attribute and entity-entity correspondences. Therefore, for correctly paired entities, the attribute- attribute correspondence is incorrect, i.f.. the corresponding antity-attribute correspondence is wrongly established. Thus, the inter-graph reliability wit could be employed to identify unreliable intra-entity attributes and weaken the emphasis them during attribute fusion. Specifically, for given entity z;, we employ the following Dually Robust Fusion (DRF) module to obtain the integrated representation.
(14) where indicates the concatenation operator. Such behavior achieves robustness against noisy antity-attribute pairs by fusing the multi-modal attributes with adaptive weights. In other words, attributes with higher reliability are emphasized, while those with lower reliability are weakened.
= #meas (w." 2.-
2.5 TEST-TIME CORRESPONDENCE REASONING
As discussed in the Introduction, the seemingly similar attributes might hinder the identification of equivalent entities. To solve the problem, we propose Test-time correspondence Reasoning (TTR) module, which uncovers the underlying attribute-attie attrrbbtt connections across graphs, thus improving the equivalent entity identification during inference. Specifically, the refined entity-entity similarity scores are given by.
Σ M
m
$
(15)
MEM
where 8 represents the similarity scores of the m-th attribute output by the MILMM and thth denotes the corresponding reliability weight. Such behavior could mitigate the negative impact of intra- entity NC, which might undermine attribute fusion during test time. More specifically, we employ Chain-of- Thought (CoT) guide the MLLM toward step-by-step reasoning. Mathematically,
T Softmax (#JeT." (CoT [= am s((i))
,
(16)
where T. denotes the set correspondences with the highest similarity in prior results s CoT indicates the reasoning process. Although feasible solution is to prompt the MLLM with simple

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Published as a conference paper at ICLR 2026
Table 1: Comparisons with state-of-the-ar methods on Non-name benchmarks under DNC setting. "Inherent DNC" refers to the setting without any additional injected noise. H@k: k: indicates the top-k retrieval accuracy while MRR denotes the mean reciprocal rank. The best and second best results are marked in bold and underline.
Setting
Method
H
ICEWS-ME ICEWS-WIKI
Hid
WIKI
MRR
H@1
ICEWS-YAGO
ICEWS YAGO
H
MRR
H@0
DBPLSK ZII-EN H
MRR
H
DBP15K 15K JA-EN H
MRR
H
DBPISK FR-EN H
MRR
H
Avg.
EVA
29.6
40.7
13:7
11.1
70.7
86.8
77.9
73.6
89.5
80.6
74.3
90.5
81.4
51.2
XGRA
61.5
46.7
41.2
93.0
86.3
82.6
94.3
87.8
94.7
88.3
Inberen
MEAformer
53.5
20.1
61.3
35.0
51.2
42.8
82.4
93.5
87.3
81.9
94.2
87.3
82.1
94.4
87.5
67.0
DNC
UMAEA
51.2
70.0
59.9
32.4
69.4
40.6
79.1
93.2
85.3
79.5
93.9
85.8
81.2
95.0
87.3
64.7
PMP
$2.6
67.9
59.9
38.3
53.2
45.4
83.9
94.6
58.0
83.9
94.9
59.0
84.4
95.3
89.6
68.6
HHEA
64.6
56.4
37.5
50.4
43.8
62.5
55.5
60.6
55.4
52.8
63.6
58.2
47.6
76.7
EVA
21.6
18.4
0.4
0.4
51.0
70.2
59.7
73,4
63.1
53.4
73.8
62.6
34.9
MCI FFA
34.5
53.6
43.5
24.6
40.4
$2.5
69.9
85.7
77.0
70.
85.6
77.2
70.7
87.1
7%.1
$4.0
XGEA
40.1
48.4
44.6
22.6
27.6
25.77
76.3
90.7
K2.7
76.6
91.1
83.0
76.9
91.2
83.7
58.5
30% DNC
MEAformer
50.8
67.5
58.4
35.9
50.77
45.0
77.7
90.6
83.4
77.8
96.9
83.6
78.0
91.5
84.0
64.0
UMAFA
64.6
89..4
89.90
82.7
82.5
90.7
83.2
HHEA
47.8
61.8
51.4
37.4
49.5
43.3
48.7
58.8
53.8
49.0
58.7
$4.0
52.5
61.7
57.1
47.1
Ours
62.4
75.1
68.5
48.3
$9.5
53.9
$1.1
92.01
86.0
WI.5
92.2
K5.6
W0.5
92.2
K5.8
70.6
EVA
0.5
0.8
0.9
0.0
0.1
0.2
17.2
30.5
23.6
18.3
32.0
24.8
14.0
27.2
20.3
10.0
MCLEA
24.5
39,9
31.9
17.4
31.1
24.1
55.2
72.1
63.1
$4,0
70.4
61.5
54.6
70.9
62.0
41.1
XGRA
47.0
43.4
27.8
26.3
83.6
74.9
83.8
25.0
83.9
75.1
53.4
50%
MEAformer
58.8
50.1
45.0
37.5
83.2
25.1
80.5
70.8
82.6
73,4
51.0
DNC
UMAEA
37.8
35.0
46.0
25.4
40.0
32.5
64.8
82.1
72.7
58.1
78.5
67.2
61.8
80.9
70.3
39.6
PMF
35.1
48.8
41.8
29.6
42.4
35.8
67.1
82.6
74.2
65.6
80.7
72.5
66.1
81.5
75.1
52.7
HHEA
43.9
57.7
50.4
34.3
46.2
40.2
45.5
55.2
50.3
46.4
55.4
51.2
50.1
59.1
54.7
44.1
Ours
69.7
63.6
37.4
52.0
85.9
79.2
84,9
77.8
71.4
84.8
77.5
64.3
instructions such as "Identify the similarities between these attributes.", such vanilla prompts fail to fully activate the deep reasoning capabilities of MILM. In contrast, the proposed CoT-based reasoning would enable the MLLM to leverage prior results and detailed steps for reasoning, preventing deviations from the prior knowledge while facilitating the mining of underlying connections. See Appendix F.3 and Appendix [ for more details. Finally, the joint similarity score could be derived as s joint
s; & and the identified equivalent entity is given by arg max s joint
EXPERIMENTS
In this section, we conduct extensive experiments on five widely-used MMEA datasets to validate the effectiveness of the proposed RULE. Due to space limitation, present more experiments in Appendix G
3.1 IMPLEMENTATION DETAILS AND EXPERIMENTAL SETTINGS
Our method contains two networks, the sttribute-speciff encoders fr and the test-time correspon- dence reasoning module. Specifically, we first utilize a pre-trained CLIP model (Radford et al. 202T) to extract features from visual and textual attributes. After that, we employ the attribute-speecie encoders to obtain the latent embeddings following (Huang et al.) [022a]] Xu et al. 2023). For the test-time correspondence module, we use S---n2..--LL-72--nnnite-
(Bai al. 2025) as default to
facilitate the test-time correspondence reasoning module (Section 2.5) Regarding hyperparameters,
we set the trade-off parameter in Eq. 9 the threshold / in Eq, 8 arr fixed 1 0.3 for all the
experiments, respectively. The temperature in Eq. 2 is set to 0.07 following (Chen et al. 2020).
We evaluate our method on five benchmark datasets: CCEWS-WIKI (Jiang et al.) 2024). ICEWS- YAGO, DBP15KZ1 (Liu et al., 2021), DBP15KjA EN. and DBPI5KER Details of the dataset and evaluation metric are provided in Appendix F.T and F As discuss in Introduction, the MMEA benchmarks including ICEWS are always contaminated by DNC which denoted as "Inherent DNC" in the paper. To further evaluate the robustness toward DNC, we manually inject noise to conduct more comprehensive evaluations by following the widely-adopted strategies in the noisy correspon- dence/label learning community (Natarajan et al. [003)] Huang et al. 2021). Specifically, the artificial noise are injected in the following three aspects: i) entity-entity NC: one entity in aligned entity pair is randomly replaced with a different entity; ii) entity- attribate NC: a visual or textual attribute is randomly reassigned different entity; iii) attribute NC: visual attributes are perturbed
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Table 2: Comparisons with state-of-the-art methods on All-attributes benchmarks under DNC setting.
Setting
Method
ICEWS WIKI
1145
ICEWS YAGO
[105
[[@
DBPL5Kmm
[105
MRR
[[@]
DBP15K
[105
DBP15Km 11:05
EN
EVA
89.8
96.6
998.7
99.8
99.2
MCLEA
93.8
98.3
95.9
92.1
97.7
94.6
94.5
98.6
96.4
97.8
99.7
98.7
99.2
99.9
99.5
95.5
XGEA
$3.5
94.4
88.6
92.9
97.3
95.8
91.4
97.4
94.1
94..3
98.0
96.0
97.3
99.3
98.2
92.1
Iaherent
MEAformer
95.2
98.8
97.2
93.8
97.9
05.7
96.7
99.0
02.2
198
92.8
09.3
99.6
100L0
99.8
97.0
DNC
UMAEA
98.7
96.6
97.9
95.4
97.0
58.
99.3
98.9
99.4
99.9
99.6
97.6
99.7
100.0
HHFA
95.5
92.5
80.7
95.3
92.2
668.1
73.2
77.0
56.0
85.8
92.2
88.7
82.1
Ours
98.9
99.2
99.1
97.6
98..
98.2
98.3
99.5
98.8
99.3
99.9
99.6
99.8
100.0
99,9
98.8
EVA
67.4
76.2
71.6
17.9
21.4
19.7
61.2
73.9
70.8
72.6
85.7
78.5
$8.0
95.2
91.3
62.0
MCLEA
89.0
95.2
91.8
85.8
95.8
92.0
91.5
97.0
94.0
95.6
98.5
97.0
97.8
99.6
9k.
