DuetGraph: Coarse-to-Fine Knowledge Graph Reasoning with Dual-Pathway Global-Local Fusion
Authors: Jin Li
Zezhong Ding
Xike Xie
Venue: NeurIPS 2025 poster ()
Keywords: Knowledge Graph Reasoning
Primary area: general_machine_learning
TL;DR: We propose DuetGraph, a dual-pathway global-local fusion model with coarse-to-fine optimization that mitigates over-smoothing in KG reasoning, achieving SOTA performance, with up to an 8.7% improvement in quality and a 1.8$\times$ acceleration.

Abstract: Knowledge graphs (KGs) are vital for enabling knowledge reasoning across various domains. Recent KG reasoning methods that integrate both global and local information have achieved promising results. However, existing methods often suffer from score over-smoothing, which blurs the distinction between correct and incorrect answers and hinders reasoning effectiveness. To address this, we propose DuetGraph, a **coarse-to-fine** KG reasoning mechanism with **dual-pathway** global-local fusion. DuetGraph tackles over-smoothing by segregating—rather than stacking—the processing of local (via message passing) and global (via attention) information into two distinct pathways, preventing mutual interference and preserving representational discrimination. In addition, DuetGraph introduces a **coarse-to-fine** optimization, which partitions entities into high- and low-score subsets. This strategy narrows the candidate space and sharpens the score gap between the two subsets, which alleviates over-smoothing and enhances inference quality. Extensive experiments on various datasets demonstrate that DuetGraph achieves state-of-the-art (SOTA) performance, with up to an **8.7\%** improvement in reasoning quality and a **1.8$\times$** acceleration in training efficiency.

DuetGraph: Coarse-to-Fine Knowledge Graph Reasoning with Dual-Pathway Global-Local Fusion
Jin Li Zezhong 2ing Xike Xiel
School of Biomedical Engineering. University of Science and Technology of China (USTC) School of Artificial Intelligence and Data Science, USTC
Data Darkness Lab, Suzhou Institute for Advanced Research, USTC {li Riijiintu,,ecconntinngg zezhongding//maail ustc. edu. xkrie@ustc.edu. cn
Abstract
Knowledge graphs (KGs) are vital for enabling knowledge reasoning across vari- domains. Recent KG reasoning methods that integrate both global and local information have achieved promising results. However, existing methods often suffer from over-smoothing, which blurs the distinction between correct and incorrect answers and hinders reasoning effectiveness. To address this, we pro- pose DuetGraph, coarse-to-fire KG reasoning mechanism with dual-pathway global-local fusion. DuetGraph tackles over-smoothing by segregating-rrater than stacking- the processing of local (via message passing) and global (via atten- tion) information into two distinct pathways, preventing mutual interference and preserving representational discrimination. In addition, DuetGraph introduces coarse-to-fine optimization, which partitions entities into high- and low-score sub- sets. This strategy narrows the candidate space and sharpens the score gap be- tween the two subsets, which alleviates over-smoothing and enhances inference quality. Extensive experiments on various datasets demonstrate that DuetGraph achieves state-of-the-eeee art (SOTA) performance, with up to an 8.7 % improvement in reasoning quality and 1.8x x acceleration training efficiency. Our code is avail- able at https: // thub. woom/SSCC-TAA DatrrrDDDaaaarreesabbbaa hwwpsssssaaaauteaaaaaaaaa git.
Introduction
Knowledge graphs (KGs) are structured representations of real-world entities and their relationships, widely applied in domains such information retrieval [1, 2], logical reasoning [3, 4], recommenda- tion systems [5, 6]. materials science [7, 8], and biomedical research [9, 10]. However, existing KGs often incomplete, missing certain factual information [1 [1 12], which limits their effectiveness in downstream applications. As result, inferring and completing missing entity information through
KG reasoning essential.
KG reasoning faces two fundamental challenges. Firstly, it requires effective aggregation and propa- gation of local neighborhood information capture multi-hop and subgraph patterns among entities. Secondly, it must capture global structure and long-range dependencies across large-scale graphs to understand complex relationships that span multiple intermediate nodes. To address these chal- lenges, a substantial line of previous research has been dedicated to developing methods to capture local neighborhood and global structure for KG reasoning. These methods be categorized into two types: message passing-bass based methods and transformer-bused methods.
Message passing-bast based KG reasoning methods [13, 14, 5] effectively capture local structural infor- mation via message passing mechanism [15], but often fail to model long-range dependencies and
Corresponding Author
Equal Contribution
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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global structural patterns [16, 17]. In contrast, transformer- based KG reasoning methods excel at capturing global KG information and long-range dependencies but tend overlook important local structures or short-range dependencies between neighboring entities [18]. To address these limita- tions, recent state-of-the-art (SOTA) studies [19, 20] have shifted to integrate both local and global information by stacking pessaae-passing networks and attention layers in a single stage.
However, such single stage stacking ap- proach tends to result in the problem of score over-smoothing, where incorrect answers re- ceive scores similar to correct ones (Figure 12), making them hard to distinguish. Accordingly, we summarize the problem into two core chal- lenges. Challenge
10
HousE
SAILLE
RED GNN
DuetGraph
10a
Total Entity number of WNIBRR, 40,932
Number of entitles
10a
10'
Existing studies [23, 24] have shown that stacking either message- passing or attention layers individually deep- ens information propagation and aggravates the over-smoothing problem. When message- passing and attention layers stacked to- gether, these effects accumulate. Challenge 2: The discriminative capacity of single stage models is typically limited [25], as they gen- erate the answer directly based on one-shot reasoning. This deficiency in discrimination further exacerbates the over-smoothing phe- nomenon [26].
10'
10:-
109
0-0.005
0-0.01 Score gap / std (Cumulative)
0-0.015
0-0.02
Figure 1: Discriminative ability of KG reason- ing models: HousE [21], SAuLE [22], and RED- GNN [5] show limited discrimination, with many incorrect answers scoring close to the correct one. In contrast, our DuetGraph achieves clearer score separation, with far fewer incorrect answers near the correct score.
To address these challenges, propose Duet- Graph, a coarse-to-fine KG reasoning mechanism with dual-pathway global-local fusion. To ad- dress Challenge 1, we propose a dual-wathway fusion model (Section 3.1) that separately processes global and local information before adaptively fusing them. By segregating message- message-passing and attention layers, rather than stacking them, our model alleviates over-smoothing and improves soning quality. For Challenge 2, we propose the coarse-to- which first employs coarse model predict and partition candidate entities into high- and low- score subsets, and then applies a fine model to predict the final answer based on the subsets. It en- hances robustness against over-smoothing and improves reasoning quality. We theoretically demon- strate the effectiveness of coarse-to-fine optimization by mitigating over-smoothing in Section 3.2. Furthermore, we demonstrate the effectiveness of this optimization in improving inference in Sec- tion 4.4.
reasoning optimization (Section 3.2),
Our contributions be summarized as follows. 1) We propose DuetGraph, a novel KG reasoning framework to alleviate score over-smoothing in KG reasoning. Specifically, DuetGraph: a) utilizes dual-patee Suualppthwwyy fusion of local and global information instead of single-pathwap method, and b) adopts a coarse-to-fin design rather than one stage design. 2) We theoretically demonstrate that proposed dual-pathway reasoning model and coarse-to-fin optimization smoothing, thus effectively enhancing inference quality. 3) DuetGraph achieves SOTA performance on both inductive and transductive KG reasoning tasks, with up an 8.7% improvement quality and 1.8x acceleration in training efficiency.
both alleviate
Background
Knowledge Graph. A knowledge graph (KG) is a structured representation of information where entities are represented as nodes, and the relationships between these entities are represented as edges. Typically, a KG g (V,E, R. is composed of: set of entities V, a set of relations R, and [(,,, rv, f.) h4, t, E V,ri E R], where each triplet represents directed edge h4 ri 1; between a head entity h; and a tail entity f,
a of triplets
Knowledge Graph Completion. Given a KG G = (V, KG completion is to infer and predict missing elements within triplets to enrich the knowledge graph. Depending on the missing component, the task can be categorized into three subtypes: head entity completion (?, t), tail entity completion (h2 r, ?). and relation completion (h, t). In this paper, we primarily focus on
"Th x-axis denotes normalized score gap
[Scoreoome Scoeguoessal and y-axis indicates entity count per inter- (Scune
val.

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tail entity completion, following the setting of recent KG works [19, 20], as the other tasks can be reformulated into this one (See Appendix D.2).
Related Works. KG reasoning methods can be classified based on their use of structural informa- tion: message passing-based methods, which primarily leverage local structures, and transformer- based methods, which mainly exploit global structures. Message passing-based methods, such as [5, 27, 28]. suffer from well-known limitations of peessage-passing networks, including incomplete- ness [29] and over-squashing [30]. Transformer-bast bessrrooreerreeseee methods, such as [31, 32], also have draw- backs. For example, they typically transform graph structures into sequential representations during knowledge encoding, potentially losing critical structural information inherent to KGs [33. Hy- brid approaches that combine message-passinggg passing and transformers, such as [19, 20], leverage the strengths of both paradigms. However, they still face key challenges in effectively integrating and balancing local features learned via message passing with global KG information captured by self- attention. Besides, there are also triplet-based methods, such as TransE [35], ComplEx [36], Dist- Mult [37], and RotatE [38], which treat triples independent instances and often ignore graphs' topological structure. Beyond these categories, other approaches include meta-learning methods like MetaSD [31], rule pathbased models like RNNLogic [39], and tensor decomposition methods such as TuckER-IVR [40]. However, the optimization process of these methods does not directly take into account the issue of score over-smoothing. In response, we propose DuetGraph, explicitly addressing the challenge of score over-smoothing in KG reasoning.
DuetGraph
This section introduces DuetGraph, as shown in Figure 2 The core architecture of DuetGraph consists of two components: dual-pathway model for training (Steps D-@), and a coarse-to- reasoning optimization for inference (Steps (-0). Section 3.1 presents the dual- -attway global- local fusion model, and Section 3.2 details the coarse-to-fine reasoning optimization.
Input Graph
Global Pathaaay
Linaur
Pernsytvanta
parallatio
Belong to
Nationally
Linear
Madhii
Mehhd
Global Weight
Grammy
Eraaderr
Place of Hote Win
Award
Taylor Swift
3 oral Pallwaay
Foeing
Graataate From
Place of Wirth
Lance
MPAA
California
parallllim
Emityy Relation
Local
Local Global Gldua-ooo
Represeiittinss
Weight
Located At
BaN
Fine Reasmingg
Yes
New York
New York
University
KD
Model
Ausevtyy
Figure/ 2: Overview of DuetGraph: I Input KG to GNN encoder (e.g., GCN [15]) and output entity and relation representations; @ Employ simple global attention mechanism [43] to compute the global weight; @ Use the query-aware message passing networks [19] to compute the local weight; @ Fuse the local and global weight using a multi-layer perceptron (MLP); @ Use the coarse model (e.g., HousE [21] and RED-GNN [5]) to get the initial entity-to-score table; @ Split the entity-to-score table into two subtables (i.e., high-score subtable and low-score subtable) based Top-k selector; 4 Update the two subtables based on the refined entity-to-scon table predicted by dual-pathway global-local fusion model; @ Output the answer based on the relationship between the maximum score gap of the two subsets and predefined threshold A.
In dual-pathway model, after obtaining the representations in Step e we employ an MLP to transform each representation into score. Loss function defined for each training triplet t): L log((r(1) (t)h,, Σn (o - (t'l/,, [4, r)). where o- h, denotes the score candidate triplet, t' denotes negative samples. Negative samples are generated by masking the correct answer and uniformly sampling with replacement from the remaining unmasked entities [41]. Finally, we update model parameters by optimizing negative sampling loss [38] with the Adam optimizer [42].
3

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3.1 Dual-Pathway Global-Local Fusion Model
As previously mentioned, a single-pathway design is more likely to cause score over-smoothing thereby impairing KG reasoning quality. Therefore, we decouple the message message-passing networks and the transformer-bases mechanism into two separate pathways, ie., local pathway (Step @) and global pathway (Step @)). Then, we fuse their outputs through an adaptive fusion model (Step @) We detail the dual- puta-p fusion model in the following paragraphs.
Adaptive Global-Local Fusion. A straightforward approach to achieve global-local information fusion is simply sum the local and global weights. However, this method may fail to fully capture the complex interactions between local and global features, potentially hurting the model perfor- mance [44]. To address it, we introduce a learnable parameter to adaptively assign weights to local and global information, enabling more effective weighted fusion of the two components. Therefore, the final entity representation matrix computed as:
Z a Zioaal + (1-a)- Zglobal,
(I)
where Zocal denotes the local weight matrix, obtained through local pathway (Step @), and Zglobal denotes the global weight matrix, obtained through global pathway (Step @).
Then, the representation matrix Z can be used for predicting the entity scores by an MLP (Step ()
Theoretical Analysis. Here, we theoretically show that our proposed dual -ual-pathway fusion model offers superior alleviation of score over-smoothing compared to the single-pathway approach. To begin with, we give the upper bounds on entity score gap for both models in Lemma 1.
and dual-pathway
Lemma 1 (Upper Bounds on Score Gap for Different Models). Let Mo denotes the weight matrix [45] of single-pathway model slucked with message passing and transformer, MD denotes the weight matrix of our dutt-pathway model. For any two entities u, u E V, the gap in their scores after l layers of iteration can be bounded by:
S.a Sel S 2 (M)) 12,
M (Mo,
(2)
where a (M) denotes the largest singular value of M, x(") denotes initial entity feature matrix, Lg is the Lipschitz constant [46], and || ||2 is Euclidean norm operation.
We provide a detailed proof of Lemma 1 in Appendix A.I. Based on Theorem 1, we theoretically establish the relationship between the score gap and the weight matrix for each respective model. Specifically, we can get that the upper bound on score gap is related to the largest singular value of the weight matrix M. To further scale the inequality in Equation 2, we derive the largest singular value upper bound of the weight matrix in Lemma 2.
Lemma 2 (Upper Bounds on Largest Singular Value). For a weight matrix M E MD). its largest singular value satisfies
Fmax (M) <.
We provide detailed proof of Lemma 2 in Appendix A.1. Based on Lemmas 1 and 2, as the number E of iteration layers increases, the upper bound on score gaps decrease exponentially with respect to Tmax {m) because of the exponential functions properties. A larger (M) results in greater upper bound and a slower decrease of it, suggesting that the model is more resistant to over-smoothing. Based on this, we further give the quantitative relationship between mmax (Mo) and maa (MD) in Lemma 3.
Lemma (Relationship between Traaze (Mo) and maxx (MD)) ). Give the the learnable parameter in Equation 1, the relationship between o maax( and F (MD) is:
(max((M)) > (1 (ammax((M)))
We provide a detailed proof of Lemma 3 in Appendix A. Based on Lemmas 1, 2, and 3, we can derive the relationship between the learnable parameter a and the upper bound of the score gap, as shown in Theorem 1.
Theorem (Relationship between a and Score Gap). Ifa= < "mae (peeMMm)(mmMeM)) the score gap model and the dual-pal patt-y model shows a slower decrease of the score gap upper bound.
upper bound of the the dual- pathway model is greater than that of the 1+ tma T (Mo)

