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.

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:

• 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.

• 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.

• Empirical Efficiency Validation: Our comprehensive evaluation against KnowFormer [2] shows consistent advantages, as shown in the table below.

The 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.

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.

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.

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.

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.

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.

This 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.

In 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.

To 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.

The 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.

Following your advice, we will include these experimental results and analysis in the revised manuscript.

W3: There are several errors in the references listed in the paper.

Response to W3: Thanks for pointing these out. We will correct all the errors about references in the revised manuscript.

Reference:

[1] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 2022

[2] Liu et al. KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning. ICML 2024

Thank you for your detailed comments. Following the widely used ranking protocol adopted in [1–4], we employ the (m+1) ranking protocol in our experiments.

Following your suggestion, we conducted experiments on DuetGraph using the strictest ranking protocol (m+n+1) (i.e., the one used in KnowFormer), and the results are shown in the tables below.

Non-deterministic ranking [5-7] means that when two entities share the same score, their original order is preserved in the ranking. Compared with the m+n+1 ranking protocol, this is more lenient.

Based on the experimental results, we can draw the following conclusions.

• Frist, switching to the strictest ranking protocol has little impact on DuetGraph’s quality. As shown in the tables above, when switching the ranking protocol from (m+1) to (m+n+1), DuetGraph’s quality is virtually unaffected, with at most a 0.003 drop in MRR, a 0.1 drop in Hits@1, and a 0.4 drop in Hits@10. This is because, n is 0 in almost all the cases . As shown in the table above, the number of test triplets impacted when replacing (m+1) with (m+n+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@1, and Hits@10. For the other baselines, as shown in Table 2 of the manuscript, we used the official code from their original papers, all of which employ protocols no stricter than (m+n+1). As shown in [8], increasing the strictness of the ranking protocol yields quality that is no higher (and often lower). Even under this tough setting, DuetGraph consistently outperforms all of them, providing strong evidence of its SOTA performance.

Following you suggestion, we will include these results and the discussion in the revised version of the manuscript. Thank you for reviewing our code and for the valuable feedback. This further demonstrates that DuetGraph delivers consistent SOTA performance under the strictest ranking protocol.

Refs:

[1] Pykg2vec: A Python Library for Knowledge Graph Embedding. J. Mach. Learn. Res.

[2] Semi-Supervised Entity Alignment via Knowledge Graph Embedding with Awareness of Degree Difference. WWW

[3] SimplE Embedding for Link Prediction in Knowledge Graphs. NeurIPS

[4] Complex Embeddings for Simple Link Prediction. ICML

[5] Multi-relational Poincaré Graph Embeddings. NeurIPS

[6] Anytime bottom-up rule learning for large-scale knowledge graph completion. VLDBJ

[7] On the ambiguity of rank-based evaluation of entity alignment or link prediction methods. arXiv

[8] A Re-evaluation of Knowledge Graph Completion Methods. ACL

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?

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]:

• 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.

• Implementation: For relation prediction, we compute a score for each candidate relation and select the one with the highest score as the prediction.

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.

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.

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.

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.

For 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.

As 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 ∆.

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?

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.

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.

In 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.

The 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.

This 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.

In 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.

The 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.

Reference:

[1] Balazevic et al. TuckER: Tensor Factorization for Knowledge Graph Completion. EMNLP/IJCNLP (1) 2019: 5184-5193

[2] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 2022

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.

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.

Clarifying KG Reasoning vs. Representation Learning. While the concepts of the two are closely related, they serve for different purposes:

• 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.

• 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.

In summary, KG representation learning provides the foundational embeddings, while reasoning uses them for knowledge inference [2].

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].

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).

Following your advice, we will revise the abstract to clarify this definition of KG reasoning and differentiate it from KG representation learning.

W2: The text description of the local and global pathways is inconsistent with Figure 1.