92.5
XGRA
67.3
71.4
80.5
92.4
96.6
20% DNC
MEAfermer
97.6
97.2
95.5
96.8
98.3
99.6
99.9
99.7
UMAEA
90.3
96.5
93.1
$6.8
95.1
90.5
94.1
95.3
95.8
97.2
98.2
98.8
99.0
99.3
93.5
PMP
92.1
96.9
94.3
90.9
96..3
93.4
94.8
98.1
96.3
97.6
99.3
98.3
99.2
99..9
99.5
94.9
HILEA
$7.6
93.8
90.5
$9.3
94.66
92.1
66.1
75.9
70.8
72.6
$1.99
77.0
83.5
90.2
86.5
79.8
Ours
98,3
98.9
98.6
97.5
98.7
98.1
97.6
99.1
96.3
99.1
99.99
99.5
99.8
100.0
99.9
98.5
EVA
3.8
0.1
31.7
33.2
$0.5
22.4
98.1
91.3
94.3
97.55
XGRA
60.3
55.3
44.5
39.8
71.3
864
78.0
70.1
77.0
88.7
95.9
91.9
63.0
10%
MEAformer
91.2
96.7
94.1
91.9
96.8
04.1
93.4
97.1
05.2
27.3
92.1
08.1
99.1
99.9
99.5
94.7
DNC
UMAEA
82.0
94.4
90.4
85.7
93.9
89.4
91.4
96.7
93.8
98.9
98.8
97.2
99L1
99.6
98.8
91.6
PMF
86.9
93.9
90.0
87.6
94.4
90.7
92.2
96.5
94.2
96.1
98.5 8
97.3
98.6
99.6
99.1
92.3
HHRA
92.8
86.1
81.1
98.3
98.0
97.0
98.3
97.6
96.3
98.1
97.2
98.7
99.7
99.1
99.7
100.0
99.8
All brstes
Claan Pain
MOLEA
13
07
2000
0.2
wrigtt
(a) Various DNC Ratios
(b) Distributions of Reliability
Figure 3: Analytic studies of various DNC ratios and reliability in Eq.
with Gaussian noise, while textual attributes are corrupted via random character replacements. The artificial noise levels are set as 20% and 50% in our experiments, which represents the proportion of corrupted E-E/E-A/A- pairs.
3.2 COMPARISONS WITH STATE-OF-THE-AN
In this section, compare method RULE with seven -fate-of-the-arr MMEA methods under the Dual-level Noisy Correspondence setting, including EVA (Liu et al.) 202T). MCLEA (Lin et al.)
2022b XGEA (Xu al. 2023), MEAformer (Chen al., 2023a), UMAEA (Chen et al. 2023b). PMF Huang et al. 2024a), and HHEA (Jiang et al. 2024). Following (Chen et al.) 2023a Huang
al. 2024a Xu et al. 2023), we conduct experiments under two widely-adopted evaluation protocols:
Non-name setting denotes all attributes except for the entity name are used, while All-attributes setting includes all available modalities. For fair comparisons, we adopt the same backbone (i.e.,
CLIP) for all baselines and our method. For more results on different backbones, please refer to Appendix G.IT
As shown in Tables performance degradation as noise increases, highlighting their vulnerability to noisy correspondences. In contrast, RULE outperforms all baselines across different datasets and noise settings, demonstrating superior robustness against DNC; ii) even without any manually-injecter noise, RULE still achieves performance gains compared to existing methods, considerable number of DNC. To further verify the effectiveness of RULE, we conduct experiments under the canuuall-iijjecte noise ratio from 0.0 to 0.7. As shown in Fig. (a), RULE not only achieves higher performance across all noise levels but also exhibits significantly slower performance degradation, which further confirms the robustness of RULE against DNC.
we could have the following conclusions: i) existing methods face substantial
the real-world MMEA datasets contain
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Table 3: Ablation study of the various modules in the train and test stages,
Stage
Setling
Non-nume H@5
MRR
All-attributes H@S
MRR
w/o DRL
31.6
45.9
38.6
82.3
90.4
86.0
57.6
Train
Only Usc.
53.5
67.8
60.2
93.6
97.4
95.4
Only Cons.
48.3
60.3
54.3
87.7
93.2
90.4
1.0
0.2
0.4
1.0
w/o DRF
52.4
66.2
59.0
95.1
97.9
96.3
Figure 4: Quantitative analysis of the uncertainty and consensus on the name attribute.
Test
TTR
$6.5
62.3
97.7
MELM Enhance
56.6
69.0
62.4
97.6
98.2
97.9
Both
Default
98.3
Clean Pairs
Reliabilitt
0.5
N-
Figure 5: Visualization of the reliability for clean entity pairs and those with manually injected E-A NC in the image and name attributes. From top bottom, the three rows denote the structure, image, and name attributes, respectively.
3.3 ANALYSIS AND ABLATION STUDY
In this section, we conduct analysis and ablation studies on the ICEWS- WIWK dataset.
Analysis Studies Uncertainty and Consensus. As discussed in Section 2.2 the estimated reliability plays key role in identifying DNC. To better understand its behavior, we visualize the reliability distribution of all training entity pairs. As shown in Fig. ()) clean pairs concentrated on the right side of the plot (indicating high reliability), while noisy pairs are predominantly on the left (indicating low reliability). This confirms that the proposed reliability serves an effective indicator for distinguishing clean and noisy pairs. To further explore how the proposed uncertainty and consensus behave under noise, we construct subsets Sy and S, by injecting synthetic noise and randomly shuffling the name attributes of the raw set Sc- As illustrated in Fig. 4 uncertainty and consensus principles successfully separate the three subsets, which supports the design of our tailored loss strategies in Eq. |
Effectiveness of Robust Fusion. To qualitatively study effectiveness RULE in handling entity- attribute noise, visualize the reliability in Eq. during the fusion process. As shown in Fig correctly associated attributes are assigned high reliability scores, while noisy or irrelevant attributes receive significantly lower scores. This behavior confirms that RULE effectively suppresses the influence of unreliable attributes during fusion, thereby enhancing robustness against entity-attribute noise.
Ablation studies. To verify the effectiveness of each component in our framework, we conduct ablation experiments the modules involved in both training and test-time phases. According to the results in T one could have the following conclusions. First, during training phase, both the "Only Unc." variant (which applies the uncertainty-guie -guided loss in Eq. (8) and the "Only Cons." " variant (which uses a consensus-bare based MSE loss) outperform the bascline "w/o DRL" (which uses only a standard MSE loss). This demonstrates the effectiveness of our proposed Dually Robust Learning mechanism in handling noisy correspondence. Second, during the test phase, the TTR module significantly improves alignment performance by uncovering latent semantic connections. In particular, the comparison between the "MLLM Enhance" (which only uses rethinking scores in Eq. 16) and "w/o TTR" settings shows that combining rethinking scores with prior similarity scores leads to complementary effects, resulting in improved robustness and accuracy. Third, the Dually Robust Fusion (DRF) module effectively mitigates the influence of intra-entity NC. Its inclusion enhances performance in both the training and testing stages.

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4 CONCLUSION
In this paper, we study a new problem in MMEA, i.e., Dual-level Noisy Correspondence, which refers the wrongly annotated intra-entity and inter-graph correspondences. To solve this problem, the proposed methods estimate the reliability of both the intra-entity and inter-graph correspondences and alleviate the negative impact of NC during the onter-graph discrepancy elimination and intra-entity attribution fusion. Beyond the training-ting time design, we employ novel correspondence reasoning module to guarantee more accurate equivalent entity identification during inference. We believe this work might remarkably enrich the learning paradigm with noisy correspondence by simultaneously considcring the noise across both training-time and test-time.
AUTHOR CONTRIBUTIONS
All authors contributed significantly to this work. Xi Peng and Mouxing Yang conceived the study, designed the RULE algorithm, refined the manuscript, and supervised the project. Haobin Li co- designed and implemented the RULE algorithm, conducted the baseline evaluations, and drafted the manuscript. Yijie Lin and Peng Hu analyzed the experimental results and contributed to the formulation of the manuscript. All authors reviewed and approved the final version.
ACKNOWLEDGMENTS
This work was supported in part by NSFC under Grant 624B2099; in part by the Fundamental Research Funds for the Central Universities under Grant CJ202303; in part by Sichuan Science and Technology Planning Project under Grant 24NSFTD0130; and part by Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China under Grant JYB2025XDXM610.
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APPENDIX
The Use of Large Language Models (LLMs)
14
Noise Statistics in Real-World Benchmarks
14
B. Statisties Analysis
14
8.2 The Underlying Reason Behind DNC
14
Related Work
16
Muli--modal Entity Alignment
16
Learning with Noisy Correspondence
16
Evidential Learning
17
Proof Theorem
18
More Implementation Details
18
Datasets
18
Networks
18
F3
Details of Dually Robust Fusion Module
19
F4
Evaluation Metric
19
R5
Details Test-time Reasoning Module
19
More Experiment Results
22
Results under the E-E, and A-A Noisy Correspondence
22
G.2
Parameter Analysis
23
More Ablation Studies
23
G.4
More Experiments under Various DNC Ratios
24
G.5
More Analytic Study of Dually Robust Fusion
24
G.6
More Analytic Study of Inter-graph Learning
................................
25
Results of Various MLLM
25
G.8
Complexity Analysis of Test-time Correspondence Reasoning
25
G.9
Results of Cntssyy Implementation
26
G.
10
More Analytic Study of the Reliability
27
G.1
More Experiments on Various Backbones
27
G.12
More Experiments FB15K-DB and 15K YAGO15K Benchmarks
28
G.13 Discussions with Active Learning Paradigm
29
Discussions with Related Works
29
G. 15 Discussions about the Reliability Estimation
29
Case Study of Dual-level Noisy Correspondence
30
Case Study of Test-time Correspondence Reasoning
30
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A THE USE OF LARGE LANGUAGE MODELS (LLMS)
Yes, we employ LLMs to aid and polish writing. Specifically, LLMs are used for language refinement in the Introduction, Method, Experiments sections, and so on. Moreover, the multi-modal large language model (MLLM) acts as one of the key parts for the test-time correspondence reasoning module (see Section 2.5) our method.
B NOISE STATISTICS IN FEAL-WORLD BENCHMARKS
In this section, we elaborate on the necessity addressing the DNC challenge in real-world scenarios and discuss the underlying reasons behind the formation of the DNC.
B. STATISTICS ANALYSIS
As discussed in the manuscript, real-world benchmarks implicitly contain both intra-entity and inter-graph noisy correspondences. To support this claim, we conducted an additional observational study to analyze the types and distributions of noise present in the datasets. Specifically, we randomly sample 1,000 entity pairs from the training set in the ICEWS- WIKI and ICEWS- YAGO benchmarks and conduct manual statistical analysis. After that, we categorize each entity pair into one of four types, i.e., "Clean", "E-E NC", "E-A NC" or "A-A NC As shown in Fig. 6 one could have the following observation and conclusions:
Even after careful manual annotation, considerable amount of DNC still exists in real- world datasets, i.e., more than 50% of entity pairs in ICEWS benchmarks suffer from the DNC challenge.