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We provide a detailed proof of Theorem 1 in Appendix A.1. Our adaptive fusion approach drives below the theoretical threshold in Theorem via parameter update with gradient descent. According to Theorem 1, the dual-pathway model outperforms the tigle-ppthway model in mitigating over- smoothing.
Complexity Analysis. In this paragraph, we compare the time complexity of our dual-pathway fusion model with single-pathway approach. For a fair comparison, we assume both models have the same number of layers, including Lm message passing layers and L, transformer layers. Under this setting, the overall time complexity of our (tal-ppahwayy fusion model and mangle-pthwway approach
is O (max( T. (|ε) d + [V] d Ta [V] d))) and ( [E] d + (Tmm + Tx)) [V] d²) respectively (we provide details in Appendix B.1.). Here, [V] and |ε| respectively denote the number of entities and triplets and d is the dimension of entity representation. In single-patwway approach, the message passing and transformer run sequentially, so their time complexity add together. By contrast, our dual-pathway fusion model processes them in parallel, so the overall complexity is only determined by the more expensive pathway. As a result, the dual-pathway model yields better time efficiency.
3.2 Coarse-to-Fine Reasoning Optimization
To address the over-smoothing issue caused by the one-stage approach as discussed in Section 1, we decompose the KG reasoning into two sequential stages: coarse stage and fine stage, as shown in Steps @, @ 3 and @ We detail the design and implementation of each stage in the following paragraphs.
Stage I: Coarse-grained Reasoning, In this stage, we first obtain an entity-to-score table by using the coarse model (Step G). Then, the table is split into two subtables based on their rankings (Step @): high-score subtable made up of the topk entities, and a low-score subtable containing the remaining ones. The formal description of this process is as follows. Given a query (h, r, ?). let T = sv)) E V, } denote the full entity-to-score table, where Su is the score of entity v. Rank(u) denotes the rank of entity v in descending order of the scores. Accordingly, we split T into two subtables as follows:
Thigh {ee s.) E T Rank(u) S k),
Tlow = [(v, s.) T Rank(v) k),
where & is hyperparameter controlling the cutoff rank. Thigh the high-score subtable and Tlow the low-score subtable.
Stage 2: line-grained Reasoning. At this stage, we firstly update Thigh and Tlow with the fine model (i.e., the dual-pathway model introduced in Section 3). Then, we extract the entities with the highest score from each subtables, denoted as (eh, Se.) for high and (et, Se,) ) for Tlow After that, compute the difference 7 se, Se, based the pre- pre-ned threshold A. If exceeds A, this indicates that the highest-score entity in the low-score subtable clearly surpasses the highest-score entity in the high-score subtable. Therefore, select the highest-score entity from Tlow as the final answer; otherwise, we select that from Thigh
By introducing this adjustable threshold A, we enable entities from both the high-score and low- score subtables to be dynamically selected as the answer. This design enhances flexibility and re- duces selection bias in the decision process.
Theoretical Analysis. In coarse-to to-fie optimization, since the final prediction is made based on comparing the highest scores from the high-score and low-score subtables. Thus, the score gap is particularly crucial for mitigating over-smoothing and we theoretically demonstrate how the coarse- to-fine optimization mitigates over-smoothing by amplifying the gap between the highest scores in the two subtables, as shown in Theorem 2.
Theorem 2 (Lower Bound on Score Gap Between High-score and Low-score Subtables). The lower bound on the expected gap between the top scores of the two subtables (Se,, and Se,) is:
1
1
E Se
Sei
N2
+1
(N₂ (N7+1)
(5)
where N₁ and Nt denote the number of entities in high-score and low-score subtables respectively. is the standard deviation of the entity score.
5

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We provide a detailed proof of Theorem 2 in Appendix A.2. Based on Theorem 2, we establish the relationship between the score gap and the number of entities. In our setup, the ratio of the number of entities in the low-score subtable to those in the high-score subtable exceeds 1,000. Therefore, based on Theorem 2. we can derive that the lower bound on the expected gap between the top scores of the two subtables is more than 0.1 (Detailed proof of this in Appendix A.2). In comparision, other baseline methods (as shown in Figure 1) exhibit score gaps between correct and incorrect answers are typically less than 0.02a. This demonstrates that our optimization can amplifying the score gap, thus mitigating over-smoothing. Building on this, we additionally present Theorem to theoretically demonstrate that coarse-to coarse-toofiine to-fine optimization also improves the quality of KG reasoning.
Theorem (Effectiveness Coarse-to-Fine Optimization), Let and P' denotes the probabil- ities of correctly identifying the answer with and without coarse-to-fie optimization, respectively. Then, we have P > PP.
We provide a detailed proof of Theorem 3 in Appendix A.3.
Complexity Analysis. In this paragraph, we compare the complexity of our coarse-to-fine
stage with one-stage approach. The time complexities of coarse-to-fine stage and one-stage are ((max(mm(() d + [V] dd),, La [V] d) + [V] log [V) and (mmax(Lm d + [V] dL), ) Ly [V] df)) respectively. We provide detail proof of these in Appendix B.2. Here, [V] and | denote the number of entities and triplets, respectively. Lm and L, represent the number message passing layers and transformer layers. d is the dimension of the entity representation. In practice, [V] log [V] is much smaller than | dZ, For example, in FB15k-237 dataset [47], the number of entities is 14,541, and the representation dimension is 32. Accordingly, [V] log [ is approximately 10 and |V dl is approximately 10". Therefore, the time complexity of the coarse- coassetoo-fine to-fine stage remains comparable to that of the one-stage.
Empirical Evaluation
In this section, we conduct extensive experiments to answer the following research questions: (RQ1) Can DuetGraph effectively improve the performance of inductive KG reasoning tasks? (RQ2) Can DuetGraph effectively improve the performance of transductive KG reasoning tasks? (RQ3) Can DuctGraph demonstrate strong scalability in KG reasoning tasks by achieving high training effi- ciency? (RQ4) How is the effectiveness of the components of DuetGraph? (RQ5) In the coarse-to- fine reasoning, what is the standard of the coarse model? (RQ6) Is DuetGraph sensitive to hyperpa- rameter k, where & denotes the number of entities in high-score subset? (RQ7) How generalizable is DuetGraph across tasks on knowledge graphs?
4.1 Experiments setup
Inductive Datasets. For inductive reasoning, following Liu et al. [19], we use the same data divi- sions of FB15k-237 [47], WNI8RR [48], and NELL-995 [49]. Each division consists of 4 versions, resulting in 12 subsets in total. Notably, in each subset, the training and test sets contain disjoint sets of entities while sharing the same set of relations.
Transductive Datasets. For transductive reasoning, we conduct experiments four widely uti- lized KG reasoning datasets: FB15k-237 [47], WNISRR [48], NELL-995 [49], and YAGO3-10 [50], adopting the standard data splits provided by prior works [28, 51].
Triple Classification Datasets. For the triple classification task, we conduct experiments three widely used knowledge graph datasets: UMLS[52], FB13[53] and WN11[53].
Triple Classification Baselines. The following four categories of SOTA models are adopted as baselines for comparison with DuetGraph in triple classification: triplet-bused (HousE (21]), mes- sage passing-bused (AdaProp [51 trunsformer-busee (HinER [54]), and hybrid message passing- transformer (KnowFormer [19]) models (SOTA methods for comprehensive comparison).

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Table 1: Inductive KG reasoning performance for various methods on 12 subsets. (The best results bolded in red with yellow highlight. Second-ber results are with blue highlight. Results are either sourced directly from original papers or reproduced based on available code.)
Method
v1
v2
v4
MRR
H@1
H@ 10
MRR
H@1 H@ MRR
H@1
H@ 10
MRR
H@1
H@
FB15k-237
DRUM [55]
57.1
30.9
NBFNet [28]
0.442
33.5
57.4
0.514
42.1
68.5
0.476
38.4
63.7
0.453
36.0
62.7
RED-GNN [5]
0.369
30.2
48.3
0.469
38.1
62.9
0.445
35.1
50.3
0.442
34.0
62.1
Net [13]
0.457
38.9
62.9
0,466
36.5
AdaProp [51]
0.310
19.1
55.1
0.471
37.2
65.9
0.471
37.7
63.7
0.454
35.3
63.8
Ingram [56]
0.293
16.7
49.3
0.274
16.3
48.2
0.233
14.0
40.8
0,214
11.4
39.7
KnowFormer [19]
0.466
37.8
60.6
0.532
70.3
0.494
40.0
65.9
0.480
38.3
DuetGraph (Ours)
0.507
42.7
63.2
0.549
44.8
72.9
0.518
42.3
69.9
0.501
39.8
67.0
WN18RR
DRUM [55]
0.666
61.3
77.7
0.646
59.5
74.7
0.380
33.0
47.7
0.627
58.6
70.2
NBFNet [28]
0.741
69.5
82.6
0.704
65.1
79.8
0.452
39.2
56.8
0.641
69.4
RED-GNN
0.701
65.3
79.9
0.690
63.3
78.0
0.427
36.8
52.4
0.651
60.6
72.1
A [13]
0.727
68.2
81.0
0,704
64.9
80.3
0.441
38.6
54.4
0.661
61.6
74.3
AdaProp [5]]
0.733
66.8
80.6
0.715
64.2
0.474
39,6
58,8
0,662
61.1
Ingram [56]
0.277
13.0
60.6
0.236
11.2
48.0
0.230
11.6
46.6
0.118
4.1
25.9
SimKGC [57]
0.315
19.2
56.7
0.378
23.9
65.0
0.303
18.6
54.3
0,308
17.5
57.7
KnowFormer [19]
0.752
71.5
81.9
0.709
65.6
81.7
0.467
40.6
57.1
0.646
60.9
72.7
DuetGruph (Ours)
0.758
72.1
81.7
0.719
66.7
81.1
0.501
44.3
62.2
0.662
62.1
73.1
NELL-995
NBENet [28]
0.584
50.0
79.5
0.410
27.1
63.5
0.425
26.2
60.6
0.287
25.3
RED-GNN [5]
0.637
52.2
86.6
0.419
31.9
60.1
0.436
34.5
59.4
0.363
25.9
60.7
AdaProp [S1]
0.644
52.2
88.6
0.452
34.4
65.2
0.435
33.7
61.8
0.366
24.7
60.7
Ingram [56]
0.697
57.5
86.5
0.358
25.3
59.6
0.308
19.9
50,9
0,221
12.4
44.0
Know/Formrr [19]
0.827
77.0
93.0
0,465
35.7
65.7
0.478
37.8
65.7
0.378
26.7
59.8
DuetGraph (Ours)
0.850
78.5
96.5
0.543
44.4
69.1
0.535
43.2
72.6
0.464
35.4
68.4
Inductive Baselines. We compare DuetGraph with baseline methods for inductive KG reasoning as shown in Table For completeness, we note that some baselines do not support certain datasets due to limitations in their released code. Details are provided in Appendix C.2.
Transductive Baselines. The following four categories of SOTA models are adopted base- lines for comparison with DuetGraph in transductive KG reasoning: triplet-based models, message passing-bee based models, transformer-based models, hybrid message passing-transformer models (in- cluding our proposed method and KnowFormer [19]) and other approaches, as shown in Table 2.
Evaluations Metrics. The model performance is measured by Mean Reciprocal Rank (MRR) [35] and Hit Rate at & (Hits@k, k, where & {1, 10)) [35]. Hits@k assesses whether the true entity of a triplet appears within the top-k ranked candidate entities. If the true entity is ranked k or higher, the result is recorded I: otherwise, is recorded 0. Metries formalized follows.
k >> and Test the test set containing Hits@k Tiall Ex,eT (rank;), where f(x) 0,
x
[Teeal triplets. Each 1, the i-th test triplet, and rank; represents the position of the correct entity in the ranked list of candidates. MRR is calculated the average of the reciprocals of the ranks assigned to the correct entities in the prediction results. MRR = |Tae Σx,T rank, where Tisa the test set, and rank; represents the rank of the entity in the candidate list for 4,,
4.2 Performance
To answer (RQ1), we evaluate DuetGraph on 12 datasets. The results, shown in Table 1, demonstrate the strong performance of DuetGraph compared to baseline models. Specifically, DuetGraph surpass SOTA methods by up to 8.6% improvement in MRR, 8.7% improvement Hits @ and 7.7% improvement Hits @ 10. ranks first in Hits @ every evaluated version (y1-v4) of the FB 15k-
7