Response to W2: You are right. There are two numbering errors in the textual descriptions of the pathways (lines 112 and 113):

• "local pathway (Step 2)" should be "local pathway (Step 3)"
• "global pathway (Step 3)" should be "global pathway (Step 2)"

We apologize for any confusion this may have caused. These corrections will be made in the revised manuscript

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.

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:

• 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.

• 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.

• Experimental Study. Incorporating α achieves better performance compared to using attention mechanism alone, as shown in the table below.

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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.

Response to W4: Thanks for your insightful comments.

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.

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).

As 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.

W5: 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?

Response to W5: Thanks for your valuable comments.

(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.

(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.

(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.

(4) Performance on Triple Classification: To demonstrate DuetGraph's generalizability, we evaluate its performance on triple classification using the following setup:

• Datasets: UMLS [14], FB13 [15] and WN11 [15] (Standard benchmark datasets for knowledge graph tasks)
• 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)

The experimental results demonstrate that DuetGraph consistently outperforms all baseline methods across all datasets, achieving new SOTA performance on the triple classification task.

Reference:

[1] Wu et al. KRLGI: Knowledge Representation Learning Based on Global Information for Reasoning. ICTAI 2024

[2] Chen et al. An Overview of Knowledge Graph Reasoning: Key Technologies and Applications. J. Sens. Actuator Networks 2022

[3] Liu et al. KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning. ICML 2024

[4] Zhu et al. A*Net: A Scalable Path-based Reasoning Approach for Knowledge Graphs. NeurIPS 2023

[5] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 2022

[6] Zhang et al. Logical Reasoning with Relation Network for Inductive Knowledge Graph Completion. KDD 2024

[7] Chen et al. Meta-Knowledge Transfer for Inductive Knowledge Graph Embedding. SIGIR 2022

[8] Sun et al. RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space. ICLR 2019

[9] Kazemi et al. SimplE Embedding for Link Prediction in Knowledge Graphs. NeurIPS 2018

[10] Wang et al. SimKGC: Simple Contrastive Knowledge Graph Completion with Pre-trained Language Models. ACL 2022

[11] Xiong et al. DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning. EMNLP 2017

[12] Lacroix et al. Canonical Tensor Decomposition for Knowledge Base Completion. ICML 2018

[13] Li et al. KERMIT: Knowledge graph completion of enhanced relation modeling with inverse transformation. Knowl. Based Syst. 2025

[14] Olivier et al. The Unified Medical Language System (UMLS): integrating biomedical terminology. Nucleic Acids Res. 2004

[15] Socher et al. Reasoning With Neural Tensor Networks for Knowledge Base Completion. NIPS 2013

[16] Li et al. HousE: Knowledge Graph Embedding with Householder Parameterization. ICML 2022

[17] Zhang et al. AdaProp: Learning Adaptive Propagation for Graph Neural Network based Knowledge Graph Reasoning. KDD 2023

[18] Chen et al. HittER: Hierarchical Transformers for Knowledge Graph Embeddings. EMNLP 2021

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?

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.

The 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

$\frac{\sigma_{max}(\mathcal{M}_{\mathrm{D}})+\sigma\_{max}(\mathcal{M}\_{\mathrm{O}})}{1+\sigma\_{max}(\mathcal{M}\_{\mathrm{O}})}$

as stated in Theorem 1 of the manuscript. This 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.

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?

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.

Response to Q2 and W1: Thanks for your insightful comments.

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. The 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.

Characteristics of a Good Coarse Model. As supported by prior work [1], architectural diversity between coarse and fine models enhances overall performance. Specifically, 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.

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.

We will include the analysis in the revised version of the manuscript to clarify these points.

Reference:

[1] Ortega et al. Diversity and Generalization in Neural Network Ensembles. AISTATS 202

[2] Bordes et al. Translating Embeddings for Modeling Multi-relational Data. NIPS 2013: 2787-2795

[3] Liu et al. KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning. ICML 2024