Among the three types of NC, entity-atriibute NC and attribute-atribbute NC account for large proportion (e.g., over 40% in ICEWS benchmarks). Compared with the entity-entity NC, these two types of NC are more fine-grained, which makes it difficult to uncover manually. It is worth emphasizing that although several NC-oriented methods have been proposed, nearly all them overlook such non-negligible fine tineggained noise MMEA, further highlighting the necessity of addressing the DNC challenge.
As mentioned above, although the two commonly-used MMEA datasets are small in scale (i.e., containing up to 30K entity pairs) and carefully annotated by humans, they still exhibit neg-negligible DNC cases. Such a DNC challenge would become even more severe in large-scale knowledge graphs such as Wikidata, DBpedia, and YAGO datasets (i.e., containing over 10M-100M entities). We believe that the DNC challenge is of the key reasons why large-scale datasets currently lacking in the MMEA field. The proposed RULE framework offers a promising solution toward achieving entity alignment on larger-scale datasets with the DNC challenge.
Clean
Inter-graph NC
Clean
Inter-graph NC
44%
46%
75%
25%
28%
31%
20%
E-E NC
26%
25%
N-EINC
Intra-entity NC
Intro-entity
(a) ICEWS-WIKI
(b)
ICEWS-YAGO
Figure 6: Distribution analysis of DNC noise in ICEWS-WIKI and ICEWS- benchmarks.
B.2 THE UNDERLYING REASON BEHIND DNC
To investigate the underlying causes of DNC, we analyze the formation of intra-entity NC and inter-graph NC from perspectives, i.e., knowledge graph construction and cross-graph annotation.
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Knowledge Graph Construction: The construction of existing knowledge graphs (Piscopo & Sim perl 2018) (e.g., Wikidata, Freebase, and YAGO) heavily relies on crowdsourcing (Paulheim 2016). L.e., user editing collaborative platforms. However, as most users lack expert knowledge, their edits are prone to errors such as incorrect data entry and conceptual misunderstandings, thereby inevitably introducing incorrect attributes within entity. As result, the editing errors in crowdsoureing would lead to intra-entity NC.
In real-world scenarios, most MMEA datasets are annotated using semi- automated methods, which would inevitably introduce the inter-graph NC. Specifically, to construct entity pairs between the ICEWS and WIKI knowledge graphs, Jaang et al. (2024) employs the name attributes from the ICEWS graph as queries and uses the Wikidata API to retrieve the most relevant matches. As a result, entity-entity pairs are established between the queries and the retrieved results. However, such process inevitably introduces inter-graph E-E NC due to the following reasons: some entities exist in ICEWS but do not appear in Wikidata, making impossible to establish correct correspondences; ii) even some entities have highly similar name attributes, they could be very obvious mismatches. For instance, as shown Fig. a) in the manuscript, the movie entity "Mr. & Mrs. Smith" may be mistakenly aligned with the life actor couple "Will Smith and Mrs. Smith." In this case, despite the similarity in names, the two refer to totally different entities with distinct multi-modal attributes. In other words, entities considered "neighbors" during cross-graph annotation (e.g., retrieved via name-based lookups), may not actually be relevant in real-world scenarios. Such fine-grained errors require expert knowledge to distinguish, and may be undetected even during manual filtering, Both of the above reasons would lead to obvious mistakes, where the aligned entity pairs totally unrelated. It worth noting that such obvious mistakes prove the reasonableness of constructing incorrect correspondences to simulate real-world noise in our experiments.
Cross-grand graph Annotation:
Moreover, once the inter inter-graph entity pairs are associated, their corresponding attributes could be treated as matched. Therefore, as the by-product of the entity- and entity- correspon- dences establishment, the association between inter-graph attributes might be misled due to the aforementioned two kinds of annotation errors. In other words, E-A NC and E-E NC would further propagate to inter-graph attribute pairs, leading to noisy A-A correspondences. Beyond explicit annotation errors in A-A pairs, some attributes may contain textual typos visual ambiguity (e.g., noise under low-light conditions) in roal-world scenarios, which would also lead to inter-graph A-A NC.
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C
RELATED WORK
In this section, we briefly review two topics related to this work, ie., multi-modal entity alignment and learning with noisy correspondence.
C.I MOLTI-MODAL ENTITY ALIGNMENT
Multi-modal entity alignment aims to eliminate the discrepancy between heterogeneous MMKGs, so that the equivalent entities from various MMKGs could be identified. Towards achieving this goal, numerous MMEA approaches have been proposed, which typically involve the following two-stage pipeline, namely, fuse the intra-entity attributes to form the representation for entities and perform cross-graph alignment the paired attributes and entities. According their primary focus, most existing approaches could be broadly grouped into two categories: i) fusion-centric methods (Chen al. 2023a] Huuag et al. 2024a), which assign different weights according to the importance of each attribute-specife attribute during the fusion stage. ii) alignment-centric methods eLi al. 20233 Lin et al. 2022b Chen al., (202), which mitigate inter-graph discrepancy by maximizing the similarity between associated pairs while minimizing that of mismatched ones across MMKGs during
the alignment stage.
Among the existing approaches, REA (Pei et al. 2020 is the most relevant to our work, while having the following remarkable differences. First, REA focuses on inter-graph uni-modality entity alignment, whereas our work tackles multi-modal entity alignment, which involves mitigating discrepancies not only between heterogeneous graphs but also across multi-modal attributes. Second, REA only considers misalignment in entity-entity pairs, while our work comprehensively reveals and studies the noisy correspondence at dual levels, namely, both the intra-entity and inter-graph. Third, unlike REA solely concentrates training- time robustness, our method further improves test-time robustness, facilitating more precise cross- cross-graph equivalent entity identification.
C.2 LEARNING WITH NOISY CORRESPONDENCE
Noisy correspondence refers inherently irrelevant or relevant samples that are wrongly regarded as associated (a.k.a, false positive) or unassociated (a.k.a, false negative), which is first revealed and studied by (Huang et al., 2021]] Yang et al., 202Ip. Considering that numerous applications require paired data as input, including but not limited to visual instruction tuning (Huang et al., 2025), vision-language pre-training (Huang et al. 2024b), object re-identification (Yang et al. 2022). and graph matching (Lin et al., 2023), how to learn with noisy correspondence rooted in data pairs has emerged as new research direction, drawing increasing attention from both academia and industry.
In this paper, focus mitigating the negative impact of the noisy positive correspondence issue. Unlike most existing noisy correspondence studies that tackle the errors correspondence of specific level (e.g., entity alignment task and reveals the specific dual-level noisy correspondence (DNC) problem for the first time. In brief, DNC refers the noisy correspondence involving in the entity-atrribute, entity-entity, and attribute-atribuue pairs, which misleads the multi-modal fusion and cross-graph alignment processes. Therefore, is desirable customize a specific approach for MMEA with the DNC problem.
pixel-to-pixel). this work delves into the multi-modal
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D EVIDENTIAL LEARNING
In this section, we provide more details about the dually robust objective function in Eq.
Following (Sensoy et al., 2018 Han al.) 2022). the Dirichlet distribution is parameterized by ai [ai, 0,22 OGiK and the probability density function in Eq. 11 is given by.
D(p: ac)) = B(a.) 1= Pij ay-1 for p: S otherwise,
(17)
where B(a;;) is the multinomial beta function, and S is the K --ddimensional unit simplex.
With the above derivation, MMEA aims to guide the query probability p; approach the annotated correspondence y;, To achieve this, the uncertainty- based loss could be formulated as follows,
Ca yi) =flIV. 11 B ((xs)
Il j=1
og dp: PM
(wi) Blasy)) + Var (pt))
(18)
j=1
Ñ
Σ
Yij
Crÿj Qi
+
Oz (Q: a.j) Q7 (Q: +
where Plyl and Var (pt) are the expected value and the variance of Pij. respectively. Follow- ing (Sensoy et al. 2018), the expected probability E Pty] could be estimated by 인.
oii Intuitively,
Eq. 18 Tenoourae higher evidence for correct correspondence compared to mismatched ones, but also prevents excessive optimization when the overall evidence is limited. In other words, the probability 0ig is proportional to the total evidence Qi, thus limiting overconfidence in noisy correspondences.
Q,
Specifically.
Theorem The uncertainty-awat probability
ai is upper bounded by 2+- which is propor- Q.
Q.
tional to Q ie.,
Ošj Q
Q: K
<
x Qi
(19)
Qi
Proof. According the definition of evidence Eq. D each correspondence satisfies ag 2 1 for all by
1 + j. Therefore, Q; is
Q: = a + Σ an 2 au + (K 1).
(20)
[tj
Rearranging the inequality yields,
ai v Qi (K- - 1).
(21)
Then, dividing both sides by Qs, we obtain desired upper bound,
Ozj Q - +1 Q Qi
(22)
where the upper bound is proportional to Q., i.e., 2--K+1 x Q.
Qi
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E PROOF OF THEOREM
In this section, we present detailed proofs for Theorem in the main paper.
Theorem A low uncertainty u, does not necessarily imply that the highest belief assigned the annotated correspondence, i.e., Y/ij =
2j with low Us + arg max b, - arg max yi-
(23)
Proof. We will prove the theorem by contradiction. Suppose that for all evidence vectors with low uncertainty ui, the highest belief is assigned to the annotated correspondence, i.c.,
Ve; with low ui, arg max b; arg max yi-
(24)
Let us now consider the two evidence vectors e, (1) and e defined as:
Qi j J1, c - - (0.
Qii i 0, otherwise,
(25)
otherwise,
where ji # j2, and Q; > 0 is fixed. According to Eq. 3 both evidence vectors yield the same total evidence Q, and hence the same uncertainty u4 However, (1) suggests (1, the most probable correspondence, while e suggests (2, as the most plausible option. However, only one of them might indicate the correct correspondence. Such example contradicts the assumption that low uncertainty invariably leads to the highest belief being assigned to the annotated correspondence Consequently, the initial assumption invalid.
F
MORE IMPLEMENTATION DETAILS
F.1 DATASETS
We place the detailed statistics of the five MMEA datasets used in our experiments in Table 4 Note that, not every entity is paired with image-type attributes.