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Table 2: Transductive KG reasoning performance for various methods on 4 datasets. (The best results are bolded in red with yellow highlight. Second-bess results are with blue highlight. Results are either sourced directly from original papers or reproduced based on publicly available code. "_" indicates unavailable results due to insufficient information for reproduction.
Method
FB15K-237
WNISRR
NELL.995
YAGO3-10
MRR H@1 1
H
MRR
H@1
H@10
MRR
H@1
H@10
MRR
H@1
H@10
Triplet-based
TransE [35]
0.330
23.2
0.222
52.8
0.507
42.4
64.8
0.510
41.3
68.1
DistMult [37]
0.358
26.4
55.0
0.455
41.0
54.4
0.510
43.8
63.6
0.566
49.1
70.4
RotalE [38]
0.337
0.477
42.8
44.8
60.8
0.495
40.2
67.0
HousE [21]
0.361
26.6
55.1
0.511
46.5
60.2
0,519
45.8
61.8
0.571
49.1
71.4
Message passing-based
CompGCN [14]
0.355
26.4
0.479
59.6
0.421
39.2
57.7
NBFNet [28]
0.415
32.1
59.9
0.551
49.7
66.6
0.525
45.1
63.99
0.563
48.0
70.8
RED-GNN [5]
0.374
28.3
55.8
0.533
48.5
62.4
65.1
0.556
48.3
68.9
A [13]
0.411
32.1
58.6
0.549
49.5
65.9
0.521
44.7
63.1
0.556
47.0
70.7
AdaProp [5]]
0.417
33.1
0.562
49.9
67.1
0.554
65.5
0.573
51.0
68.5
ULTRA [58]
0.368
27.2
56.4
0.480
41.4
61.4
0,509
44.1
66.0
0.557
47.1
71.0
Transformer-bused
HinER [54]
0.373
27.9
0.503
46.2
58.4
43.7
65.9
0.339
25.1
50.8
KGT5 [59]
0.276
21.0
41.4
0.508
48.7
54.4
0.426
36.8
52.8
N-Former [60]
0.373
27.9
55.6
0.489
44.6
58.1
[23]
0.360
26.8
54.5
0.491
45.4
55.8
0.512
42.2
66.0
0.475
36.7
68.2
Others
MetaSD [31]
0.391
30.0
57.1
0.491
44.7
57.0
0.516
45.5
61.5
00M
0OM
00M
RNNLogic [39]
0.344
25.2
53.0
0.483
44.6
55.8
0.516
46.3
57.8
0.554
50.9
62.2
TackeER-IVR [40]
0,368
27.4
55.5
0.501
46.0
57.9
0.505
42.8
63.7
0.581
50.8
71.2
Hyhrid
KnowFormer [19]
0,430
34.3
60.8
0.579
52.8
68.7
0,566
50.2
67.5
0.615
54.7
73.4
DuetGraph (Ours)
0.453
36.1
62.4
0.593
54.2
69.9
0.590
52.1
71.2
0.631
56.1
74.8
237, WNI and NELL-995 datasets, indicating its strong ability accurately predict the correct entity at the top rank. Importantly, our method relies solely on the structural information the KG, without relying external textual features, highlighting its strong generalization capability.
To answer (RQ2), we evaluate the performance of DuetGraph on four widely utilized transductive KG reasoning datasets. Table 2 demonstrates the impressive performance of DuetGraph compared to baseline models. Specifically, DuetGraph demonstrates substantial performance gains over baseline methods, with improvements of up 37.1% 1% in MRR, 52.8% in Hits @ 1, and 24.0% in Hits @ 10.
It is worth noting that in inductive KG reasoning. the entities to be predicted ing, which not only aligns more closely with real-world scenarios but also poses greater challenge. Based on these results, DuetGraph exhibits remarkable generalization and adaptability.
unseen during train-
4.3 Efficiency
To answer (RQ3), we evaluate Hits throughout training on the FB15k-237 and YAGO3-10, the latter being large-scale dataset with millions of training triples. We compare DuetGraph with the best models each category-AdaProp (message passing-basedy SAuLE (transformer-basee and KnowFormer (hybrid). As shown in Figure 3, DuetGraph finally achieves SOTA performance on FB15k-237 while reducing training time by nearly 50% compared to the second-best method. We also observe from Figure 3 that DuetGraph achieves SOTA performance on TAGO3-10 while requiring less training time compared to other methods. These results show that DuetGraph achieves scalability through high training efficiency. The observed improvement is primarily attributable to this dual- -athway design, which enables parallel training of both local and global pathways.
Furthermore, to demonstrate the efficiency of DuetGraph on very large KGs, we conduct experi- ments on Wikidata5M [61] and Freebase [62], and compare DuetGraph with highly efficient rule- based methods (e.g., AnyBURI. [63]). It is worth noting that for the Wikidata5M and Freebase datasets, the AnyBURL. paper [63] does not explicitly specify under which data split the results in Table 2 of [63] were obtained. For fair comparison,
the same data split as in [62].

---

AdaProp
SACTLE
KnowForrm Fowforeeerreooo DuetGraph
0.48
0.70
0.44
34.0
0.60
0.40
0.50
26.0
HitS
0.32
0.28
22.0
0.30
0.24
0.20
14.0
0.10
Training time: hour
Training time: hour
Training time: hour
Training time: hour
Figure 3: Hits
and MRR w.r.t. time on FB15k-237 and YAGO3-10.
Table 3: Comparison of different methods across very large knowledge graphs. (The best results are
bolded in red with yellow highlight.)
Method
WikidataSM
Freebase
MRR
H6P
H 10
Learning
Inference
MRR
H@1 1
H 10
Learning
Inference
AnyBURL (Rule-based)
0.350
30.9
42.9
10,000s
4,462s
0.588
53.6
68.2
10,000s
3,142s
Know Know Former (Emh-hased
0.332
26.7
46.3
31 31,436s
105s
0.684
65.7
73.6
32,109x
176s
DuctGraph (Emb-bascd)
0.363
32.7
49.5
28,866s
80s
0.697
69.3
73.8
30.158s
141s
As shown in Table 3, DuetGraph achieves SOTA quality performance with learning time in the same order of magnitude as AnyBURL [63], and demonstrates a significant reduction inference time compared AnyBURL [63]. demonstrates that DuetGraph maintains high efficiency and strong quality even when applied to extremely large knowledge graphs.
4.4 Ablation Study
To address (RQ4), we perform an ablation study by removing key components of DuetGraph: (1) the local pathway, (2) the global pathway, (3) the coarse-to-fine reasoning optimization (i.e., reducing DuetGraph model to the dual-pathway fusion alone), (4) the dual-pathway fusion model (i.e., leaving only the coarse-grained reasoning), and (5) the threshold A in the fine-grained stage, which prevents correction for low-score predictions.
As shown in Table 4, removing either the local global pathway degrades performance, confirm- ing the necessity of both information types. Eliminating coarse-to-fin reasoning leads to a notable drop in Hits 1, demonstrating its effectiveness in refining predictions. Excluding the dual-pathwer module results the largest performance loss, which underscores its crucial role in reasoning per- formance. Finally, removing the threshold A reduces accuracy due to uncorrected errors in cases where the correct entity is excluded from the high-score subset during coarse reasoning.
To answer (RQ5). we additionally evaluate the performance of DuetGraph on four transductive KG reasoning datasets using three different types of coarse-grained reasoning models: a triplet- based model (HousE [21]), message passing-bast based model (RED-GNN [5]). and hybrid message massing-transfore model (KnowFormer [19]). The triplet-based model focuses exclusively on local triple-level patterns. The message passing model captures neighborhood-level information, and the transformer model handles global patterns (like our fine model).
As shown in Table 5, DuetGraph, when integrated with any of the three coarse- sorrse-grained models, consistently outperforms its competitors. Among them, the triplet-based model achieves the best performance as coarse model. This aligns with prior work [64], which shows that maximizing architectural diversity between coarse and fine models leads better overall performance; this the triplet-based model benefits from its maximal architectural difference from global- information-focusee fine model.
4.5 Parameter Analysis
To answer (RQ6), we conduct experiments by varying the hyperparameter introduced Sec- tion 3.2 across four different transductive datasets. As shown in Figure 4, DuetGraph is insensitive to the parameter k suggesting stable performance. We further conduct hyperparameter experiments on inductive datasets, presented in Appendix D.4, and obtain consistent results.

---

Table 4: Different components ablation study of DuetGraph on transductive KG reasoning datasets.
(The best results are bolded in red with a yellow highlight.)
Method
FB15k-237
WNISRR
NELL.-955
YAGO3-10
DuetGraph
0.453
36.1
62.4
0.593
54.2
69.9
0.590
52.1
71.2
0.633
56.1
74.8
wro local
0.584
0.582
0.617
woo global
0.441
34,9
61.4
0.565
51.7
66.6
0.586
51.0
69.8
0.614
53.8
74.4
w/o Coarse-to- Fo-nee reasoning
0.437
34.8
61.1
0.580
53.0
68.9
0.567
50.5
6777
0.616
54.8
73.5
w/b Dual-Pachway fusion model
0.355
54.7
0.512
0.534
0.563
w/o threshold value &
0.395
31.7
55.8
0.551
48.9
66.1
0.544
49.8
66.5
0.595
53.4
70.9
Table 5: Different coarse-grained model ablation study of DuetGraph 4 transductive KG reason- ing datasets. (The best results are bolded in red with yellow highlight.)
Method
FB15L-237
WNISRR
NELL-9E
YAG03-10
MRR
11G
MRR
1161
11910
MRR
1141
1161
11G
DuctCingh (ur iiplet based model course model)
0.453
36.1
62.4
0.593
54.2
69.9
0.590
52.1
71.3
0.631
56.1
74.5
DuntCiphh (wr meseage passing-bsaal model modd)
0.446
35.4
61.3
0.580
53.5
69.0
0.584
51.7
70.3
0.62
55.4
73.9
DuctCingh cansforma--tsee mode moddl)
0.445
34.8
62.
0.586
53.2
69.4
0.579
50.8
70.5
0.24
55.7
74.2
FB15k-237
WN18RR
NELL-995
YAGO3-10
0.68
0.64
58.0
77.0
0.60
54.0
75.0
0.56
@ 46.0
50.0
73.0
0.52
42.0
71.0
0.48
38.0
69.0
0.44
34.0
67.0
11
1
11
11
13
k
k
k
Figure 4: Effect of l on the performance metrics of KG reasoning for different datasets (Transduc- tive).
4.6 Generalization
To answer (RQ7), we evaluate DuetGraph's performance on the triple classification task. The exper- imental results in Table demonstrate that DuetGraph consistently outperforms all baseline methods across all datasets, achieving new SOTA performance on the triple classification task, which further highlights the task generality of our proposed DuetGraph framework.
Table 6: Comparison of triple classification accuracy on different datasets. (The best results are bolded in red with yellow highlight.)
Method
UMLS Ace (%)
FB13 Acc (%)
WN11 Acc (%)
HousE [21]
83.1
69.8
65.3
HitER [54]
59.4
62.2
69.6
AdaProp [51]
77.0
71.9
67.1
KnowFormer [19]
83.1
77.3
70.2
DuetGraph
84.3
80.0
71.9
Conclusion
This paper proposes DuetGraph, coarse-to-fne KG reasoning mechanism with dutl-way global-local fusion to alleviate score over-smoothing KG reasoning. DuetGraph mitigates over- smoothing by allocating the processing of local (via message passing) and global (via attention) information to two distinct pathways, rather than stacking them. This design prevents mutual inter- ference and preserves representational discrimination. Experimental results show that DuetGraph outpeforms SOTA baselines on both quality and training efficiency.
Acknowledgements:
This work was supported by the National Natural Science Foundation of
China (NSFC) under Grant 62472400.
10

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Contents of Appendix
A Proof's of Theorems
23
A.1 Dual-Pathway Global-Local Fusion Model Effecitively Alleviating Over-Smoothing.
23
A.2 Coarse-to-Fine Reasoning Optimization Alleviates the over-smoothing in KG.
24
A.3 Coarse-to-Fine Reasoning Optimization Improves the Quality of KG Reasoning.
25
Time Complexity Computation
25
B.1 Time Complexity Computation of Dual- Paal-Pa Global-Local Fusion Model.
25
B.2 Time Complexity Computation of Coarse-to-Fine Stage.
25
Additional Baseline Discussion
26
C.1 DuetGraph vs. Methods based on pre-trained language models.
26
C.2 Baseline Details.
27
Experimental Details
27
D.I Transductive and Inductive Reasoning.
27
D.2 Relation Prediction Task.
27
D.3 Dataset Statistics
27
D.4 Hyperparameters Setup
28
D.5 Random Initialization.
30
D.6
Ranking Protocol.
30
More Experimental Results
31
E.
Model Size and Inference Time.
................................
31
E,2
The difference between and graph attention.
31
Limitations and Broader Impacts
32
F.1
Limitations
32
F.2
Broader Impacts
32
22

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A Proofs of Theorems
In this section, provide the theorem proofs in method part, including 1) why our proposed dual- pathway global-local fusion model can alleviate the over-smoothing in KG; 2) why our proposed coarse-to-fine reasoning optimization alleviate the over-smoothing in KG; 3) why our proposed coarse-to-fine reasoning optimization can improve the quality of KG reasoning.
A.1 Dual-Pathway Global-Local Fusion Model Effecitively Alleviating Over-Smoothing.
Proof. Let entity initial representation be denoted as x E IRaxd symmetrically normalized adja- cency matrix in message passing networks is denoted as A RRax. The attention matrix computed by single layer of global attention is denoted as P R=xx. We construct weight matrix of one-pathway model stacked with L message passing layers and transformer layer defined as:
Mo = P
We construct weight matrix of dual-pathway fusion model defined as: MD = aA + (1 - P
(7)
where is the learnable parameter in Equation 1. We first focus the entity representation obtained after e iterations:
X _) ,M [Mo
(8)
According to basic properties the matrix paradigm, we can get spectral norm of ((m)
satisfies
| = X|Mx S |M (X 1| S (omax ||x (1
(9)
The representation discrepancy between any two entities u and U satisfies
|- - - 2| = ||=(0/12 + ||= ll2 = (1 1l2 S 2 (a ||x(0
(10)
Then, entity representations are mapped to scalar scores through a multilayer perceptron (MLP). According to the principle Lipschitz continuity, the score gap between any two entities can be bounded by
ssw - Sol s L ||=/{0 x2!" S (m |X
(11)
where f : Rd + denotes the MLP and L, the Lipschitz constant [46]. Since A is sym- metrically normalized adjacency matrix, spectral theory ensures that its eigenvalues { satisfy 1 = A > A2 2 ... 2 An > 1. Hence, we conclude that largest eigenvalue A is equal to 1, and its largest singular value a max (A4) is equal
Since the attention matrix P is row-stochastic, its largest eigenvalue is 1, and all other eigenvalues satisfy |na| < 1. According to the definition of singular values, it follows that the largest singular value max (P) of less than 1.
Therefore, we can get
mmax (Mo) = max (PA*) max (P) max = maxx (P) <
(12)
and since the spectral norm and the maximum singular value are equal we can get
max (MD) |aA4 4 Pl2 s ||aA41124 11 a11 s + (1- 1 (13)
Then, we have
maxx (M) 11 Me [Mo.Mp]
(14)
Since the spectral norm and the maximum singular value are equal, we can use the inverse triangle inequality derive the following:
Tmax (Mp) A (1 (1-a) PI12 2 |||aA4112 - 11(1 a1 la a (P) (15)
According to Equation 12, we have
m (max 2 (1 ax) (P) 2 a
a) ma (Mo)
(16)
Therefore, as long as the learnable parameter a is less than aman (Ma) man (Mo) mmax(M)) will
14-0mar (Ma)
necessarily be greater than (Mo). The result of Equation 11 indicates that as the number of iterations & increases, the score gap between any two entities will decrease exponentially with respect (M). This implies that If a < (Mn)
the score gap upper bound of the dual- pathway model is greater than that of the one-pathway model and the dual- dual-pathway model shows a slower decrease the score gap upper bound. Consequently, duth-ay model effectively mitigates the oversmoothing.
[+dmsx(MM)
23

---

A.2 Coarse-to-Fine Reasoning Optimization Alleviates the over-smoothing in KG.
Proof. For a set of scores {81, $2,..., J set a score threshold I. = 1 + d' T. where jí' is the mean of this set of scores and o' is the standard deviation of this set of scores. Using Cantelli inequality,
2) = P(s, 2
(17)
k
02 + (E)
12 +1
The probability that at least one s of the l scores is more than is
P(max 2 11)21 (1
k
1.2 +1
2
1.2
+1
(18)
Therefore,
E|max st] 2 t- P(max s; 21) 2 (u' + +7) P(max 9; 2 (n'
(19)
k +1
Let the scores of candidate entities in fine-stage follow distribution with mean μ and standard deviation o. Let the total number of entiities be N, with the high-score subset containing N₁, entities and low-confidence subset containing N₂ entities. Denote the maximum score within the high-score subset as
Sen I,...,,, N,
(20)
Denote the maximum score within the low-score subset as
Se: max 8: im N2 + I
(21)
According to Eqn 19, then the expectation of the maximum of the two subsets satisfies
N
E.SeA.] 2 (++
N
N +1
(22)
S[J,]] 2 (
+
0
Nj
N
N? +1
The gap between the two is
N₂
N
E E[S.,I1
2
(p +
(μ +
Nn
N
+
1
N
N²
(23)
Nn
N
1
N
NZ
N7
N?
0
In our implementation, N2 is less than 10 and the number of entities in all datasets is more than 10000. Then, we have Ni 1000, and the function f(x) सें is monotonically decreasing for x > 1. Therefore,
1
[Saa R0, 2
N2
N
1
(24)
(1000N,)² 12
N2 +1 .
0.10.1.
By Jensen's inequality, we have
Blse. Sc,11 > E[[S..] E(Sc,]1 > 0.1
(25)
We have demonstrated that, in our coarse-to- torrse-tt-fine tone reasoning optimization, the expected score gap between the high- and low-score subsets is at least 0.1 times the standard deviation. In compar- ision, other baseline methods (as shown in Figure 1) exhibit score gaps between correct and incorrect answers typically less than 0.02o. This demonstrates that our optimization can amplify the score gap, thus mitigating over-smoothing.
24

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A.3 Coarse-to-Fing Reasoning Optimization Improves the Quality of KG Reasoning.
Proof. In coarse-grasd graseegraiied reasoning. the candidate entities are divided into two subsets, the high- score subset is denoted as Thigh The highest-score entity in each subset, as computed by our proposed dual-pathwer aual-pathway fusion model, is denoted as:
= arg max s(e); eET
= arg max me). Th
(26)
where the s(-) denotes score computing by dual-pathway fusion model. Let PA denote the probabil- ity that the difference between en and ej is less than or equal i.c. PA P(e eh S A).
Let P and P' denotes the probabilitics of correctly identifying the answer with and without coarse- to-fine optimization, respectively. Let event A denote that the HousE model assigns the ground-truth answer a score that ranks within the top-k among all candidate entities, and event B denote that our proposed dual-pathway model correctly infers the ground-truth answer. Therefore, the probability that coarse-to-fine reasoning accurately infers the correct answer is:
P Pa P(B A) + (1 Pa) p'
Pa P(B P) Pa P
(27)
(P(B A) P*) PA + P
In the following, we compare the magnitude relationship between P(B A) and P P(B A) represents the probability of event B occurring given that event A has occurred. Specifically, the probability that the dual-pathway fusion model correctly infers the correct answer given that the correct answer ranked within the high-score subset by coarse-grained reasoning. Evidently, the probability of the dual-pathway fusion model correctly inferring the correct answer is higher when the correct answer is already ranked within the high-score subset by coarse stage, compared to the unconditional probability of the dual-pathway fusion model's 's correct inference. This is because the high-score subset from coarse provides the dual-pathway fusion model with a more focused and promising subset.
Therefore,
obtain that P(B A) 2 P' which leads to P 2 P', thus demonstrating that the probability that coarse-to-fine reasoning optimization accurately infers the correct answer is more than the probability that dual-pathway fusion model without coarse-to-iine optimization correctly infers the correct answer.
B Time Complexity Computation
In this section, we provide details of time complexity computation in Section 3.1 and Section 3.2
B.1 Time Complexity Computation of Dual-Pathway Global-Local Fusion Model.
Time complexity of dual-pathway fusion model. We assume dual-pathway fusion model includs Lm message passing layers and L, transformer layers. Here, [V| and |E] respectively denote the number of entities and triplets and d is the dimension passing layer, its time complexity is O(EEd + (VZl). For each transformer layer, its time plexity is ((Vv2), )). Because of message passing layer and transformer in parallel, the overall time complexity of our duth-aat fusion model is O (max(Lmm(E)) (1E) d)) L, (V] d²)).
entity representation. For each message
Time complexity of one-pathway model. We assume one-pathway fusion model includs Lm message passing layers and L, transformer layers. For each message passing layer, its time plexity is O(EEd+ (vd)). Here, [V] and []] respectively denote the number of entitics and triplets and d is the dimension of entity representation. For each transformer layer, its time complexity is (()dd)). Because message passing layer and transformer is sequntial, the overall time complexity of our dual-pathwa, fusion model are (Lmm [| d (Im L,) [V] d²).
B.2 Time Complexity Computation of Coarse-to-Fine Stage.
The coarse-to-fine reasoning stage has two additional operations of coarse-grained reasoning and sorting all entities compared ote-stage. In coarse-to-fine reasoning, parallel reasoning with coarse
25

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Table 7: Transductive KG reasoning performance for DuetGraph, SimKGC and McCoKGC on FB FB15k-237 and WNISRR. (The best results are bolded red with a yellow highlight.
Value
FB15k-223 -337
WNISRR
MRR
H@1 1
@@
10
MRR
H@1
@@ 10
SimKGC[57]
0.336
24.9
51.1
0.666
58.5
80.0
MoCoKGC[65]
0.391
29.6
43.1
0.742
66.5
79.2
DuetGraph(ours)
0.456
36.1
62.8
0.594
54.2
70.0
model and fine model. Moreover, the time complexity of the coarse model we employ is ((Eld) where |8] denote the number of triplets and d is the dimension of entity representation. The time complexity of this sorting process is ((VV[log)V)) where [V] denote the number of entities. The one- stage reasoning only includes dual-pathway fusion model. Therefore, the overall time complexity of the coarse-to-fing reasoning stage is ((max (|ε) d d2) Le d)) + [V] log [V)).
C Additional Baseline Discussion
C.1 DuetGraph vs. Methods based pre-trained language models.
We observe that language model-based reasoning methods such as SimKGC [57] and Mo- CoKGC [65] achieve unusually high results on WN18RR, but perform poorly on other datasets, as shown in Table 7. To better understand this phenomenon, we take these two methods as represen- tative examples for further analysis. We note that WNI8RR is derived from WordNet, large lexical database of English that naturally encodes rich semantic relations between words. Pre-trained lan- guage models are well-suited to capturing such general semantic information, which may explain their strong performance on WNISRR. In contrast, FB 153-2237 involves more domain-specinn rela- tional knowledge, which poses greater challenges for these models, leading to weaker performance (as shown in Table 7).
Additionally, we consider the possibility that the textual descriptions of entities in WN18RR may have appeared in the pretraining corpus of language models, potentially leading to data leakage. Therefore, adopt the detection method proposed by [66] to estimate the proportion of WNI8RR entity texts that are likely included the pretraining data of the language model used by SimKGC and MoCoKGC (i.e., bert-base-uncased).
Specifically, for an entity text, select the e of tokens with the lowest predicted probabilities from the language model. Then, compute the average log- lig-likeldhood of these low-probability tokens. If the average likelioll exceeds certain threshold, we consider that the text is likely to have appeared in the language models pre-training data.
The detailed results are presented in Table 8. We observe that under smaller (e.g..10% and 20%) that means selecting the of tokens that are most difficult to be recognized by the language model, over 70% of the entity texts in WNI8RR appear be memorized by the language model, suggesting a significant potential for data leakage.
Table 8: Pre-training overlap rate under varying c, where c represents the proportion of low proba- bility tokens predicted by language model.
Pretraining Overlap Rate
10.0%
70.11%
20.0%
77.46%
82.60% 50.0%
60.0%
81.92%
26

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C.2 Baseline Details.
In this section, we explain the reasons for not comparing with some baseline methods on certain datasets. SimKGC [57] requires additional textual information as part of its input data. Since the public repository does not provide textual information for some datasets (e.g.. NELL--955), compar- isons on those datasets are not conducted. DRUM [55] and A Net [13] do not provide the specific parameters required to construct the inductive datasets as described their papers. Therefore, they cannot be applied to certain datasets (c.g., NELL-995vI).
D Experimental Details
D.1 Transductive and Inductive Reasoning.
Following the formal definition in [67], transcucttvve reasoning assumes that all test entities appear during training, while inductive reasoning handles completely unseen entities during testing. This difference is fundamental to evaluating model generalization capabilities.
Therefore, following the methodology in [68], we construct our inductive evaluation datasets by ensuring complete separation between training and test entities. This strict partitioning, where test entities are excluded from training, enables reliable assessment of the model's 's generalization ca- pability to unseen knowledge.
D.2 Relation Prediction Task.
The relation prediction task (h, ?, t) can indeed be transformed to fit our tail completion paradigm through the approach in [69]]
Scoring Mechanism: For relation prediction, fix head (h) and tail (f) entities, then score all candidate relations. For tail prediction, we fix the head (h) and relation (r), then score all candidate tails. Both tasks the same underlying scoring function.
Implementation: For relation prediction, we compute and select the one with the highest score as the prediction.
for each candidate relation
This approach maintains fundamental consistency with tail entity prediction. While the surface-level structures differ, both tasks share the same underlying computational paradigm: evaluating possible completions against fixed components of the triple using a unified scoring mechanism.
D.3 Dataset Statisties.
We conduct experiments four knowledge graph reasoning datasets, and the statistics of these datasets are summarized in Table 9. The specific dataset details are as follows:
The FB15k-237 [47] dataset is subset of FB15k [35]. Toutanova and Chen [47] pointed out that WN18 and FB15k have a test set leakage problem. Therefore, they extracted FB15k-237 from FB15k.
The WN18RR [48] dataset is subset of WN18 [35]. All inverse relations in the WN18 dataset were removed by Dettmers et al. [48] to obtain the WNI8RR dataset.
NELL-995 [49] is a refined subset of the NELL knowledge base, curated for multi-hop reasoning tasks by filtering out low-value relations and retaining only the top 200 most frequent ones.
YAGO3-10 [70] is a subset of YAGO3, containing 123,182 entities and 37 relations, where most relations provide descriptions of people. Some relationships have hierar- chical structure such as playsFar or or actedIn, while others induce logical patterns, like isMorriedTo.
Additionally, we perform experiments on three inductive knowledge graph reasoning datasets, each of which contains four different splits. The statistics of the inductive datasets are summarized in Table 10.
27

---

Table 9: Dataset Statistics for Tranductive Knowledge Graph Reasoning Datasets.
Triplet
Dataset
Relation
Entity
Train
Valid
Test
FB15K-237 [47]
237
14,541
272,115
17,535
20,466
WN18RR [48]
40,943
86,835
3,034
3,134
NELL-995 [49]
200
74,536
149,678
543
2,818
YAGO3-10 [70]
123,182
1,079,040
5,000
5,000
Table 10: Dataset Statisties for Inductive Knowledge Graph Reasoning Datasets. In each split, one needs to infer Query triplets based Fact triplets.
Train
Valid
Test
Dutaset
Relation
Entity
Entity
Query
Fact
Entity
Qucry
Fact
Entity
Query
Fact
(yl)
1,594
1,594
4,245
4,245
4,245
200 (v2)
2,608
2,608
9,739
9.739
2,608
1,166
9,739
1,660
478
4,145
FB15k-237 [47]
215 (v3)
3,668
3,668
17,986
17,986
3,668
2,194
17,986
2,501
863
7,406
219 (v4)
4,707
4,707
27,203
27,203
4,707
3,352
27,203
3,051
1,424
11,714
9 (vl)
2,746
2,746
5,410
5,410
2,746
630
5,410
922
188
1,618
(v2)
6,954
6,954
15,262
15,262
6,954
1,838
15.262
2,757
441
4,011
WN18RR [48]
9 (v3)
12,078
12,078
25,901
25,901
12,078
3,097
25,901
5,084
605
6,327
9 (v4)
3,861
3,861
7,940
7,940
3,861
934
7,940
7,084
1,429
12,334
(v1)
3,103
3,103
4,687
4,687
3,103
414
4,687
225
100
833
(y2)
2,564
2,564
15,262
8,219
2,564
8,219
2,086
4,586
NELL-995 [49]
(v3)
4,647
4,647
16,393
16,393
4,647
1,851
16,393
3,566
809
8,048
(v4)
2,092
2,092
7,546
7,546
2,092
876
7,546
2,795
7,073
731
D.4 Hyperparameters Setup.
Coarse-to-Fine reasoning model. In the coarse- gaannee reasoning stage, we directly adopt exist- ing models without any modifications to their original hyperparameter settings.
Paal-Pathway fusion model. For each dataset, we perform hyperparameter tuning on the valida- tion set. We conduct grid search over the following hyperparameters:
Learning rate: (10-1, 5 10-A, 10-3, 5 10-3, 10-2)
Weight decay: {10-5, 10 10-4]
Hidden dimension: {16, 32, 64, 128]
Negative sampling size: (128, 256, 512]
Message passing layers in input encoder: {1, 2, 3}
Message passing layers in local pathway: {1, 3)
Transformer layers in global pathway: {1, 2, 3}
In addition, we initialize the value of randomly within the range (0, 1). Since we use the same ran- dom seed for all datasets, the initial value of a is identical across different datasets and is 0.549. And we report the range of values observed during training across different datasets, as shown in the Ta- blell, Table 12 and Table13. The results show that a consistently converges to stable value during training. with negligible fluctuations afterward (less than 0.001). Across all datasets, converges reliably as expected. Moreover, a remains below the theoretical threshold (Mp))+00mmms (Mo) as stated in Theorem 1.
1+0max(Mo)
Coarse-to-Fine Optimization. In the coarse-to-fine optimization, two key hyperparameters involved: the number of entities the high-confidence subset k and the decision threshold A.
We analyze the impact of the hyperparameter k, which denotes the number of entities in the high- score subset. We conduct experiments on the validation sets of all transductive datasets using our model. We set & to (1, 2, 3, 4, 5, 6, 7, 8. 9, 10, 11, 12, 13, 14, 15). See Table 15. We ultimately
28