Table Details MMEA datasets. "E-E pairs" indicates the number of cross- goos-graph entity-entity
correspondences.
Dataset
KG
Entity
Triples
Numeric
Image
E-E pairs
DBPI5K
ZH (Chinese)
19388
70414
8111
15912
15000
EN (English)
19572
95142
7173
14125
15000
DBPI5K
JA (Japanese)
19814
77214
5882
12739
15000
EN (English)
19600
93484
6066
13741
15000
DBP15KFR
FR (French)
19661
105998
4547
10599
15000
EN (English)
19993
115722
6422
13858
15000
ICEWS-WIKI
ICEWS
11047
3527881
33341
5058
WIKI
15896
198257
47688
5058
ICEWS-YAGO
ICEWS
26863
4192555
80589
18824
YAGO
22734
107118
68202
18824
F.2 NETWORKS
In this section, we describe the network architectures used for encoding multi-modal attributes. For the name and image attributes, we first employ the pre- pre-trained CLIP ViT-L/14 (Radford al.) (221]) model to obtain the features. Note that, all the experiments are conducted on the same visual and textual features for fair comparison. Following (Chen al.) 2023a), employ trainable fully connected layers to project the image and name attributes into embedding vectors. Missing image attributes are handled by assigning vectors their embeddings.
For the DBP15K benchmarks, the multi-modal attributes include structure, relation, numerical value, image, name, and character attributes. Following (Xu et al. 2023), adopt cross-modal graph
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networks to encode the structure and relation attributes. For the numerical attribute, employ the Bag-of- Words (BoW) model to encode the relations as fixed-length vectors. Besides, the character attributes are derived from character bigrams of the translated entity names.
For the ICEWS benchmarks, the multi-modal attributes include structure, image, and name attributes. Following (Chen al.] 2023a), utilize Graph Attention Networks GAT' to reduce the computational cost of encoding structural information, as the number of relation triplets in the ICEWS benchmark is significantly larger than that of the DBPI5K benchmark.
F.3 DETAILS OF DUALLY ROBUST FUSION MODULE
To achieve robustness against intra-entity E-A NC, we propose dually robust fusion that assigns low weights to unreliable attributes. Here, we provide more details on how to construct the initial subset for the greedy strategy in Eq. 7 Although some attributes are often weakly associated even irrelevant to the entity, we assume that most attributes should be correctly associated, otherwise, the cross- gassph correspondence would not hold. Based on this assumption, adopt the following strategy for constructing the initial subset To.
M +1
if 23
mol
(26)
M < 2.
Such behavior ensures that the initial subset contains at least half or more of the multi-modal attributes.
Notably, the formulation of the attribute uncertainty u!th and consensus cith relies correct cross- graph entity-entity correspondence. However, the cross-graph correspondences are mismatched when E-E NC occurs, leading to unreliable u." and c.". Thus, we employ DRF only to entities z; that satisfy
(1 u)) + 1.
(27)
In other words, DRF is adopted to entities with reliable correspondences, which could prevent erroneous fusion.
F.4 EVALUATION METRIC
We evaluate multi-moda entity alignment using Hit@ 1 and Mean Reciprocal Rank (MRR) (Huang et al. 2024a):
Hit k measures the percentage of cases where the ground-truth candidate appears in the top-k retrieved entity.
Mean Reciprocal Rank (MRR) assesses the average inverse rank of the correct entity.
F.5 DETAILS OF TEST-TIME REASONING MODULE
In the manuscript, we propose test-time reasoning module capture the underlying connections between attribute pairs. Here, we provide more details on the MILM rethinking presented in Eq. T6
To reduce the computational cost of MLLM reasoning, we avoid rethinking attribute pairs that satisfy the conditions as follows,
max (x))) 2 0.2 V
max(x"") 2 0.2, Vs o max(s;
(28)
Such behavior not only reduces the overhead of certain attribute pairs, but also encourages reasoning on unreliable pairs and thus improves MMEA performance. Notably, for the missing image attributes the DBP15K benchmark, the corresponding rethinking scores are set to zero.
Taking the entity pair 7125 26134 as an example, employ the following Chain-of-Thoughe for the Nom-name and All-attributes setting.
For given query entity 2;. the output results of the MLLM denotes as [o:1; 0:2) 0.1]] where each similarity satisfies S oi < 10. After that, o, is normalized as follow,
à (o, 5)/5.
(29)
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Such normalization ensures that the range of the MLLM output is consistent with that of the similarity vector 8; in Eq. The Ōg could then employed to derive the rethinking scores via Eq. I6 i.e.,
BJeT," (CoT 2 (z))) s Ō;
Chain-of-Thoughh for Non-name Setting
Prompt:
Help me align or match entities of different knowledge graphs according to the given images and prior retrieval results.
AFRICAN DEVELOPMENT FUND
AEAIDE
FONDS AFRICAIN DE DEVELOPPEMENT OPPMENT
ID:7125
ID:26134
Prior Results:
Below are prior retrieval results focusing on visual similarity of the given images.
Candidate Entities List which may be aligned with QUERY Entity (ID:7125) are shown in the following list [Format: ID Similarity]:
22646 0.40.
22946 0.36,
23688 0.30,
26364 0.26,
22619 0.20,
26052 0.14.
26134 0.10,
26518 0.02.
Rethinking Image Similarity:
The two provided images represent the query (ID:7125) and the candidate (ID:26134).
Please evaluate the probability that the QUERY and the CANDIDATE belong the same entity STEP BY STEP:
1. Rethink the visual similarities based on the prior retrieval results and the given images.
2. Analyze the similarities of detailed visual contents between the provided images.
3. Consider the underlying connections between the given images.
of 10, where A is in range 00.11..344.566,7.888. 1,9, which represents the levels from VERY LOW to VERY HIGH. NOTICE: You MUST output strictly in this format: [IMAGE SIMILARITY]= A out of 10.
[Output Format]: [IMAGE SIMILARITY]=
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Chain-of-Thought for All-attributes Setting
Base Prompt:
Help align match entities of different knowledge graphs according the given names,
images and prior retrieval results.
AFRICAN DEVELOPMENT FUND
T AYDE
FONDS AFRICAIN DE DEVEL EEVEOOPPMEET
ID:7125 NaricAfrican Development
ID:26134 Name:African Development
Fund
Bank
Prior Results:
Below prior retrieval results focusing visual and textual similarity of the given images and names, respectively.
Candidate Entitics List which may be aligned with QUERY Entity (ID:7125 Namc:African Development Fund) are shown in the following list [Format: ID Name Similarity):
26364 African Development Bank 0.42,
22619 Southern African Development Community 0.32,
26052 Joseph Ki-Zerbo 0.24,
22946 United Nations African Union Mission in Darfur 0.15,
23688 OHADA 0.07.
22646 Food and Agriculture Organization 0.05,
26134 Jorg Asmussen -0.02,
26518 Joyce Banda -0.08.
Rethinking Image Similarity:
The two provided images represent the query (ID:7125 Name:African Development Fund) and the candidate (ID:26134 Name:African Development Bank).
Please evaluate the probability that the QUERY and the CANDIDATE belong the same entity STEP BY STEP:
Rethink visual similarities based on the prior retrieval results and the given images.
2. Analyze the similarities of detailed visual contents between the provided images.
3. Consider the underlying connections between the given images.
[Output Format]: [IMAGE S[MILARITY]= A out of 10, where A is in range
10.11.23344556667.. 100, which represents the levels from VERY LOW VERY HIGH. NOTICE: You MUST output strictly in this format: [IMAGE SIMILARITY A out
Rethinking Name Similarity:
The two provided names represent the query (ID:7125 African Development Fund) and the candidate (ID:26133 34 Name: African Development Bank).
Based on the prior retrieval results and the given names, identify the similarities between the query entity and candidate entity.
[Output Format]: [NAME ARMTYY out of 10, where B in range 10, 2,5,,44,5667..8, 7,899,100 which represents the levels from VERY LOW to VERY HIGH. NOTICE: You MUST output strictly in this format: [IMAGE
B out of 10.
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G MORE EXPERIMENT RESULTS
In this section, we provide more experimental results of the proposed RULE. Unless otherwise specified, all experiments are conducted on the ICEWS-WIKI dataset under the 50% DNC setting.
G.1 RESULTS UNDER THE E-E, E-A AND A-A NOISY CORRESPONDENCE
In the manuscript, we have carried out experiments under DNC settings. Here, we further provide more results under single-type NC scenarios, i.e., E-E, E-A, and A-A NC. From the results in Table 6 RULE significantly outperforms all baselines across various settings and datasets.
Table 5: Comparisons with state-of-the oftte-of-hhearr methods Non-name benchmarks under NC setting regarding the Hits and MRR metrics.
ICEWS-WIKI
D8P15K2HES
DHPI5Ki,. 1N
DBPI5K
Aug.
Setting Method
H@1
H85
MRR
H@
1185
MRR
H@Q
H185
MRR
11855
MRR
H@
H
MRR
H
EVA
4.4
6.9
5.7
0.1
0.1
0.2
17.4
30.6
23.6
21.9
34.9
28.1
18.9
31.1
24.9
12.5
MCLEA
28.6
43.9
36.2
30.3
34.7
27.4
58.2
75.6
66.
58.2
74.6
65.8
59.1
75.1
66.6
44.9
XGEA
47.4
44.0
26.5
24.7
85.2
75.9
68.9
82.1
74.2
68.8
81.9
72.0
53.9
50%
MEAfeemar
83.1
75.3
80.5
81.4
73.5
B-E
UMAFA
60.4
51.9
28.1
43.5
35.5
66.8
82.8
74.0
62.2
79.4
70.1
80.4
71.2
NC
PMP
38.6
53.9
46.0
32.6
45.4
38.8
68.4
83.5
75.2
67.1
81.8
75.8
67.5
82.1
74.2
54.8
HHEA
45.6
59.1
52.
37.0
48.5
42.6
47.7
56.2
$2.0
49.3
56.8
53.5
52.2
59.4
$6.0
46.4
Ours
61.0
72.5
66.6
48.7
S9.5
54.0
73.6
86.1
79.3
71.6
84.6
77.6
71.5
84.7
77.6
65.3
EVA
9.4
83.4
86.1
76.0
39.1
90.9
XGEA
40.0
47.9
4-.3
22-4
27.9
25.7
76
91.2
82.6
75.8
91.2
K2.5
76.0
92.1
83.3
58.1
50%
MEAformer
$3.1
68.6
COLA
37.4
52.8
44.8
75.3
91.1
$2.5
75.8
91.8
$2.9
26.6
92.6
83.2
63:2
E-A
UMAEA
30.7
67.5
58.5
34.3
$9.0
41.6
72.3
89.8
80.1
72.2
90.2
60L2
73.8
91.6
B1.7
60.7
NC
PMF
41.8
59.4
$1.9
34.9
48.5
41.5
74
89.7
81.1
74.4
90.4
K1.5
76.0
92.3
83.2
60.9
HHEA
63.7
56.4
35.8
48.9
42.1
60.8
53.6
61.2
54.6
64.0
58.5
59.1
53.5
92.4
92.5
EVA
29.3
41.1
35.1
10.3
8.1
70.2
86.4
77.5
72.3
89.1
79.8
73.6
90.4
80.9
50.2
MCLEA AA
43.2
62.8
$2.4
29.7
47.1
58.3
74.8
89.5
81.4
75.4
90.2
$2.0
76.
90.7
82.6
59.8
XGEA
40.8
48.8
45.1
24.2
29.7
27.6
78.2
92.1
84.4
78.8
92.9
$4.9
81.0
93.9
86.6
60.6
50%
A-A
UMAEA
MEAformer
53.4
68.0
69.1
60.9
58.0
34.5
51.1
45.8
42.6
37.6
93.5
02.1
87.0
94.2
123.5
87.0
94.4
93.5
87.5
85.6
66.7
NC
67.5
59.4
52.5
44.8
93.1
86.2
93.4
86.6
82.7
94.5
38.0
66.7
НHEA
48.6
63.3
55.5
37.0
50.2
43.4
46.6
61.1
53.8
47.3
59.7
53.5
50.1
62.4
56.5
45.9
Ours
63.6
76.7
69.7
48.6
60.3
54.4
85.6
94.7
89.7
85.1
95.4
89.5
85.0
95.5
69.6
73.6
Table 6: Comparisons with state of of-the-art methods on All-attributes benchmarks under NC settings regarding the Hits and MRR metrics.
Setting Method
ICEWS-WIKI
ICEWS-YAGO -AGO HOB5
DBPL5Kgga
DBP1SKKWEN H
DBP15K
Avg.
H0B5
MRR
MRR
HGB5
MRR
MRR
EVA
53.6
61.8
57.7
5:7
5.1
25.6
38.3
31.6
32.6
44.3
38.2
51.2
61.1
55.0
33.5
MCLEA
85.0
92.7
88.5
36.4
94.5
90.1
39.2
91.9
91.8
91.3
97.7
95.8
98.1
99.5
98.8
90.5
XGEA
57.4
68.8
62.9
57.0
68.9
62.7
87.8
95.1
91.2
91.6
92.0
94.1
96.6
99.0
97.7
78.1
50%
E-E
UMAEA
MEAformer
92.2
97.1
94.2
97.0
94.1
97.5
95.6
99.2
98.3
99.2
99.8
99.5
95.0
NC
PMF
96.3
38.4
91.5
92.7
96.6
96.4
97.4
08.6
99.7
НHEA
88.7
93.9
91.2
89.7
94.7
92.1
67.9
75.4
72.8
76.7
85.7
80.8
87.8
93.2
90.3
8.2.2
Ours
98.4
99.0
98.7
97.5
98L6
98.8
980.
96.4
98.2
98.6
97.33
99.1
99.6
90.9
99.8
98.3
EVA
64.8
73.0
68.8
9.1
10.9
10.1
69.3
$6.0
76.7
75.6
$9.9
82.0
58.9
96.1
92.1
61.6
MCI
93.99
85.7
97.9
97.9
99.7
92.4
XGEA
50%
E-A
MEAformer
UMAEA
94.6
91.1
96.6
98.0
96.1
93.6
97.0
86.9
97.3
95.1
90.6
94.3
93.1
95.1
95.0
95.3
96.5
97.9
99.1
986
97.7
99.3
98.6
99.8
99.8
99.6
99.2
93.2
95.8
NC
PMF
91.1
95.7
93.2
$9.7
95.8
92.1
95.0
98.5
96.5
98.0
99.
98.7
99.1
99.8
99.7
91.5
HHEA
$5.8
95.1
91.7
89.2
94.8
91.8
72.0
$4.9
9
79.7
39.4
84.2
90.0
95.7
92.5
83.9
Ours
98.4
98.9
98.7
97.5
98.6
98.7
96,0
97.7
99.3
99.4
98.4
99.4
99.7
100.0
99.8
98.6
EVA
91.5
61.7
69.5
95.4
99.3
97.6
MCI
97.3
97.1
91.7
97.9
95.9
09.3
97.3
97.8
99.6
98.7
93.9
XGRA
56.3
67.8
61.8
87.1
94.6
90.6
88.3
96.1
91.8
91.8
97.2
04.2
94.5
98.0
96.0
85.6
10%
MEAformec
95.1
98.3
96.6
93.0
97.9
95.2
96.3
99.0
97.6
98.6
99.8
99.3
99.4
99.8
99.8
96.6
A-A
UMAFA
92.1
97.3
14.4
86.7
95.1
00.5
05.3
96.9
06.9
07.1
9906
98.7
99.0
99.7
09.2
94.2
NC
PMF
98.6
96.4
99.0
97.5
08
99.4
99.8
HHEA
95.2
91.8
95.5
92.2
716.6
70:0
78.5
73.9
OHrs
99.0
98.7
97.5
98.7
98.9
9%.1
98.3
99.5
99.6
99.9
99.6
99.8
100.0
90.9
98.7
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G.2 PARAMETER ANALYSIS
As mentioned in the manuscript, the hyperparameters in RULE include the trade-off parameter À in Eq. 9 the temperature T in Eq.2 and the threshold in Eq. 8 Here, we conduct detailed parameter analysis to study their individual impacts and one could have the following conclusions: i) RULE exhibits stable performance when within the range of [2e-5, 5e-4], within [0.05, 0.2), and B within [0.2, 0.4] ii) when À is excessively large, the model would overemphasize the regularization term in Eq. resulting in performance drop.
200
05
70
1it (56)
70
35
40
40
N20n nome
Ncn-name
Non NOmT
Alluttt/Bbutss
Al-sttrioutas
Allattribuns
10
3eu2
1863
Sert
20rd 18s4
Sec5
20-5
l
10
0.21
0.02
0.05
0.07
0.1
0.5
1.0
40
0.1
022
0.4
(a) X
(b)
(c)
Figure 7: The parameter analysis of the trade-off off parameter À in Eq. and the threshold in Eq.
the temperature T in Eq.
G.3 MORE ABLATION STUDIES
To further verify the effectiveness of the proposed RULE, we conduct additional ablation studies of the loss terms and the test-time recitification module. Specifically, investigate the loss terms and the pair division module in Table resulting in the following conclusions. First, the regularization loss penalizes the evidence of negative pairs, thereby enhancing the performance. Second, employing tailored strategies to either S₁ or Sy would contribute to the performance improvement.
Table 7: Ablation study of the loss terms and the correspondence division module on the ICEWS- WIKI benchmark.
Setting LDR
Non-name H5
All-attribuees Hits@5
LReg
Hits@
MRR
Hits@
MRR
55.8
68.3
61.8
93.0
97.7
96.1
56.5
68.6
62.3
94.0
97.7
95.7
w/o S, 55.6
67.8
61.5
93.5
97.4
95.4
w/o Su
54.8
67.9
61.1
93.5
97.2
95.2
As discussed in the manuscript, the test-time reasoning module would help to capture the underlying connection and thus boost the performance. Here, carry out more ablation studies about the test-time reasoning module. From the results in Table 8 the proposed TTR module significantly improves performance on both the Non-name and All-attribute benchmarks. It is worth noting that, despite the missing image attributes in the DBP15K benchmark, RULE still achieves stable performance gains.
Table 8: Ablation study of TTR module on Non-name benchmarks under different DNC settings.
Setting
Method
H&a
ICEWS. WIKI ICEWS-WIKI H@S
MRR
H@l
ICEWS-YAGO H65
YAGO
MRR
H@1
DBPL5KmmsN
HRS
MRR
H6
DBPL5K H@S
MRR
H@1
DBP15K H@S
MRR
Inbevent DNC
wio TTR
62.1
76.6
68.8
46.4
59.6
$3.0
85.5
94.8
89.7
85.0
95.3
89.4
85.2
95.4
89.7
TTR
64.2
76.7
70.0
48.8
60.5
54.6
85.6
94,8
89.7
85.2
95.4
89.6
85.1
95.4
89.6
20%
74.7
67.0
46.2
58.6
80.9
92.0
85.9
85.6
80.6
92.2
DNC
TTR
62.4
75.1
68.5
48.3
39.5
53.9
81.1
92.0
86.0
80.5
92.2
85.6
80.5
92.2
85.8
50%
TTR
56.5
68.6
62.3
44.5
56.0
50.3
73.2
86.0
79.0
71.5
84.7
77.6
71.3
84.7
77.5
DNC
TTR
58.2
69.7
63.6
46.9
57.4
$2.0
73.4
85.9
79.2
71.8
84.9
77.8
71.4
84.8
77.5
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Table 9: Ablation study of TTR module on All-attributes benchmarks under different DNC settings.
Setting
H@1
ICEWS-WIKI H@S
MRR
H@
ICEWS- YAGO
H@5
MRR
H@!
DBPI 5Ka
H@B
MRR
HG@
DBPI5KAM H@B
MRR
H@!
DBP15Kea.N HGS
MRR
Inbcrent
TTR
96.7
98.9
97.8
95.2
98.5
96.7
97.4
99.4
98.3
99.2
99.9
99.5
99.7
100.0
99.8
TTR
97.6
98.8
99.5
98.8
99.3
99.9
99.8
100.0
20%
wio TTR
95.8
98.4
97.1
95.1
98.4
96.6
96.4
98.8
97.5
98.8
99.8
99.3
99.6
100.0
99.8
TTR
98.3
98.9
98.5
97.5
98.7
98.1
97.6
99.1
98.3
99.1
99.9
99.5
99.8
100.0
99.9
50% DNC
wlo TTR
94.0
97.7
95.7
94.3
97.8
95.9
94.9
97.9
96.2
98.0
99.5
98.7
99.3
99.9
99.6
TTR
97.7
98.3
98.0
97.0
98.2
97.6
96.3
98.1
97.2
98.7
99.7
99.1
99.7
100.0
99.8
G.4 MORE EXPERIMENTS UNDER VARIOUS DNC RATIOS
In the manuscript, we have carried out the experiments under various DNC ratios on the ICEWS- WIKI dataset. Here, we provide more experiments under various DNC ratios on the DBP15KzHEN dataset. As shown in Fig g the proposed RULE significantly outperforms all the baselines.