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Table 11: The range values observed during training on FB15k-237.
Datasets
FB FB15k-237v1
FB15K-237v2
FB15k-237v3
FB1
Theoretical threshold
2.27
2.44
2.40
2.46
a (Epoch=0)
0.549
0.549
0.549
0,549
(Epoch=2)
0.538
0,518
0.513
0,507
a (Epoch=4)
0.531
0,501
0.498
0.486
(Epoch=6)
0,522
0.485
0.477
0,465
(Epoch=8)
0.514
0,468
0,460
0,450
(Epoch=10)
0.508
0.457
0.445
0,437
(Epoch=12)
0.509
0,458
0,445
0.439
(Epoch=14)
0,511
0.460
0.447
0,440
(6poch=16)
0.512
0,461
0.448
0.441
a (Epoch=18)
0,512
0.461
0.449
0,441
(Epoch=20)
0.512
0.461
0.449
0.441
Table 12: The range a values observed during training on WNI8RR.
Datasets
WNI8RRv1
WNI8RRv2
WNI8RRv3
WNISRRv4
Theoretical threshold
2.17
2.00
2.03
2.10
(Epoch=0)
0.549
0.549
0.549
0.549
a (Epoch=2)
0.539
0.543
0.546
0.543
(Epoch=4)
0.534
0.531
0.534
0.540
a (Fpoch=6)
0.533
0.524
0.536
0.537
(Epoch=8)
0.532
0.512
0.523
0.536
a (Epoch=10)
0.531
0.504
0,511
0.532
(Epoch=12)
0.531
0.505
0.511
0.532
a (Epoch=14)
0.533
0.505
0.510
0.533
(Epoch=16)
0.533
0.505
0.511
0.533
a (Epoch=18)
0.533
0.505
0.511
0.533
(Epoch==0)
0.533
0.505
0.511
0.533
Table 13: The range of a values observed during training on NELL-995.
Datasets
NELL-995v1
NELL-995v2
NELL-995v3
NELL995v4
Theoretical threshold
2.49
2.58
2.54
2.42
(Epoch=0)
0.549
0.549
0.549
0.549
a (Epoch=2)
0.544
0.536
0.526
0.536
(Fpoch=4)
0.539
0.532
0.496
0.516
a (Epoch=6)
0.523
0.525
0,474
0.500
a (Epoch=8)
0,514
0.517
0.447
0.487
a (Epoch=10)
0,514
0,509
0,424
0,477
a (Epoch=12)
0.514
0.509
0.425
0.475
a (Epoch=14)
0,512
0,510
0,425
0,476
a (Epoch=16)
0.512
0.510
0.426
0.476
a (Epoch=18)
0.512
0.510
0.427
0,476
a (Epoch=20)
0.512
0.510
0.427
0.476
select for all the datasets, these settings yield relatively high and stable results across three key metrics MRR, Hits@ 1, and Hits rather than optimizing single metric isolation. We also conduct the same experiments 4 inductive datasets (As shown in Figure 5).
Additionally, We analyze impact of the hyperparameter, iments on all transductive datasets with our model. We set A to [0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5.5, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10). For FB15k-237 and WN 8RR, we set A and for NELL-995 and YAGO3-10. The results are shown in Table 14.
decision threshold A. We run exper-

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1915k
Hova10 (S)
8 8
FB15X 23741
2SV5
0.50
15156-23122
10 1219
19156227ed
Figure 5: Effect of hyperparameter I on the performance metrics of KG reasoning for different datasets (inductive).
Table 14: The results transductive knowledge graph reasoning datasets with different A.
Value
FB15k-237
WNISRR
NELL-995
YAGO3-10
MRR
H@1 1
H@ 10
MRR
H@1
H@ 10
MRR
H@1 1 H@10
MRR
H@1
H@
0.0
0.411
31.9
58.0
0.581
52.5
68.7
0,553
48.1
66.5
0.600
53.0
72.3
0.5
0.423
33.0
59.2
0.584
53.0
68.9
0.572
50.1
69.3
0.613
54.3
73.0
1.0
0,436
34.1
60.6
0.588
53.4
69.0
0.579
50.8
69.8
0.619
54.8
73.5
1.5
0.443
34.7
61.3
0.589
53.6
69.0
0.585
51.4
70.5
0.623
55.2
74.0
2.0
0.447
35.2
61.7
0.590
53.7
69.1
0.589
$1.7
71.1
0.626
55.5
74.4
2.5
0.448
35.3
61.7
0.591
53.8
69.1
0.590
51.8
71.2
0.628
55.7
74.6
3.0
0.450
35.5
61.8
0.591
53.8
69.1
0.592
$2.0
71.2
0.630
55.8
74.7
3.5
0.451
35.6
61.9
0.591
53.8
69.2
0.592
$2.1
71.2
0.631
56.0
74.8
0.452
35.7
62.0
0.591
53.9
69.2
0.592
52.1
71.2
0.632
55.1
74.8
4.5
0.452
35.7
62.1
0.591
53.9
69.2
0.592
52.1
71.2
0.632
56.1
74.9
0.453
35.8
62,2
0.592
53.9
69.2
52.2
71.2
0.632
56.1
74,9
35.8
62,2
0.592
69.2
52.2
71.1
0.632
56.1
74,9
35.9
62.2
0.592
69.2
52.2
71.1
0.632
56.1
74.8
0.454
35.9
62.3
0.592
53.9
0.592
52.2
0.632
56.1
74.8
7.0
0.455
36.0
62.4
0.592
54.0
69.2
0.592
52.2
71.0
0.632
56.1
74.9
7.5
0.456
36.1
62.5
0.593
54.2
69.9
0.592
52.2
71.0
0.632
56.1
74.9
8.0
0.456
36.1
62.8
0.594
54.0
70,0
0.592
52.1
71.0
0.632
56.1
74.9
8.5
0.457
36.1
62.7
0.593
54.0
69.9
0.592
52.1
69.9
0,632
56.0
74.9
9.0
0.456
35.9
62.6
0.593
54.0
69.9
0.592
52.1
69.9
0.632
56.0
74.9
9.5
0.454
35.9
62.6
0.593
54.0
69.2
0.592
52.1
69.9
0.632
56.0
74.9
10.0
0.454
35.9
62.2
0.593
54.1
69.3
0.592
52.1
69.9
0.632
56.0
74.9
Computational Environment. The experiments conducted using Python 3.9.21, PyTorch 2.6.0, and CUDA 12.1, with an NVIDIA A100 80GB GPU.
D.5 Random Initialization.
We run each model three times with different random seeds and report the mean results. We do not report the еттоr bars because our model has very small errors with respect to random initialization. The standard deviations of the results are very small. For example, the standard deviations of MRR. H@ and H 10 of DuetGraph are 9.8 x 10-?, 5.6 6 x 10-7 and 1.95 x 10-5 on FB15k-237 dataset, respectively. WN18RR dataset, the standard deviations of MRR, H@ and H@@ of DuetGraph are 1.607 10-6, 7.77 10-6 and 8.94 x 10-6 respectively. On NELL--955 dataset, the standard deviations of MRR, H@I and H@ 10 of DuetGraph are 5.625 x 10-7 1.0 x 10-8 and 1.89 x 10-5, respectively. On YAGO3-10 dataset, the standard deviations of MRR. H@ and H@ 10 of DuetGraph are 2.64 x 10 6 4.3 10-7 and 2.5 x 10-5, respectively. This indicates that our model is not sensitive the random initialization.
D.6 Ranking Protocol.
Following previous work [19], we conducted experiments on DuetGraph using the strictest ranking protocol (m + 1), where is the number of entities with higher scores than the correct answer and n is the number of entities that receive the same score as the correct answer. We also conducted experiments using widely used but more lenient ranking protocols, namely (m 1) adopted in [71, 36, 72, 73], as shown in Table 16 and Table 17.
Based on the experimental results, can draw the following conclusions.
30

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Table 15: The results on transductive knowledge graph reasoning datasets with different
Value
FB15K-237
WNISRR
-EI.I--95
YAGO3-10
MRR
H@1
H@ 10
MRR
H@1
H@ 10
MRR
H@1
H@ 10
MRR
H@
H@ 10
0.455
37.7
61.6
0.602
55.0
70.4
0.592
$4.6
68.1
0.638
58.3
74.2
0.457
37.0
61.9
0.599
53.6
70.6
0.594
54.6
68.2
0.636
57.0
74.4
0.456
36.4
62.3
0.595
52.4
70.9
0.592
54.1
68.4
0.634
56.5
74.6
4 0.456
36.1
62,8
0.593
52.2
71.2
0.592
54.1
68.5
0.632
56.1
74.9
5
0,454
35.8
63.0
0.591
52.0
71.4
0.593
54.1
68.7
0.631
55.9
75.2
0,452
35.5
63,4
0,589
51.9
71.5
0.593
54.1
69.0
0.629
55.7
73,4
0,452
35.4
63.9
0,589
51.8
71.7
0.594
$4.2
69.3
0.628
55.5
75.6
0,451
35.4
64.2
0.588
51.7
71.9
0.593
54.1
69.5
0.627
55.4
75.8
0,451
35.4
64.6
0.588
51.7
72.1
0.594
54.2
69.8
0.626
55.3
75.9
10 0.450
35.3
65.1
0.587
51.6
72.4
0.594
54.2
70.0
0.626
55.3
76.2
11
0.450
35.3
65.2
0.587
51.5
72.1
0.595
54.1
70.1
0.625
55.2
76.2
12
0.450
35.3
65.2
0.584
51.0
72.1
0.593
53.9
70.0
0.624
55.1
76.2
13
0.449
35.2
65.1
0.583
50.9
72.2
0.592
53.9
69.9
0.624
55.0
76.1
14 0.449
35.2
65.0
0.583
50.9
72.1
0.592
53.9
69.9
0.623
55.0
76.0
15
0.447
35.0
64.9
0.582
72.0
0.591
53.8
69.8
0.623
54.9
75.8
Table 16: Comparision of different under ranking protocols across four datasets.
Method
FB1SK-237
WNISRR
NELL-995
YAGO3-10
MRR
H@1
H@10
MRR
H@1
H@10
MRR
H@1
H@10
MRR
H@1
H@100
KnowFormer (m + v 0.430
34.3
60.8
0.579
68.7
0.566
67.5
0.615
73.4
DuetGraph 0.453
36.1
62.4
0.593
54.2
69.9
0.590
52.1
71.2
0.631
56.1
74.8
DuctGraph (m +
0.456
36.1
62.8
0.594
54.2
70.0
0.593
52.2
71.2
0.632
56.1
74.9
First, switching to the strictest ranking protocol has little impact DuetGraphs quality. As shown in the tables above, when switching the ranking protocol from fm++1) to (m++++1) +1) DuetGraphs quality is virtually unaffected, with most 0.3% drop in MRR, 0. % drop in Hits @ I, and a 0.4% drop in Hits 10. This is because, is 0 in almost all the cases. As shown in the table above, the number of test triplets impacted when replacing (m with (m + + 1) is less than 1%.
Second, DuetGraph achieves SOTA results even under the strictest ranking protocol. As shown above, it surpasses AnyBURL and KnowFormer across all datasets in MRR, Hits and Hits@ 10. For the other baselines, as shown in Table 2 used the official code from their original papers, all of which employ protocols stricter than (m + + 1). As shown in [76], increasing the strictness of ranking protocol yields quality that no higher (and often lower). Even under this tough setting, DuetGraph consistently outperforms all of them, providing strong evidence of its SOTA performance.
E
More Experimental Results
E.1
Model Size and Inference Time.
Despite employing two-stage reasoning strategy, DuetGraph exhibits significantly superior infer- ence efficiency compared to KnowFormer[19]] This advantage is primarily attributed our inno- vative parallel processing architecture and a lightweight coasse-grained model selection mechanism. These components work synergistically, enabling DuetGraph to achieve this higher efficiency at comparable model scale, detailed in Table 18.
As shown in Table 18, the inference efficiency improvement is especially notable large-scale knowledge graphs, such as YAGO3-10, where our method achieves 34.2% increase in inference efficiency compared the SOTA model KnowFormer[[9]].
E.2 The difference between a and graph attention.
The main differences reflected in the following three perspectives:
31

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Table 17: Comparison of different ranking protocols across very large knowledge graphs. (Non- deterministic ranking [74, 63, 75] means that when two entities share the same score, their original order is preserved in the ranking. Compared with the + n + ranking protocol, this is more lenient.)
Method
Wikidata5M
Freebase
MRR
H@1
@@1 10
MRR
H@1 1
@@ 10
AnyBURL (Non-Detenn) Denermetriiiiittcc Ranking)
0.350
30.9
42.9
0.588
53.6
68.2
KnowFormer (m + n + 1)
0.332
26.7
46.3
0.684
65.7
73.6
DuetGraph (m + n + 1)
0.363
32.7
49.5
0.697
69.3
73.8
DuetGraph (m +
0.363
32.7
49.5
0.699
69.4
73.9
Table 18: Comparison of Model Size and Inference Time across different datasets.
Datasets
FB15k-237
WNISRR
NELL-995
YAGO3-10
Metries
Size (M)
Time (ms)
Size (M)
Time (ms)
Size (M)
Time (ms)
Size (M)
Time (ms)
DuetGruph
347.07
292.49
7.2
261.32
3,4
397.22
(Onaee && Faz: S9)
(Coana: 09 Fixc
(Chane: Fizz
(Comc Fax: Li)
KnowFormer[[
499.71
392.40
5.2
360.40
1.0
905.22 22
As illustrated in Figure 2, the graph attention mechanism (Step 2) first learns global weights, which subsequently inform the learning of the control parameter a (Step 4). The attention weights serve as intermediate representations that enable a to effectively balance local and global information.
Technical Role.:
Theoretical Advantage:: Introducing a allows for better fusion of the global weights cap- tured by the attention mechanism (Step 2) and the local weights acquired via message passing (Step 3), which helps mitigate over-smoothing and enhances the models quality, as shown in Theorem 1.
Experimental Study.: Incorporating a achieves better performance compared to using attention mechanism alone, shown in Table 19.
Table 19: Results comparing the model with and without the parameter.
Metrics
1B31k-2377
WNISRR
NELL-995
YAGO3-10
MRR
Hite01
Hiss
MRR
Hits@1
MRR
Hits@
His
MRR
Hiss@0
Hit@@
w/
0.456
36.1
62.8
0.594
54.2
70.0
0.593
52.2
71.2
0.632
56.1
74.9
only atteution
0.445
35.1
61.2
0.584
54.1
69.0
0.582
51.0
70.3
0.617
54.2
73.7
Limitations and Broader Impacts
F.1 Limitations
Although DuetGraph has demonstrated its effectiveness in improving reasoning performance on several public benchmarks, many challenges remain be addressed. For instance, its black-box decision process poses challenges for domains such as biomedicine, where expert interpretability and traceability are essential. Future work may incorporate explainability modules along with in- teractive visualization tools to help users understand the reasoning process of the model, thereby improving trustworthiness and applicability in real-world scenarios such as clinical diagnosis and drug discovery [77].
F.2 Broader Impacts
DuetGraph is framework for knowledge graph reasoning that offers strong support for predicting missing information in real-world social networks. And DuctGraph holds great potential for accel- erating discovery in biomedical domains, such drug repurposing and disease-gene association prediction.
32


Reviews:
[{"review_id": "DvVABsQnvM", "reviewer": "Reviewer_qRnh", "summary": "This paper introduces DuetGraph, a novel knowledge graph (KG) reasoning framework designed to mitigate the problem of \"score over-smoothing\"  which often blurs the distinction between correct and incorrect answers in existing KG reasoning methods. DuetGraph addresses this through two main innovations: a dual-pathway global-local fusion mechanism and a coarse-to-fine reasoning optimization.", "questions": "Adaptive Fusion Parameter (α): The paper mentions that the adaptive fusion approach \"drives α below the theoretical threshold in Theorem 1 via parameter update with gradient descent\". Could the authors elaborate on how this parameter α is initialized and empirically how its value changes during training across different datasets? Are there any cases where α does not converge as expected, and what might be the implications?\n\n\nImpact of Coarse Model Choice: Table 4 shows DuetGraph's performance with different coarse models. While the results are consistently good, can the authors provide more insight into the characteristics of a \"good\" coarse model for DuetGraph? For instance, does the performance of the coarse model directly correlate with the final DuetGraph performance, or does DuetGraph's coarse-to-fine mechanism mitigate weaknesses of less effective coarse models?", "limitations": "Yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Originality: The core idea of segregating local and global information processing into dual pathways, rather than stacking them, is novel and directly addresses the identified problem of score over-smoothing. The coarse-to-fine optimization further enhances this by refining the candidate space\n\nGeneralizability of Coarse Models: While DuetGraph shows consistent outperformance with various coarse-grained models, deeper analysis into why certain coarse models might perform better or worse within the DuetGraph framework could provide more insight.", "was_revised": true, "final_justification": "agree to accept", "rebuttal": ">**Q1: Adaptive Fusion Parameter (α): The paper mentions that the adaptive fusion approach \"drives α below the theoretical threshold in Theorem 1 via parameter update with gradient descent\". Could the authors elaborate on how this parameter α is initialized and empirically how its value changes during training across different datasets? Are there any cases where α does not converge as expected, and what might be the implications?**\n\n**Response to Q1**: Thanks for your comments. In our setting, we initialize the value of α randomly within the range (0, 1). Since we use the same random seed for all datasets, the initial value of α is identical across different datasets and is 0.549, as shown in the table below. Following your advice, we report the range of α values observed during training across different datasets, as shown in the table below.\n\n| Datasets | FB15k-237_v1 | FB15k-237_v2 | FB15k-237_v3 | FB15k-237_v4 |\n|:--------:|:------------:|:------------:|:------------:|:------------:|\n| Theoretical threshold |     2.27     |     2.44     |     2.40     |      2.46    |\n| α (Epoch=0) |     0.549    |     0.549    |    0.549    |     0.549    |\n| α (Epoch=2) |     0.538    |     0.518    |    0.513    |     0.507    |\n| α (Epoch=4) |     0.531    |     0.501    |    0.498    |     0.486    |\n| α (Epoch=6) |     0.522    |     0.485    |    0.477    |     0.465    |\n| α (Epoch=8) |     0.514    |     0.468    |    0.460    |     0.450    |\n| α (Epoch=10) |     0.508    |     0.457    |    0.445    |     0.437    |\n| α (Epoch=12) |     0.509    |     0.458    |    0.445    |     0.439    |\n| α (Epoch=14) |     0.511    |     0.460    |    0.447    |     0.440    |\n| α (Epoch=16) |     0.512    |     0.461    |    0.448    |     0.441    |\n| α (Epoch=18) |     0.512    |     0.461    |    0.449    |     0.441    |\n| α (Epoch=20) |     0.512    |     0.461    |    0.449    |    0.441    |\n\n| Datasets | NELL-995_v1 | NELL-995_v2 | NELL-995_v3 | NELL-995_v4 |\n|:--------:|:------------:|:------------:|:------------:|:------------:|\n| Theoretical threshold | 2.49    | 2.58    | 2.54    | 2.42    |\n| α (Epoch=0) | 0.549   | 0.549   | 0.549   | 0.549   |\n| α (Epoch=2) | 0.544   | 0.536   | 0.526   | 0.536   |\n| α (Epoch=4) | 0.539   | 0.532   | 0.496   | 0.516   |\n| α (Epoch=6) | 0.523   | 0.525   | 0.474   | 0.500   |\n| α (Epoch=8) | 0.514   | 0.517   | 0.447   | 0.487   |\n| α (Epoch=10) | 0.514   | 0.509   | 0.424   | 0.477   |\n| α (Epoch=12) | 0.514   | 0.509   | 0.425   | 0.475   |\n| α (Epoch=14) | 0.512   | 0.510   | 0.425   | 0.476   |\n| α (Epoch=16) | 0.512   | 0.510   | 0.426   | 0.476   |\n| α (Epoch=18) | 0.512   | 0.510   | 0.427   | 0.476   |\n| α (Epoch=20) | 0.512   | 0.510   | 0.427   | 0.476   |\n\n|       Datasets        | WN18RR_v1 | WN18RR_v2 | WN18RR_v3 | WN18RR_v4 |\n| :-------------------: | :-------: | :-------: | :-------: | :-------: |\n| Theoretical threshold |   2.17    |   2.00    |   2.03    |   2.10    |\n|      α (Epoch=0)      |   0.549   |   0.549   |   0.549   |   0.549   |\n|      α (Epoch=2)      |   0.539   |   0.543   |   0.546   |   0.543   |\n|      α (Epoch=4)      |   0.534   |   0.531   |   0.534   |   0.540   |\n|      α (Epoch=6)      |   0.533   |   0.524   |   0.536   |   0.537   |\n|      α (Epoch=8)      |   0.532   |   0.512   |   0.523   |   0.536   |\n|     α (Epoch=10)      |   0.531   |   0.504   |   0.511   |   0.532   |\n|     α (Epoch=12)      |   0.531   |   0.505   |   0.511   |   0.532   |\n|     α (Epoch=14)      |   0.532   |   0.505   |   0.510   |   0.533   |\n|     α (Epoch=16)      |   0.533   |   0.505   |   0.511   |   0.533   |\n|     α (Epoch=18)      |   0.533   |   0.505   |   0.511   |   0.533   |\n|     α (Epoch=20)      |   0.533   |   0.505   |   0.511   |   0.533   |\n\nThe results show that α consistently converges to a stable value during training, with negligible fluctuations afterward (less than 0.001). Across all datasets, α converges reliably as expected. Moreover, α remains below the theoretical threshold \n\n$\\frac{\\sigma_{max}(\\mathcal{M}_{\\mathrm{D}})+\\sigma\\_{max}(\\mathcal{M}\\_{\\mathrm{O}})}{1+\\sigma\\_{max}(\\mathcal{M}\\_{\\mathrm{O}})}$\n\nas stated in **Theorem 1** of the manuscript. \nThis supports our claim that the proposed dual-pathway model more effectively mitigates score over-smoothing than the single-pathway model, aligning with the theoretical bound.\n\n>**Q2: Impact of Coarse Model Choice: Table 4 shows DuetGraph's performance with different coarse models. While the results are consistently good, can the authors provide more insight into the characteristics of a \"good\" coarse model for DuetGraph? For instance, does the performance of the coarse model directly correlate with the final DuetGraph performance, or does DuetGraph's coarse-to-fine mechanism mitigate weaknesses of less effective coarse models?**\n>\n>**W1: Generalizability of Coarse Models: While DuetGraph shows consistent outperformance with various coarse-grained models, deeper analysis into why certain coarse models might perform better or worse within the DuetGraph framework could provide more insight.**\n\n**Response to Q2 and W1**: \nThanks for your insightful comments. \n\n***Key Observations from Table 4.*** Our experiments in **Table 4** evaluate different coarse model categories (triplet-based, message passing-based, and transformer-based) and their effect on final model quality. \nThe results show: triplet-based models perform best as coarse models; message passing-based models rank second; and transformer-based models yield the weakest performance in this role.\n\n***Characteristics of a Good Coarse Model.***\nAs supported by prior work [1], **architectural diversity between coarse and fine models enhances overall performance**. \nSpecifically, the fine model of DuetGraph captures global information, while the triplet-based coarse model focuses only on local triple-level patterns, maximizing architectural difference. In contrast, transformer-based coarse model also handles global information, making its architectural gap from the fine model the smallest. The message passing-based model captures information from local neighborhoods and offers a moderate diversity. This explains why the triplet-based model—despite its simplicity—emerges as the most effective coarse model.\n\n***Does Coarse Model Performance Directly Affect DuetGraph?*** The answer is **NO**. As shown in **Tables 2** and **4** of the manuscript, the performance of DuetGraph does not depend on the standalone performance of the coarse model. Instead, it compensates for weaker coarse models by refining their outputs. For example, when integrating the **worst** triplet-based model (e.g., TransE [2]) into the coarse model in dataset WN18RR, DuetGraph boosts its **MRR** (Model Quality Metric) from **0.222** to **0.593**, **Hits@1** from **1.4%** to **54.2%**, and **Hits@10** from **52.8%** to **69.0%**, resulting in significant improvements of **0.371**, **52.8%**, and **16.2%**, respectively. Moreover, the enhanced performance of TransE [2] exceeds that of the SOTA model (e.g., KnowFormer [3]), with respective **MRR**, **Hits@1**, and **Hits@10** values of **0.579**, **52.8%**, and **68.7%**, as presented in **Table 2** of the manuscript.\n\nWe will include the analysis in the revised version of the manuscript to clarify these points.\n\n---\n**Reference**: \n\n[1] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 202\n\n[2] Bordes et al. Translating Embeddings for Modeling Multi-relational Data. NIPS 2013: 2787-2795\n\n[3] Liu et al. KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning. ICML 2024"}, {"review_id": "M9RhA3N1dL", "reviewer": "Reviewer_GAC5", "summary": "This paper proposed a framework named DuetGraph for knowledge graph reasoning designed to overcome the over-smoothing problem that plagues existing methods. Duet Graph achieves this through two key techniques, dual-pathway global-local fusion and coarse-to-fine reasoning optimization. The core contributions include:\n- Targets the over-smoothing issue: By decoupling and adaptively fusing information, DuetGraph mitigates the problem of incorrect answers receiving scores similar to the correct ones.\n- Theoretical justification: The paper provides theoretical proofs for the effectiveness of the proposed model and optimization, providing a strong foundation for its claims.\n- Performance improvement: Extensive experiments on various datasets and tasks validate the effectiveness of the proposed method.", "questions": "No further questions. Please refer to the weaknesses.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n- The paper targets a fundamental task and a critical issue, i.e., the over-smoothing problem.\n- The paper provides theoretical proofs for the effectiveness of the proposed model and optimization.\n\nWeaknesses:\n- The presentation needs improvement. I can hardly understand the task when I first read the abstract, especially the concept of KG reasoning. It seems the task is the same with KG representation learning.\n- The text description of the local and global pathways is inconsistent with Figure 1.\n- In Equation (1), $\\alpha$ is used to balance the local and global information. Please clarify the difference between learning the control parameter and using the graph attention network to learn different attention weights.\n- In the coarse-to-fine reasoning, what is the standard of the coarse model? It seems all the baseline models could act as coarse models, and the proposed fine reasoning conducts re-ranking.\n- In the evaluation, 1) What is the task definition of inductive and transductive reasoning? 2) In inductive reasoning, why divide the datasets? 3) In the transductive reasoning, the paper claims the baseline results are directly from the original papers, but there are some inconsistencies, e.g., the RotatE. If the results are reproduced based on publicly available code, please clarify where the gaps exist. 4) Section 2 claims the paper primarily focuses on the tail entity completion. Triple classification is also a typical task. Can the framework be applied to it?", "was_revised": true, "final_justification": "The responses clarify most of my concerns, and I decided to raise my ratings accordingly.", "rebuttal": "> **W1: The presentation needs improvement. I can hardly understand the task when I first read the abstract, especially the concept of KG reasoning. It seems the task is the same with KG representation learning.**\n\n**Response to W1**: Thanks for your advice. We appreciate the opportunity to clarify the relationship between KG reasoning and representation learning, as well as to improve the presentation of the abstract.\n\n***Clarifying KG Reasoning vs. Representation Learning***. While the concepts of the two are closely related, they serve for different purposes:\n\n- **KG Representation Learning** encodes KG entities and relations into vector representations, capturing their semantic and structural relationships. This enables computational understanding and enhances KG's expressiveness.\n\n- **KG Reasoning** focuses on inferring missing information (e.g., predicting new facts) from existing data, thus addressing KG incompleteness. As noted in Section 1 of [1], reasoning relies on the embeddings learned through representation learning to perform tasks such as link prediction.\n\n**In summary**, KG representation learning provides the foundational embeddings, while reasoning uses them for knowledge inference [2].\n\n**Definitions in the Manuscript**. We define KG reasoning explicitly in **lines 21-22 (Section 1)** and **lines 81-86 (Section 2)**, following the way of concept formulation in prior work, e.g., **Section 3 of [3]**, **Section 2 of [4]**, and **Section 1 of [1]**. \n      \n**Transferability of Learned Representations**. Beyond reasoning tasks, DuetGraph's learned KG representations demonstrate strong transferability, achieving SOTA performance on downstream tasks like triplet classification (see Response to W5(4) for experimental results).\n      \nFollowing your advice, we will revise the abstract to clarify this definition of KG reasoning and differentiate it from KG representation learning.\n\n\n> **W2: The text description of the local and global pathways is inconsistent with Figure 1.**\n\n**Response to W2**: You are right. There are two numbering errors in the textual descriptions of the pathways (**lines 112 and 113**):\n\n-  \"local pathway (Step 2)\" should be \"local pathway (Step 3)\"\n-  \"global pathway (Step 3)\" should be \"global pathway (Step 2)\"\n\nWe apologize for any confusion this may have caused. These corrections will be made in the revised manuscript \n\n> **W3: In Equation (1), α is used to balance the local and global information. Please clarify the difference between learning the control parameter and using the graph attention network to learn different attention weights.**\n\n**Response to W3**: Thank you for your insightful question regarding the distinction between learning the control parameter α and using graph attention weights. We clarify this difference from three perspectives:\n\n- **Technical Role**. As illustrated in Figure 2, the graph attention mechanism (Step 2) first learns global weights, which subsequently inform the learning of the control parameter α (Step 4). The attention weights serve as intermediate representations that enable α to effectively balance local and global information.