Non-name
All attribures
11P10 (50
MELLA
NCLAA
MNC PAT1
V00 Raft
Figure 8: Performance with various DNC ratios on the DBP15KZH dataset.
G.S MORE ANALYTIC STUDY OF DUALLY ROBUST FUSION
We conduct more analytic studies on the ICEWS- (CEWS-WIKI dataset to verify that the DRF achieves better performance by estimating the correct correspondence during the test time. From the results in Table 10 the estimated correspondence achieves higher accuracy compared to the vanilla fusion method, i.e., simple concatenation. Consequently, RULE benefits from the estimated correspondence and the DRF module, resulting in better performance. Note that, different from previous fusion methods (Lin et al. 2024 2022a), the proposed DRF further explores robust fusion on the reasoning scores output by the MILMMs.
Table 10: The analytic study of the estimated correspondence on the (CHWS-WIK) dataset.
Non-name Hits@5
All-attribures Hits@s
Setting
Hits@1 1
MRR
Hits@1
MRR
w/o DRF
$1.4
66.7
58.6
93.0
97.3
94.9
Estimated
55.3
65.0
60.2
94.1
97.4
95.7
DRF
56.5
68.6
62.3
94.0
97.7
95.7
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G.6 MORE ANALYTIC STUDY OF INTER-GRAPH LEARNING
As discussed in 3.3 and G.3 the proposed RULE improves the performance by adopting the tailored strategies the divided subsets, i.e., Su. S₁ and Sc- Here, we carry out more analytic studies about the statistics of the three kinds of pairs. From the results in Fig. annd Table Fig.Dand
one could observe that the proposed correspondence division module effectively distinguishes the three subsets and thus boosts the performance. Different from previous discrepancy elimination methods (Gong et al. 202T 2024, 2022), the proposed DRL not only divides correspondences into positive and negative, but also further distinguishes different types of negatives and adapts the tailored strategy to mitigate the negative impacts of them.
Von-name
A All-attributes
3.
1.
NMC Pair
VNC hain
Clean halm
Gsan Farr
Corrensu
Corsarous
0.0
0.2
0.5
02
0.6
7.5
Figure 9: Quantitative analysis the uncertainty and consensus on the integrated entity.
Table 11: Statistics of three kinds pairs.
Entity
Sc
Si
Sy
Non-name
14.8%
33.9%
51.3%
All-attributes
14.1%
37.0%
48.9%
G.7 RESULTS OF VARIOUS MLLM
To verify the generalizability of the TTR module, we conduct additional experiments on the MILM with various architectures and parameter scales. Specifically, we evaluate the performance of the TTR module on Qwen2.5-VL models with 3B, 7B, and 72B parameters, 1.6 (Liu et al. 2023) with 34B parameters. As shown in Table [2] RULE achieves consistent performance improvements across various model architectures and parameter scales, demonstrating the effectiveness of the proposed TTR module.
well as LLaVA-
Table 12: Performance comparison of different MILMS on Non-name and All-attributes settings.
Non-name H5
All-attributes H
Methods
Hits @
MRR
Hits@1
MRR
w/o TTR
56.5
68.6
62.3
94.0
97.7
95.7
Qwen2.5.Ve
57.2
68.8
62.7
96.5
97.3
Qwen2.5.VL VL
57.4
69.0
62.9
97.1
98.2
97.6
Qwen2.5-VI. 72B
58.2
69.7
63.6
97.7
98.3
98.0
1.L 34B
57.0
68.8
62.6
95.5
97.9
96.6
G.8 COMPLEXITY ANALYSIS OF TEST- TIME CORRESPONDENCE REASONING
To assess the efficiency of the TTR module, we report the time cost and memory cost across various parameter scales of Qwen2.5-Vv L. Note that all experiments were conducted on the NVIDIA RTX 3090 GPUs From the results in Table [3] one can observe that employing Qwen2.5-VL. 3B or 7B for TTR leads to considerable performance boost, with up 5x speedup. Furthermore. when resources are limited, RULE can be deployed without MLLMs. Even without TTR, RULE still significantly outperforms the strongest baselines, achieving 56.5% 43.9% (best-performing
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baseline) in the "Non-name setting and 94.0% 91.9% (best-performing baseline) in the "All- attributes" setting. Moreover, the lightweight solutions substantially reduce the memory cost as well.
Table 13: Experiment results the complexity analysis on the ICEWS-WIIS dataset.
Non-name Time Cost
All-attrihutes Time Cost
Methods
Memory Consumption
H@1
H@1
w/o TTR
56.5
103
94.0
109
IGPU ~ ~16G
Qwen2.5-VV 5-.1.VVV.3 3B
57.2
2122
96.5
1008
IGPU x ~8GB
Qwen2.5- VL 7B
57.4
2690
97.1
1329
IGPU x ~8GB
Qwen2.5-VL 72B
58.2
10043
97.7
4373
8GPU X ~0GG
G.9 RESULTS OF CROSS-ENTROPY IMPLEMENTATION
As discussed in (ensoy et al. 2018) the uncertainty-basee loss could be implemented using either the Mean Squared Error (MSE) loss the Pross-Entropy (CE) loss. In Appendix [ derive the uncertainty- proposed dually robust loss in Eq. 11 Here, derive the dually robust loss using the cross-entropy formulation as follows,
formulation based on MSE loss, which also serves as the foundation of the
N
/
CDR(a, 0:) =Iu S Ba)
Σ
in log(pes)
D(p: as)) dp,
(30)
II Ba) Σ ūis (v(Q:) pp(a)))),
where v/()) is the digamma function. To further investigate the effectiveness of the proposed DRI, conduct additional experiments of the cross-entropy implementation based Eq. 30 From the results in Table [1,, both implementations based on MSE and CE losses achieve competitive performance compared other baselines shown Tables and
Table 14: Comparisons of RULE with MAE and CE objectives under the DNC setting.
Objective
Setting
Non-name Hits@5
All-attributes Hits@5
Hits@1
MRR
Hits@
MRR
Inherent DNC
62.1
76.6
68.8
96.7
98.9
97.8
MAE
20% DNC
60.3
74.7
67.0
95.8
98.4
97.1
50% DNC
56.5
68.6
62.3
94.0
97.7
95.7
Inherent DNC
61.7
76.2
68.6
96.3
98.8
97.5
CR
20% DNC
59.6
74.0
66.3
95.9
98.6
97.2
50% DNC
54.4
68.5
61.1
92.5
97.0
94.5
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G.10 MORE ANALYTIC STUDY OF THE RELIABILITY
Here, we explore alternative strategies that dynamically manipulate the weights assigned to uncertainty Wy and consensus er in Eq. i.e. (1 - (1) +
(31)
where is the balance parameter. From the results in Table 15 one could have the following conclusions: employ either uncertainty (7 1) consensus ( 0) is inadequate identifying DNC, leading to degraded performance; ii) thanks to the normalization in Eq. and Eq. 5 simple linear combination of uncertainty and consensus could yield considerable performance improvements. The results above indicate that our design for combining uncertainty and consensus is reasonable and effective.
Table 15: Analytic Experiments of the weighting strategy on the ICEWS- WWIK dataset under the "Non-name" setting.
H@]
H@@5
MRR
51.8
62.4
57.0
0.2
53.4
64.4
58.7
54.9
66.5
60.4
0.5
56.5
68.6
62.3
0.6
55.1
67.1
60.8
0.8
53.9
66.6
60.0
1.0
52.5
65.7
58.8
G.11 MORE EXPERIMENTS ON VARIOUS BACKBONES
The proposed RULE is agnosiii method, which could be employed any mainstream vision- language backbones. To verify this, we further verify the effectiveness of RULE in various backbones. Specifically, we adopt SigLIP (Zhai et al., 2023) and BLIP (Li et al. 2022) as the backbones for extracting image and text features. Notably, experiments for fairness and select the best rest-performing baselines from Tables 2 for comparisons.
do not employ MLLM-based based reasoning in the
The results in Table [6 demonstratt that RULE outperforms all baselines across various backbones, which confirms the generality and effectiveness of RULE.
Table 16: Experiment results on the ICEWS-WIK, dataset with SigLIP and BLIP as backbone.
SigLIP
BLIP Non-name
Setting
Methods
Non-name
All-attribtees
All-attribuees
MEAformer
45.3
93.8
33.4
95.1
UMAEA
41.5
92.0
31.5
93.6
Inherent DNC
PMF
45.2
92.3
30.8
95.3
Ours
55.2
95.2
39.1
96.8
MEAformer
42.2
89.0
28.9
95.0
UMAEA
39.4
89.3
26.8
91.3
20% DNC
PMF
37.8
89.0
26.6
89.7
Ours
52.3
94.5
34.9
96.7
MEAformer
32.2
88.5
19.6
93.2
UMAEA
27.4
85.5
15.3
89.5
50% DNC
PMF
28.1
83.9
16.8
80.9
Ours
45.4
93.2
24.4
97.1
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G.12 MORE EXPERIMENTS ON FB 55-DB15K AND FB15K- YAGO15K BENCHMARKS
benchmarks with their inherent handcrafted features. Notably, the data for these datasets is longer available, so we don't employ MLLM for reasoning at test-time. Here, we select the best-performing baselines from Tables 2 for comparisons. The results in Table 17 18 demonstrate that RULE outperforms all baselines on FB15K-DB 15K and FB FB15K-YAGON YAGOI5K datasets under the settings with various DNC ratios.
Here, we conduct additional experiments on the FBISK-DBISK and
Table 17: Experiment results on the FBISK-DE DB 15K dataset under the "Non-name" setting, "Inherent DNC" refers to the setting without any additional injected noise.