\n  \n- **Theoretical Advantage**. Introducing α allows for better fusion of the global weights captured by the attention mechanism (Step 2) and the local weights acquired via message passing (Step 3), which helps mitigate over-smoothing and enhances the model’s quality, as shown in **Theorem 1** of the manuscript.\n  \n- **Experimental Study**. Incorporating α achieves better performance compared to using attention mechanism alone, as shown in the table below.\n\n|Dataset| FB15k-237|||WN18RR|||NELL-995|||YAGO3-10|||\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|Metrics|MRR|Hits@1|Hits@10|MRR|Hits@1|Hits@10|MRR|Hits@1|Hits@10|MRR|Hits@1| Hits@10|\n|w/ α|**0.456**|**36.1**|**62.8**|**0.594**|**54.2**| **70.0**|**0.593**|**52.2**|**71.2**|**0.632**|**56.1**| **74.9**|\n|only w/ attention|0.445|35.1|61.2|0.584|54.1|69.0|0.582|51.0| 70.3|0.617|54.2|73.7|\n\n\n​    \n> **W4: In the coarse-to-fine reasoning, what is the standard of the coarse model? It seems all the baseline models could act as coarse models, and the proposed fine reasoning conducts re-ranking.**\n\n**Response to W4**: Thanks for your insightful comments. \n\n**Architectural Diversity Principle.** As established in prior work [5], maximizing architectural diversity between coarse and fine models leads to better overall performance. This principle also applies for coarse model selection in DuetGraph.\n\n**Performance Validation.** Our experiments in **Table 4** evaluate different coarse model categories (triplet-based, message passing-based, and transformer-based) and their effect on final model quality, where triplet-based model focuses exclusively on local triple-level patterns, message passing model captures neighborhood-level information, and transformer model handles global patterns (like our fine model). \n\nAs demonstrated in **Table 4**, the triplet-based model achieves the best performance as a coarse model due to its maximal architectural difference from our global-information-focused fine model. This supports the diversity principle.\n\n\n\n>**W5: In the evaluation,**  \n>(1) **What is the task definition of inductive and transductive reasoning?**  \n>(2) **In inductive reasoning, why divide the datasets?**  \n>(3) **In the transductive reasoning, the paper claims the baseline results are directly from the original papers, but there are some inconsistencies, e.g., the RotatE. If the results are reproduced based on publicly available code, please clarify where the gaps exist.**  \n>(4) **Section 2 claims the paper primarily focuses on the tail entity completion. Triple classification is also a typical task. Can the framework be applied to it?**\n\n**Response to W5**: Thanks for your valuable comments. \n\n(1) **Transductive vs. Inductive Reasoning:** Following the formal definition in [6], transductive reasoning assumes that all test entities appear during training, while inductive reasoning handles completely unseen entities during testing. This difference is fundamental to evaluating model generalization capabilities.\n\n(2) **Dataset Construction for Inductive Evaluation:** Following the methodology in [7], we construct our inductive evaluation datasets by ensuring complete separation between training and test entities. This strict partitioning, where test entities are excluded from training, enables a reliable assessment of the model's generalization capability to unseen knowledge.\n\n(3)  **Reproduction of RotatE Results:** We clarify that the results of RotatE are reproduced based on publicly available code in [8]. For more rigorous evaluations, we adopted the widely used data augmentation strategy in [9, 10, 11] by incorporating inverse triplets [12] during both training and inference, because this can ensure symmetry and coherence between queries and answers, as shown in [13]. Notably, this differs from the original RotatE implementation [8], which excluded inverse triplets. This accounts for the performance variation observed.\n\n(4)  **Performance on Triple Classification:** To demonstrate DuetGraph's generalizability, we evaluate its performance on triple classification using the following setup:\n\n- Datasets: UMLS [14], FB13 [15] and WN11 [15] (Standard benchmark datasets for knowledge graph tasks)\n- Baselines: triplet-based (HousE [16]), message passing-based (AdaProp [17]), transformer-based (HittER [18]), and hybrid message passing-transformer (KnowFormer [3]) models (SOTA methods for comprehensive comparison)\n\n|Method|UMLS Accuracy (%)|FB13 Accuracy (%)|WN11 Accuracy (%)|\n|:-:|:-:|:-:|:-:|\n|HousE|83.1|69.8|65.3|\n|HittER|59.4|62.2|69.6|\n|AdaProp|77.0|71.9|67.1|\n|KnowFormer|83.1|77.3|70.2|\n|DuetGraph|**84.3**|**80.0**|**71.9**|\n\nThe experimental results demonstrate that DuetGraph consistently outperforms all baseline methods across all datasets, achieving new SOTA performance on the triple classification task.\n\n---\n**Reference:**  \n\n[1] Wu et al. KRLGI: Knowledge Representation Learning Based on Global Information for Reasoning. ICTAI 2024\n\n[2] Chen et al. An Overview of Knowledge Graph Reasoning: Key Technologies and Applications. J. Sens. Actuator Networks 2022\n\n[3] Liu et al. KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning. ICML 2024\n\n[4] Zhu et al. A\\*Net: A Scalable Path-based Reasoning Approach for Knowledge Graphs. NeurIPS 2023\n\n[5] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 2022\n\n[6] Zhang et al. Logical Reasoning with Relation Network for Inductive Knowledge Graph Completion. KDD 2024\n\n[7] Chen et al. Meta-Knowledge Transfer for Inductive Knowledge Graph Embedding. SIGIR 2022\n\n[8] Sun et al. RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space. ICLR 2019\n\n[9] Kazemi et al. SimplE Embedding for Link Prediction in Knowledge Graphs. NeurIPS 2018\n\n[10] Wang et al. SimKGC: Simple Contrastive Knowledge Graph Completion with Pre-trained Language Models. ACL 2022\n\n[11] Xiong et al. DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning. EMNLP 2017\n\n[12] Lacroix et al. Canonical Tensor Decomposition for Knowledge Base Completion. ICML 2018\n\n[13] Li et al.  KERMIT: Knowledge graph completion of enhanced relation modeling with inverse transformation. Knowl. Based Syst. 2025\n\n[14] Olivier et al. The Unified Medical Language System (UMLS): integrating biomedical terminology. Nucleic Acids Res. 2004\n\n[15] Socher et al. Reasoning With Neural Tensor Networks for Knowledge Base Completion. NIPS 2013\n\n[16] Li et al. HousE: Knowledge Graph Embedding with Householder Parameterization. ICML 2022\n\n[17] Zhang et al. AdaProp: Learning Adaptive Propagation for Graph Neural Network based Knowledge Graph Reasoning. KDD 2023\n\n[18] Chen et al. HittER: Hierarchical Transformers for Knowledge Graph Embeddings. EMNLP 2021"}, {"review_id": "F4li07znhb", "reviewer": "Reviewer_CuGL", "summary": "This paper introduces DuetGraph, a new method for knowledge graph reasoning that solves the over-smoothing problem in deep models. The authors point out two main issues: combining local and global reasoning in one path causes over-smoothing, and single-stage models lack enough reasoning power. DuetGraph uses a dual-pathway design to separate local and global reasoning and combines their results with a learnable weight. It also uses a coarse-to-fine strategy, where a simple model first selects candidates, and a stronger model refines the results. A score gap-based method helps choose the final answer. The paper includes theory showing DuetGraph reduces over-smoothing better than older models, and experiments prove it achieves strong performance on multiple datasets.", "questions": "* Q1: In Line 81, the authors state that other KG completion tasks can be reformulated as tail entity completion. Could the authors explain how the relation prediction task (h, ?, t), which is structurally distinct, can be transformed into tail entity prediction task?\n* Q2: The manuscript introduces the hyperparameter ∆ in the coarse-to-fine reasoning stage. Could the authors clarify how ∆ is set in the experiments? Additionally, it would be valuable to include an ablation study analyzing the sensitivity of model performance to different values of ∆, to better understand its impact.\n* Q3: The coarse ranking model plays a crucial role in the DuetGraph framework. Could the authors provide an ablation study or analysis to quantify how much the coarse ranking component contributes to the overall performance?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "# Strengths\n\n* The paper proposes a novel dual-pathway architecture that decouples local (message passing) and global (transformer) reasoning. This design mitigates over-smoothing and enables parallel computation, leading to both improved performance and training efficiency.\n* The paper provides rigorous theoretical analysis, including score gap bounds and convergence behavior, to support the proposed architecture and its claimed benefits.\n* The experiments cover diverse datasets, include key ablation studies, and provide comparison on LLM based methods (performance and data leakage), offering solid empirical support for the proposed method.\n\n# Weaknesses\n\n* The hyperparameter ∆ used in the coarse-to-fine stage appears important to the final decision, yet its selection strategy is not discussed. There is no ablation study to show its impact on performance.\n* The contribution of the coarse ranking model to overall performance is unclear. An ablation experiment isolating the effect of modifying the coarse stage would strengthen the claims.", "was_revised": true, "final_justification": "Regarding Q1, the explanation on reformulating relation prediction into the tail entity completion paradigm is clear. The clarification that both tasks rely on the same scoring mechanism—fixing two elements and ranking the third—is convincing and consistent with prior approaches.\n\nFor Q2/W1, the discussion on the hyperparameter ∆ is now sufficiently addressed. The authors provided a clear grid search strategy and included a detailed ablation analysis demonstrating the model’s robustness to different ∆ values. The empirical results show stable improvements and low sensitivity, which alleviates the initial concern.\n\nRegarding Q3/W2, the ablation study and architectural comparisons in Tables 3 and 4 effectively demonstrate the impact of the coarse ranking module. The quantitative degradation observed when removing the component, along with the justification for using the triplet-based architecture, provide strong support for its importance in the framework.\n\nOverall, the author responses have resolved my concerns. I have no further questions at this point. I would like to keep my score.", "rebuttal": ">**Q1: In Line 81, the authors state that other KG completion tasks can be reformulated as tail entity completion. Could the authors explain how the relation prediction task (h, ?, t), which is structurally distinct, can be transformed into the tail entity prediction task?**\n\n**Response to Q1**: Thanks for your comments. The relation prediction task (h, ?, t) can indeed be transformed to fit our tail completion paradigm through the approach in [1]:\n\n- **Scoring Mechanism:** For relation prediction, we fix head (h) and tail (t) entities, then score all candidate relations. For tail prediction, we fix the head (h) and relation (r), then score all candidate tails. Both tasks use the same underlying scoring function.\n\n- **Implementation:** For relation prediction, we compute a score for each candidate relation and select the one with the highest score as the prediction. \n\nThis approach maintains fundamental consistency with tail entity prediction. While the surface-level structures differ, both tasks share the same underlying computational paradigm: evaluating possible completions against fixed components of the triple using a unified scoring mechanism. \n\n>**Q2: The manuscript introduces the hyperparameter ∆ in the coarse-to-fine reasoning stage. Could the authors clarify how ∆ is set in the experiments? Additionally, it would be valuable to include an ablation study analyzing the sensitivity of model performance to different values of ∆, to better understand its impact.**\n>\n>**W1: The hyperparameter ∆ used in the coarse-to-fine stage appears important to the final decision, yet its selection strategy is not discussed. There is no ablation study to show its impact on performance.**\n\n**Response to W1 and Q2 :** Thanks for your advice. Due to space limitations, we have provided a preliminary discussion on the design strategy of ∆ in **Section D.2 (lines 722–725)** of the appendix. \n\nFor all datasets, we set ∆ to {0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10} and report the best results. For FB15k-237 and WN18RR, we set ∆ as 8 and set ∆ as 5 for NELL-995 and YAGO3-10. We additionally report the detailed model performance and its variation with different ∆, as shown in the table below.\n\n| Dataset | FB15K-237 |           |            | NELL-985  |           |            |  WN18RR  |           |            | YAGO3-10  |           |            |\n| :-----: | :-------: | :-------: | :--------: | :-------: | :-------: | :--------: | :-------: | :-------: | :--------: | :-------: | :-------: | :--------: |\n| Metrics |    MRR    | Hits@1(%) | Hits@10(%) |    MRR    | Hits@1(%) | Hits@10(%) |    MRR    | Hits@1(%) | Hits@10(%) |    MRR    | Hits@1(%) | Hits@10(%) |\n|   ∆=0   |   0.411   |   31.9    |    58.0    |   0.553   |   48.1    |    66.5    |   0.581   |   52.5    |    68.7    |   0.600   |   53.0    |    72.3    |\n|  ∆=0.5  |   0.423   |   33.0    |    59.2    |   0.572   |   50.1    |    69.3    |   0.584   |   53.0    |    68.9    |   0.613   |   54.3    |    73.0    |\n|   ∆=1   |   0.436   |   34.1    |    60.6    |   0.579   |   50.8    |    69.8    |   0.588   |   53.4    |    69.0    |   0.619   |   54.8    |    73.5    |\n|  ∆=1.5  |   0.443   |   34.7    |    61.3    |   0.585   |   51.4    |    70.5    |   0.589   |   53.6    |    69.0    |   0.623   |   55.2    |    74.0    |\n|   ∆=2   |   0.447   |   35.2    |    61.7    |   0.589   |   51.7    |    71.1    |   0.590   |   53.7    |    69.1    |   0.626   |   55.5    |    74.4    |\n|  ∆=2.5  |   0.448   |   35.3    |    61.7    |   0.590   |   51.8    |    71.2    |   0.591   |   53.8    |    69.1    |   0.628   |   55.7    |    74.6    |\n|   ∆=3   |   0.450   |   35.5    |    61.8    |   0.592   |   52.0    |    71.2    |   0.591   |   53.8    |    69.1    |   0.63    |   55.8    |    74.7    |\n|  ∆=3.5  |   0.451   |   35.6    |    61.9    |   0.592   |   52.1    |    71.2    |   0.591   |   53.8    |    69.2    |   0.631   |   56.0    |    74.8    |\n|   ∆=4   |   0.452   |   35.7    |    62.0    |   0.592   |   52.1    |    71.2    |   0.591   |   53.9    |    69.2    |   0.631   |   56.0    |    74.8    |\n|  ∆=4.5  |   0.452   |   35.7    |    62.1    |   0.592   |   52.1    |    71.2    |   0.591   |   53.9    |    69.2    |   0.631   |   56.1    |    74.9    |\n|   ∆=5   |   0.453   |   35.7    |    62.1    | **0.593** | **52.2**  |  **71.2**  |   0.592   |   53.9    |    69.2    | **0.632** | **56.1**  |  **74.9**  |\n|  ∆=5.5  |   0.453   |   35.8    |    62.2    |   0.593   |   52.2    |    71.1    |   0.592   |   53.9    |    69.2    |   0.632   |   56.1    |    74.9    |\n|   ∆=6   |   0.454   |   35.9    |    62.2    |   0.593   |   52.2    |    71.1    |   0.592   |   53.9    |    69.2    |   0.632   |   56.1    |    74.8    |\n|  ∆=6.5  |   0.454   |   35.9    |    62.3    |   0.592   |   52.2    |    71.1    |   0.592   |   53.9    |    69.2    |   0.632   |   56.1    |    74.8    |\n|   ∆=7   |   0.455   |   36.0    |    62.4    |   0.592   |   52.2    |    71.0    |   0.592   |   53.9    |    69.2    |   0.632   |   56.1    |    74.9    |\n|  ∆=7.5  |   0.456   |   36.1    |    62.5    |   0.592   |   52.2    |    71.0    |   0.593   |   54.0    |    69.9    |   0.632   |   56.1    |    74.9    |\n|   ∆=8   | **0.456** | **36.1**  |  **62.8**  |   0.592   |   52.1    |    71.0    | **0.594** | **54.2**  |  **70.0**  |   0.632   |   56.1    |    74.9    |\n|  ∆=8.5  |   0.457   |   36.1    |    62.7    |   0.592   |   52.1    |    69.9    |   0.593   |   54.0    |    69.9    |   0.632   |   56.0    |    74.9    |\n|   ∆=9   |   0.456   |   35.9    |    62.6    |   0.592   |   52.1    |    69.9    |   0.593   |   54.0    |    69.9    |   0.632   |   56.0    |    74.9    |\n|  ∆=9.5  |   0.454   |   35.9    |    62.6    |   0.592   |   52.1    |    69.9    |   0.593   |   54.0    |    69.2    |   0.632   |   56.0    |    74.9    |\n|  ∆=10   |   0.454   |   35.9    |    62.2    |   0.592   |   52.1    |    69.9    |   0.593   |   54.1    |    69.3    |   0.632   |   56.0    |    74.9    |\n\nAs shown in the table, the model performance consistently improves as ∆ increases from 0, then gradually stabilizes (< 0.1% variation in MRR, Hits@1 and Hits@10) around its optimal value. Also, the model's performance is not sensitive to the value of ∆.