Sctting
Methods
H@1
H@5
MRR
MEAformer
40.8
62.7
51.0
UMAFA
40.8
62.0
50.7
Inherent DNC
PMF
43.0
65.3
53.2
Ours
44.4
63.6
53,8
MEAformer
28.1
49.7
39.6
UMAEA
29.5
51.4
41.1
20% DNC
PMF
29.6
51.4
41.2
Ours
36.0
56.0
45,9
MEAformer
12.0
26.6
20.7
UMAEA
15.0
32.1
24.7
50% DNC
PMF
15.1
31.7
24.6
Ours
20.3
36.9
28.9
Table 18: Experiment results on the FB 1111-5YAO1555 dataset under the "Non-name" setting.
Setting
Methods
H@1
H@5
MRR
MEAformer
31.8
50.5
40.7
UMAEA
31.2
50.9
40.3
Inherent DNC
PMF
34.6
55.0
44.3
Ours
38.9
55.7
47.0
MEAformer
20.5
38.1
30.1
UMAEA
22.6
40.0
31.8
20% DNC
PMF
23.7
42.0
33.2
Ours
31.7
49.0
40.4
MEAformer
10.3
20.7
16.2
UMAEA
11.9
24.0
18.6
50% DNC
PMF
11.3
22.8
17.9
Ours
17.9
31.9
25.1
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G.13 DISCUSSIONS WITH ACTIVE LEARNING PARADIGM
One intuitive approach to address DNC is to introduce additional expert annotations and the active learning paradigm (Brame, 2016) might be the most representative paradigm. However, argue that active learning is inadequate for addressing DNC for the following reasons:
Existing MMEA-oriented active learning methods (Xu et al. 2024) focus on annotating E-E correspondences, which have not explored the establishment of E-A and A-A associations. As a result, even with expert involvement, active learning is unable to solve E-A or A-A NC. It is important emphasize that these two types of NC are highly practical in real- world scenarios, with their total proportion exceeding 40% commonly-used ICEWS benchmarks.
Active learning requires expert involvement, which is time-consuming and labor-intensive. In contrast, RULE provides a robust learning paradigm in an automated manner. Moreover, even after careful manual annotation, over 50% of the data suffer from DNC challenge in real-world datasets, which indicates that expert annotation remains prone to errors.
Active learning selects the most valuable samples for human annotation to improve model performance. However, most active learning methods require an initial set of labeled data for value model training before conducting active learning. As a result, the DNC challenge is still inevitable in the initial set, thus degrading the performance of the value model and then undermining the active learning.
G.14 DISCUSSIONS WITH RELATED WORKS
Recently, several related studies have explored to address noise issues MMEA task. Among them. DESAlign (Wang et al. 2024) might be the most relevant to our work. However, DESAlign and the proposed RULE differ in the following aspects: i) Different Motivations. DESAlign focuses on addressing disparities in attribute counts the absence of certain modalities, while RULE aims to mitigate the negative impacts of E-E NC, E-A NC, and A-A NC on intra-entity attribute fusion and inter- enter-graph discrepancy elimination; ii) Different Key Ideas. DESAlign employs robust semantic learning to mitigate semantic inconsistency and interpolates missing modality through a propagation strategy. In contrast, RULE not only adopts intra-entip attribute fusion and an inter-graph loss to achieve robustness against DNC, but also leverages the test-time reasoning module to mine underlying associations between attributes and thus guarantees accurate equivalent entity identification.
G.15 DISCUSSIONS ABOUT THE RELIABILITY ESTIMATION
To alleviate the negative impact of DNC, it is desirable to establish unified reliability principle so that both intra-entity and inter-graph NC could identified. intuitive approach is to estimate the reliability of inter-graph pairs by leveraging intra-entity pairs, intra-entity NC may further contaminate inter-graph attribute pairs. However, such a vanilla nnternal-to-extent approach is limited, since some mismatched entity pairs may result from annotation errors (as shown in Fig. (a)) rather than intra-entity NC. To remedy this, we explore a novel external-to-intemas estimation paradigm. On the one hand, the reliability of inter-graph correspondences could be directly assessed. On the other hand, since intra-entity NC would inevitably lead to mismatched inter-graph attribute pairs, these attribute pairs could be employed to estimate the reliability of intra-entity associations.
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H
CASE STUDY OF DUAL-LEVEL NOISY CORRESPONDENCE
In this section, we showcase some DNC examples from the ICEWS benchmark in Fig. 10
E-E NC
E-A NC
A-A NC
CiU
Faoi Songja (Poever)
Spogg Dusii
Cerveratn
Cansrgiac Far
Drearooki NeTW choc
Figure 10: Examples of DNC in the ICEWS benchmark.
I CASE STUDY OF TEST-TIME CORRESPONDENCE REASONING
In this section, we visualize the test-time reasoning process in TTR module. Specifically, we present several representative successful and failure cases, and further provide visualizations of performing TTR on ambiguous and missing attributes.
Successful Cases: As illustrated in Fig, II 12 the TTR module uncovers the underlying connections between image and name attribute pairs, thus boosting performance.
Failure Cases: Although the TTR module could rectifyy MMEA results by mining implicit associa- tions, we still observe several failure cases as illustrated Fig. [3] results, attribute these failure cases to the following might lack enough knowledge to perform correct reasoning. For example, when the query refers the abbreviation of Toronto Metropolitan University, the MLLM does possess the necessary background knowledge and thus cannot find the corresponding university logo. On the other hand, the MLLM might sometimes resort to shortcut cues rather than performing deep reasoning. leading to undiscovered associations even after reasoning, For instance, the MLLM may still rely on visual similarity when identifying coastal cities, while ignoring underlying semantic cues that indicate the corresponding country.
According to the visualization reasons. On the one hand, the MLLM
Ambiguous Cases:
TTR could perform correct test-time reasoning even when the attributes are ambiguous. As illustrated in Fig. [4 the image attributes of the candidates are highly similar. Nevertheless, the TTR module able to uncover meaningful associations, such as identifying the same individual across different scenes recognizing variations in clothing and appearance.
Missing Cases: Multimodal knowledge graphs often contain missing attributes, particularly missing images (Chen et al. 2023b). We present several visualizations in Fig, [5 to illustrate how TTR module behaves under missing attributes scenario. From the results, we observe that when the image attribute of the correct candidate is missing, the TTR module assigns low similarity scores to other images and instead relies on the available and more reliable textual attributes for more accurate reasoning. As result, the TTR module could still achieve correct alignment even in the presence of missing attributes, demonstrating the effectiveness and robustness of RULE.
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Query
Candidate
Prior Rank: 7
Final Rank:
MILM Anclysis:
Chories Leslie Folconer
Charles Lesile Falconer Baron Falconer
The nomes "Cherles Leslie" and "Chorles Lestie, Baron Felcorer of Thorston' share the first and middle incicating level similarity, the additional the condidate suggests person.
of Thoroton
[Nome SIMILARITY]
Query
Candidate
Prior Rank: 3
Final Rank:
MLLM Anclysis:
Andrey Vladimirovich Kazyrev
Andrei Kozyrey
The 'Andrey Vladmmirovich Kozyrev' and "Andrei Kozyrey' share the
similar first with "Andrey' "Andrel" present
nome.
SIMILARITY)
Query
Candidate
Prior Rank: 5
Final Ronk:
MILM Andlysis:
"Peronist Youth" and "Perorisn" indicating strong being on the younger members of the movement.
"Peron,"
Poronist Youth
Perorism
political
asseciated Juan Perón despite the specific focus "Perorist Youth"
[Nome SIMILARETY]
Query
Candidate
Prior
Final
MLLM Andlysis:
"Brick City" is widely recognized nicknome for "Nkawrr, New Jersey". indicating strong cultural and contextual link between the two nomes.
Brick City
New Jersey
Nework
While they differ lexically, they often refer the same place, suggesting high degres of nome similority.
[Nome SRMILARITY] out 10.
Figure 11: Reasoning process for the name attributes in test-time reasoning.
Query
Condidate
Prior Ronk: 2
Final Rank:
MLL/M Arolysis:
The first image Qatar's emblen, fecturing soilboot, palm trees, and desert, while the second highlights its location map. Bath images ef effectively represent Qutar, with the emblen reflecting cultural identity and the showing its geographical position.
[IMAGE SIMILARITY]
of 10.
Query
Condidate
Prier Rank: 5
Final Rank:
MLLM Analysis:
The indivicuuls in both life. indicated by the consistent faciel features and posture. The both images suggests formal military reyel further supporting the likelhood they represent
be the some person of different
entity.
[IMAGE
Query
Candidate
Prior Rank: 6
Final Rank: 1
MLLM Analysis:
The emblem the first image matches logo disployed the
image, indicating they belong institution. Additionally, text Pontificia Universided catdiica both images confires connection
some entity.
[IMAGE SIMILARITY] out of 10.
Query
Candidate
Prior Ronk: 5
Finol Rank:
Analysis:
indivicual both images appears similer focial features, color, and style. slight differences in expression and context do not detract significantly from the strong visual resumblance.
some person, they
[IMAGE SIMILARITY] out of 10.
Figure 12: Reasoning process for the image attributes in test-time reasoning.
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Query
Candidate List
Prior Rank: 2
Final Rank: 3
YORK
Image
Sim: 6
Sim: Rank 2
Sim:
Sim: 3 Rank
Image Sim
Rank 1
Rank
Query
Condidate List
Prior Rank:
Final Rank: 4
Image Attr
Sim: 5
Sim: Rank
Sim:
Sim: 1 Rank
Image Sim
Rank
Rank
Figure 13: Failure cases in test-time reasoning.
Query
Candidate List
Prior Rank:
Final Rank:
Image Attr
Sim: 9
Sim: 8
Sim:
Sim: 3
Image Sim
Rank 1
Rank
Rank
Rank
Query
Candidate List
Prior Rank:
Final Rank:
Image Attr
Sim: Rank 1
Sim: Rank
Sim: Rank
Sim:
Image Sim
Rank
Figure 14: Ambiguous attributes in test-time reasoning.
Query
Candidate List
Final
Image Attr
Sim:
Image
Necmettin Erbakan
N.
Süleyman Demirel
Maurice Obstfeld
Erbakan
Chamsley
Sim: 9
Sim:
Sim:
Sim:
Nome Sim
Rank
Rank
Rank
Query
Candidate List
Prior Ronk:
Pinal
Image Attr
Sim:
Sim:
Sim:
Sim:
Image Sim
Graz
The City of Graz
Bregenz
Sankt Pälten
Salzburg
Name Attr
Sim: 9
Sim:
Sim:
Sim:
Name Sim
Rank
Rank
Rank
Rank
Figure 15: Missing attributes in test-time reasoning.
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Reviews:
[{"review_id": "vlWiNs56Q5", "reviewer": "Reviewer_65Cw", "summary": "This paper addresses the overlooked problem of Dual-level Noisy Correspondence in multi-modal entity alignment, where both intra-entity attributes and inter-graph alignment pairs contain substantial noise. The authors propose RULE, a unified framework that estimates pair reliability through uncertainty and consensus modeling, performs noise-aware robust learning and multi-modal fusion during training, and further integrates a test-time reasoning module using an MLLM to refine alignment decisions. Experiments on several benchmarks demonstrate that RULE significantly improves robustness across a wide range of noise levels and achieves clear gains over state-of-the-art methods.", "questions": "1. How sensitive is RULE to the thresholds in pair division? Are there universal settings across datasets, or does each dataset require tuning?\n\n2. What is the computational overhead of TTR? How many calls to the MLLM are required per entity, and is inference feasible for large-scale KG alignment?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "S1. The paper convincingly argues that Dual-level Noisy Correspondence is ubiquitous in real MMKG scenarios, yet largely ignored by prior MMEA works. The motivation is well-founded and supported by quantitative evidence of high noise ratios.\n\nS2. RULE provides an end-to-end framework that integrates reliability estimation, noise-aware learning, multi-modal fusion, and test-time reasoning. The combination of training-time robustness and inference-time semantic reasoning is novel and compelling.\n\nS3. Experiments cover multiple datasets, modalities, and a wide spectrum of noise levels (0%–70%). Results show large improvements over SOTA baselines in both low-noise and extremely noisy regimes, demonstrating the practical robustness of RULE.\n\nS4. The evidential uncertainty modeling and greedy consensus estimation are well-justified. Visualizations (e.g., Fig. 3) clearly show distinguishable distributions between clean and noisy correspondences.", "weaknesses": "W1. RULE contains several components (uncertainty estimation, consensus reasoning, robust learning, fusion, test-time MLLM reasoning). While each part is motivated, the overall system introduces significant complexity, making it hard to isolate which component contributes most.\n\nW2. Although TTR appears effective, the paper lacks a thorough analysis of computational overhead, scalability, and failure modes. Using a large MLLM at inference time raises concerns for deployment.\n\nW3. Although TTR is conceptually strong, the paper could benefit from more real examples illustrating how MLLM reasoning corrects embedding-based mistakes, especially under ambiguous or incomplete attribute sets.", "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": "ejuN30H7pq", "reviewer": "Reviewer_Xav9", "summary": "The paper addresses a critical issue in MMEA, namely Dual-level Noisy Correspondence (DNC), which refers to the misalignments at both the intra-entity, entity-attribute, and inter-graph, entity-entity, attribute-attribute, levels. This noise can severely degrade performance in multi-modal knowledge graph alignment tasks, which is a common problem in real-world benchmarks. To tackle this issue, the authors propose a framework called RULE, which robustly estimates the reliability of these correspondences using a two-fold principle, uncertainty and consensus. RULE mitigates the impact of noisy correspondences during training and incorporates a test-time correspondence reasoning module to enhance the robustness during inference. Experiment demonstrates that RULE outperforms existing state-of-the-art methods across several datasets and noise settings.", "questions": "1. Could you provide a more detailed analysis of how the hyperparameters (λ, β, τ) affect the performance of RULE under different noise levels? Are there specific configurations where the model is more or less sensitive? It would be useful to explore whether hyperparameter tuning plays a significant role in noise resilience.\n\n2. How do you think RULE compares to methods like graph matching or other representation learning-based approaches that also handle noisy correspondences? Some methods like [1] also addresses noise in multi-modal entity alignment, which names semantic consistency. It would be better if you can compare and analyze them.\n\n3. I`m wondering how does RULE perform in extreme noise scenarios like >50% noise or heavily corrupted attributes in one modality? Would the model still perform robustly, or would it need additional modifications?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The identification and study of dual-level noisy correspondence is a novel and significant contribution to the MMEA task. It acknowledges that real-world knowledge graphs often contain significant noise both within entities and across graphs, which previous methods have largely ignored.\n\n2. The proposed RULE framework leverages reliability estimation using uncertainty and consensus to combat noisy correspondences. The test-time correspondence reasoning module is a key innovation that improves entity identification at inference time, ensuring better alignment even when certain correspondences are noisy or unreliable.", "weaknesses": "1. This paper includes some parameter analysis like trade-off parameter λ, threshold β, and temperature τ, but there is no comprehensive discussion of how these hyperparameters affect the model’s robustness under various noise settings. For instance, how does RULE perform with different datasets or in cases where the noise level is very high, e.g., >50%?\n\n2. RULE relies heavily on pre-trained CLIP models for image and text embeddings. While this is a reasonable approach, it could limit the flexibility of the model in scenarios where domain-specific or fine-grained embeddings are needed.\n\n3. It seems lack of how the framework handles extreme cases, such as when the noise level exceeds 50%, or when the correspondence noise is extremely high in one modality (e.g., image attributes).\n\n4. While the TTR module improves the robustness during inference, it may introduce additional computational overhead. The reasoning process involves complex reasoning steps and large language model queries, which could be slow and computationally expensive, especially for large-scale graphs.", "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": "D1EiEtmVEU", "reviewer": "Reviewer_ny9k", "summary": "This paper makes the first attempt to explore dual-level noisy correspondences (DNC) in the field of multi-modal entity alignment (MMEA). To address this issue, the proposed RULE could not only achieve robust cross-graph learning and multi-modal fusion during training, but also incorporates a correspondence reasoning module to enhance test-time robustness and thus achieves more accurate entity alignment across heterogeneous multi-modal knowledge graphs. Extensive experiments demonstrate that RULE outperforms state-of-the-art MMEA methods, while showing significantly slower performance degradation as noise levels increase.", "questions": "Please see the Weaknesses.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "1. This paper is well-motivated and is clearly organized.\n2. The intuitive illustrations in Figure 1 make the DNC phenomenon and its negative impacts clear.\n3. The experiments are convincing, e.g., the visualizations (Figure 3b) of the reliability estimation, pair division process (Figure 4) further prove the effectiveness of the proposed RULE.\n4. Most impressively, Appendix B not only analyzes the noise statistics in real-world datasets but also discusses the underlying causes of DNC. Correspondingly, the framework demonstrates strong performance under both noise-injected and inherent DNC settings, further validating the presence of DNC in real-world datasets.", "weaknesses": "1. Since both uncertainty and consensus are estimated through cross-graph relationships, I don’t understand why such relationships could be employed to estimate reliability of intra-graph attributes. A more intuitive and detailed explanation of this design would be very helpful for understanding.\n2. In my understanding, the MLLM-based reasoning module aims to uncover underlying associations between attributes. I am interested in what kinds of associations can be further mined by the MLLM, for example, beyond the cases illustrated in Figure 1(c). Furthermore, I wonder whether the proposed MLLM-based reasoning module could be extended to other tasks, such as image-text retrieval.\n3. Since the proposed RULE is a model-agnostic framework, which means RULE could be applied on various backbones. It would further strengthen the contribution if the authors could demonstrate the generalizability of RULE across more diverse backbones.\n4. I want to see more details about the computational complexity of the proposed RULE. In particular, the MLLM-based reasoning module may introduce considerable time and memory. It would be valuable for the authors to provide a detailed analysis of the reasoning time, GPU requirements.", "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": "BcfJIS3c0t", "reviewer": "Reviewer_1ndq", "summary": "In this paper, the authors study a new and practical problem in MMEA called dual-level noisy correspondence (DNC), where both intra-entity and inter-graph correspondences might be noisy. To address this, the authors propose a robust framework (RULE) that estimates correspondence reliability based on a two-fold principle. With the estimated reliabilities, RULE performs noise-aware attribute fusion and discrepancy elimination, and further introduces a correspondence reasoning module to enhance test-time robustness. The authors conduct thoughtful experiment designs and the results show that RULE achieves significant improvements over existing methods. Overall evaluation, this is a good paper with interesting motivation and solid results.", "questions": "- Provide more discussion on the differences between the proposed method and existing NC-oriented approaches and the related work [A].\n- Explain the choice of noise ratios (0%, 20%, 50%) in the experiments.\n- Justify the necessity of the consensus principle.\n- Visualize the test-time reasoning process to offer more intuitive insights into how the TTR module rectifies correspondences.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "This paper reveals a highly practical yet underexplored challenge (DNC) in MMEA. I appreciate the motivation of this work and believe that tackling DNC is valuable, as intra-entity and inter-graph noisy correspondences are often inevitable in real-world datasets. Particularly, the authors further provide statistical analysis of the noise distribution in real-world datasets in the Appendix, which is convincing and further highlights the necessity of addressing DNC. To address the DNC problem, the paper proposes a unified principle to estimate the reliability of correspondences across different levels. Based on the estimated reliability, RULE enhances robustness against DNC in both the training and inference phases, pioneering a full-process robust learning paradigm for MMEA. Overall, the paper tackles a meaningful and practical problem with a technically sound solution.", "weaknesses": "Although the paper is well-motivated and presents a technical-sound solution, I have several questions and suggestions for further improvement as follows:\n- There are some prior efforts on learning with noisy correspondence (NC) in cross-modal retrieval. Since DNC could be viewed as a special case of NC in MMEA, I wonder whether existing NC-oriented methods are adequate for addressing the DNC challenge. I encourage the authors to clarify the distinctions and advantages of RULE over prior NC-oriented studies. Moreover, I notice that the paper ``Tackling Uncertain Correspondences for Multi-Modal Entity Alignment [A]” share some similar motivation with this submission, could the authors give some discussions?\n- I am curious about how the DNC ratios (0%, 20%, and 50%) used in the experimental settings are determined. Are these noise ratios chosen based on empirical observations or following prior studies? It would be helpful if the authors could clarify the reasons behind these choices.\n- As far as I know, uncertainty has been widely used as a principle for identifying noise input in classification tasks. However, I’m not clear about why uncertainty is insufficient to measure the reliabilities of the correspondences in MMEA. In other words, what motivates the introduction of the consensus principle?\n- I am particularly curious about how the TTR module rectifies correspondences during test time. It is recommended that the authors include visualization examples to illustrate this process.", "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 (Oral)