\n\n\n>**Q3: The coarse ranking model plays a crucial role in the DuetGraph framework. Could the authors provide an ablation study or analysis to quantify how much the coarse ranking component contributes to the overall performance?**\n>\n>**W2: The contribution of the coarse ranking model to overall performance is unclear. An ablation experiment isolating the effect of modifying the coarse stage would strengthen the claims.**\n\n**Response to W2 and Q3**: Thanks for your insightful comments. The importance of this component is quantitatively demonstrated in our ablation studies presented in **Tables 3 and 4** of the manuscript.\n\nIn **Table 3**, the \"w/o Coarse-to-Fine reasoning\" condition reveals that removing the coarse ranking component leads to performance degradation of up to **2.7%** in MRR and **2.5%** in Hits@1 metrics. This significant drop confirms the crucial role of the coarse model in our framework's overall performance.\n\nThe impact of different coarse model architectures is systematically evaluated in **Table 4**. Our analysis shows that the triplet-based model emerges as the most effective choice, consistently outperforming both message passing-based and transformer-based alternatives. \n\nThis finding aligns with the architectural diversity principle established in prior work [2], which suggests that **complementary model architectures yield better combined performance**. The superiority of the triplet-based approach stems from its maximal architectural difference from our fine model. While the fine model of DuetGraph specializes in capturing global information, the triplet-based coarse model focuses exclusively on local triple patterns, **maximizing architectural difference**. \n\nIn contrast, the transformer-based coarse model shows weaker performance due to its **functional overlap** with our fine model's global processing. The message passing-based model takes a middle position, capturing neighborhood-level information that partially overlaps with both approaches.\n\nThe results collectively show that our method performs the **best** when compared with different architectures, where the triplet model's local focus provides **the most complementary functionality** to our fine model's global view.\n\n---\n**Reference**:\n\n[1] Balazevic et al. TuckER: Tensor Factorization for Knowledge Graph Completion. EMNLP/IJCNLP (1) 2019: 5184-5193\n\n[2] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 2022"}, {"review_id": "LbcgGxa2dH", "reviewer": "Reviewer_hDcp", "summary": "This paper presents DuetGraph, a dual-pathway architecture for knowledge graph reasoning that integrates local and global information via a coarse-to-fine strategy. Experiments show consistent gains over strong baselines across multiple benchmarks.\n\nWhile the design is novel and results are promising, concerns remain. The inference efficiency and model size are not evaluated, despite the system’s complex two-stage structure. The motivation for the parallel fusion mechanism is unclear and not empirically supported. Notably, removing the coarse-to-fine module results in performance worse than KnowFormer, raising questions about the necessity of this design. Additionally, the paper contains several reference errors.", "questions": "- The proposed model combines both global and local knowledge graph information. However, KnowFormer also adopts a hybrid strategy. The paper does not clearly articulate the novelty or necessity of introducing a parallel structure in this context. According to the ablation study, removing the Coarse-to-Fine reasoning module leads to performance even worse than that of KnowFormer, which raises further questions about the justification and effectiveness of this structural design.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n- The dual-pathway architecture is a valuable contribution that effectively combines local and global information, addressing a common limitation in existing models.\n- The empirical results are impressive, showing significant improvements over baseline methods in various datasets, which indicates the practical utility of the proposed approach.\n\nweaknesses:\n\n- Despite the demonstrated training efficiency and time complexity analysis, I remain concerned about the inference efficiency and model size due to the algorithm's complex two-stage and parallel structure. This concern is not addressed experimentally in the paper.\n- The motivation behind the parallel design for fusing global and local information is insufficiently explained. Moreover, this aspect is not supported or verified through targeted experiments.\n- There are several errors in the references listed in the paper.", "was_revised": true, "final_justification": "The performance of DuetGraph appears to be good, but I have identified some serious issues during the discussion period:\n\n* All evaluation lacks **transparency and rigor** because the authors have used a different evaluation protocol compared to baselines. Although the authors have claimed that this difference does not have a high impact, all evaluations should be recomputed.\n* Too many things should be revised: 1) all evaluation results (i.e., all tables and all figures for analysis); 2) more discussions on the evaluation protocol; 3) additional experiments.\n* Limited novelty: after reviewing their code, I found that the global pathway comes from existing methods like KnowFormer and the local pathway comes from existing methods like RED-GNN. This work can be seen as an ensemble approach to pursuing high performance.\n\nI remain a positive score because the authors have made many efforts in addressing my concerns.", "rebuttal": "> **W1: Despite the demonstrated training efficiency and time complexity analysis, I remain concerned about the inference efficiency and model size due to the algorithm's complex two-stage and parallel structure. This concern is not addressed experimentally in the paper.**\n\n**Response to W1**: We appreciate your thoughtful comments regarding efficiency and model size. We would like to address these points through both architectural design choices and empirical validation:\n\n- **Parallel Architecture Advantage:** Our design's parallel operation of message passing and attention modules during inference provides inherent efficiency gains compared to sequential one-pathway architectures. This parallelism enables faster inference while maintaining model performance.\n\n- **Lightweight Coarse Model Selection:** We intentionally employ efficient triplet-based models for the coarse stage, which: 1) achieves the best performance due to its architectural diversity [1] (**Table 4**); 2) maintains a model size comparable to baselines.\n\n- **Empirical Efficiency Validation:** Our comprehensive evaluation against KnowFormer [2] shows consistent advantages, as shown in the table below.\n\n| Datasets   | FB15k-237  |                       | WN18RR     |                       | NELL-995   |                       | YAGO3-10   |                       |\n|------------|------------|-----------------------|------------|-----------------------|------------|-----------------------|------------|-----------------------|\n| Metrics    | Model Size | Inference Time (One Batch) | Model Size | Inference Time (One Batch) | Model Size | Inference Time (One Batch) | Model Size | Inference Time (One Batch) |\n| DuetGraph  | 6.5M (Coase Model size: 0.6M, Fine Model Size: 5.9M) | **347.07ms**      | 1.3M (Coase Model size: 0.9M, Fine Model Size: 0.4M) | **292.49ms**     | 7.2M (Coase Model size: 2.3M, Fine Model Size: 4.9M) | **261.32ms**     | 3.4M (Coase Model size: 2.3M, Fine Model Size: 1.1M) | **597.22ms**     |\n| KnowFormer | 6.1M       | 499.71ms              | 0.4M       | 392.40ms              | 5.2M       | 360.40ms              | 1.0M       | 905.22ms              |\n\nThe results show that the inference efficiency improvement is especially notable on large-scale knowledge graphs, such as YAGO3-10, where our method achieves a **34.2%** increase in inference efficiency compared to the SOTA model KnowFormer [2]. We will incorporate this analysis in the revised manuscript to better highlight these efficiency advantages.\n\n\n\n> **Q1: The proposed model combines both global and local knowledge graph information. However, KnowFormer also adopts a hybrid strategy. The paper does not clearly articulate the novelty or necessity of introducing a parallel structure in this context. According to the ablation study, removing the Coarse-to-Fine reasoning module leads to performance even worse than that of KnowFormer, which raises further questions about the justification and effectiveness of this structural design.**\n>\n> **W2: The motivation behind the parallel design for fusing global and local information is insufficiently explained. Moreover, this aspect is not supported or verified through targeted experiments.**\n\n**Response to Q1 and W2:** We appreciate your thoughtful questions regarding the parallel architecture design. We would like to clarify both the theoretical motivations and empirical advantages of our parallel design.\n\n**Theoretically**, as shown in **lines 43-58 (Section 1)** of the manuscript, the one-pathway architecture tends to aggravate the **over-smoothing** problem. In contrast, our parallel design alleviates over-smoothing by increasing the score gap, thereby improving model quality, as demonstrated in **Theorem 1**.\n\n**Experimentally**, we would like to clarify that the number of training epochs differs between the results for w/o Coarse-to-Fine reasoning (**Table 3** of the manuscript) and KnowFormer [2] (**Tables 2 and 4** of the manuscript). Specifically, the ablation experiments without Coarse-to-Fine reasoning were conducted with 15 epochs, whereas KnowFormer [2] was trained for 20 epochs.\n\nThis is because DuetGraph converged in only 15 epochs, while other baselines (e.g., KnowFormer [2]) converged in 20 epochs. Therefore, to ensure **a fair comparison**, we trained all models (including DuetGraph) for 20 epochs, as shown in **Table 2** of the manuscript. \n\nIn the ablation experiments (as shown in **Table 3** of the manuscript), we trained the model without Coarse-to-Fine reasoning for 15 epochs, matching the number of epochs required for DuetGraph to reach convergence, to ensure a **fair and consistent** comparison in the ablation experiments.\n\nTo ensure a **rigorous and fair comparison** between the model without Coarse-to-Fine reasoning and KnowFormer [2], we additionally conducted ablation studies for both models under the same number of training epochs (i.e., 20 epochs), as shown in the tables below. \n\n\n|           Dataset            | FB15k-237 |          |          |  WN18RR   |          |          | NELL-995  |          |          | YAGO3-10  |          |          |\n| :--------------------------: | :-------: | :------: | :------: | :-------: | :------: | :------: | :-------: | :------: | :------: | :-------: | :------: | :------: |\n|           Metrics            |    MRR    |  Hits@1  | Hits@10  |    MRR    |  Hits@1  | Hits@10  |    MRR    |  Hits@1  | Hits@10  |    MRR    |  Hits@1  | Hits@10  |\n| w/o Coarse-to-Fine reasoning | **0.437** | **34.8** | **61.1** | **0.580** | **53.0** | **68.9** | **0.567** | **50.5** | **67.7** | **0.616** | **54.8** | **73.5** |\n|          KnowFormer          |   0.435   |   34.3   |   60.8   |   0.579   |   52.8   |   68.7   |   0.566   |   50.2   |   67.5   |   0.615   |   54.7   |   73.4   |\n\n| Dataset                        | FB15k-237 | WN18RR   | NELL-995  | YAGO3-10   |\n|:------------------------------:|:---------:|:--------:|:---------:|:----------:|\n| Metrics                        | One Epoch Time | One Epoch Time | One Epoch Time | One Epoch Time |\n| w/o Coarse-to-Fine reasoning   | **3,026.8s**   | **2,968.2s**   | **12,037.9s**  | **206,919.1s** |\n| KnowFormer                     | 3,471.6s       | 3,026.4s       | 12,329.2s      | 242,313.2s     |\n\nThe results demonstrate that the parallel design not only outperforms the SOTA KnowFormer [2] in **quality** because of **alleviating over-smoothing**, but is also more **efficient** in terms of computational cost, including average epoch runtime cost. This is because parallel architectures, which are designed to leverage **parallel strategies**, are **more efficient** compared to sequential one-pathway architectures. \n\nFollowing your advice, we will include these experimental results and analysis in the revised manuscript.\n\n> **W3: There are several errors in the references listed in the paper.**\n\n**Response to W3**: Thanks for pointing these out. We will correct all the errors about references in the revised manuscript.\n\n----\n**Reference**:\n\n[1] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 2022\n\n[2] Liu et al. KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning. ICML 2024"}]

Author rebuttal:

Meta-review: This paper presents DuetGraph, a novel dual-pathway, coarse-to-fine framework for knowledge graph reasoning that effectively mitigates the over-smoothing problem. The architecture is well-motivated, supported by theoretical analysis, and demonstrates state-of-the-art performance across a wide range of benchmarks.

The authors' exemplary engagement during the rebuttal period was pivotal. They comprehensively addressed all reviewer concerns by conducting significant new experiments. Key initial weaknesses regarding efficiency, scalability, and evaluation rigor were transformed into strengths. Notably, the authors:
1) Validated DuetGraph's efficiency and scalability on very large KGs (Wikidata5M, Freebase), demonstrating superior performance over challenging baselines.

2) Re-ran all evaluations using a stricter ranking protocol suggested by a reviewer, confirming the robustness of their state-of-the-art claims.

In summary, the authors addressed every point raised with new experiments and detailed analysis. While Reviewer hDcp adjusted some sub-scores downwards based on a revised perspective of the work's novelty, they acknowledged that all their technical questions were answered and maintained their overall positive recommendation. This extensive rebuttal was pivotal in solidifying the paper's contribution and justifying its acceptance.
Decision: Accept (poster)