We sincerely thank the Reviewer 2LyR for the thorough and insightful feedback. Our detailed responses to your concerns are listed as follows:

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Q1. In the second paragraph of Section 3.3, the use of $M$ as a mask in the node representation is not well explained. The explanation needs clarification.

A1. Thank you for your helpful feedback. In our method, $M$ is a learnable parameter, initialized randomly and updated during training. It is applied as a soft mask on graph neural network weights to enable domain invariant feature learning during model reprogramming. The sentence referencing weights with small gradients with respect to $M$ being masked was intended to illustrate how uninformative components are implicitly suppressed during training via gradient-based optimization, not that $M$ is derived from another process. We will revise this paragraph in the final version to make the role of $M$ as a learnable soft mask more explicit and remove any misleading phrasing that may have caused confusion.

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Q2. In the same section, the hyperparameter $\rho$ is mentioned, but its definition and role in the model are not clearly described. Additionally, a dynamic adaptive threshold is referenced but not sufficiently explained. Since this is claimed as a key contribution, it should be fully justified and elaborated.

A2. Thank you for pointing this out. The hyperparameter $\rho$ is used to control the sparsity of the learned mask $M$ in the model reprogramming process. Specifically, it determines the proportion of weights to be retained, allowing the model to focus on the most informative components of the representation while suppressing less relevant ones. We set the lowest $\rho$ percent of gradient values in $M$ to zero, leaving the remaining elements at one. These sparse masks are then applied to prune the weight matrix $W$, resulting in a reprogrammed sparse model that emphasizes informative regions of the feature space.

For dynamic threshold, we mean we adopt a logit augmentation strategy, where we append an additional logit dimension to represent the "unknown" class. This augmented logit vector is then passed through a softmax layer, allowing the model to assign a probability distribution over both known and unknown classes. The final prediction is simply the class with the highest posterior probability. The "dynamic threshold" referenced in the text refers not to an explicit numerical threshold, but to the model's ability to adaptively learn the decision boundary between known and unknown classes based on the input node representation $z$ and the augmented classifier outputs. This formulation removes the need for hand-tuned thresholds and makes the open-set detection process fully data-driven and end-to-end trainable. We will revise the wording in the final version to avoid ambiguity and better reflect this mechanism.

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Q3. On line 200, it is unclear how $\Delta{A}$ is computed. If it is a learnable parameter, how is the binary matrix learned? Also, the choice of the budget $B$ is not discussed.

A3. Thank you for your thoughtful question. To maintain a discrete and sparse adjacency structure, we treat each entry in $\Delta{A}$ as a Bernoulli random variable, where the probability of an edge being present is learned. During training, we sample the learned graph structure from these Bernoulli distributions, allowing the model to adaptively reprogram the input graph while keeping the structure binary. This formulation enables stochastic but learnable structure refinement in a principled manner.

Regarding the budget $B$, it is used to constrain the total number of edges that can be added or modified in $A$, which helps control overfitting and keeps the reprogramming meaningful. In practice, we set $B$ as a fixed percentage (e.g., 20%) of the total possible edges and have provided an ablation study in Figure 2(b) to analyze its impact. We will add a more detailed explanation of this process, along with the default setting in the final version of the paper.

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Q4. The paper employs a Beta mixture model, which appears nearly identical to the one proposed.

A4. Thank you for your feedback. We agree that the Beta mixture model we adopt is closely aligned with the previous work. We would like to clarify that our primary contribution is not in designing a new loss function, but in introducing a novel learning paradigm, i.e., dual reprogramming for open-set graph domain adaptation, which integrates model and graph reprogramming to address challenges specific to graph-structured data. The Beta mixture model is used as a standard component within our framework to support open-set recognition, consistent with prior work.

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Q5. While the proposed method shows strong performance in most scenarios in Tables 2 and 3, it would be helpful to discuss the cases where the method does not achieve the best results and explore possible reasons why.

A5. Thank you for your insightful comment. We appreciate your suggestion to analyze the cases where our method does not achieve the best performance. Upon reviewing the results in Tables 2 and 3, we note that in a few scenarios, our method performs slightly below certain closed-set baselines. These cases often occur in settings where the known class distribution is very similar with unknown class distributions across the two domains. We compute the Maximum Mean Discrepancy (MMD) between known and unknown classes within each domain and then calculate their MMD gap between the source and target domains. We find that DBLPv7->ACMv9 (0.003) and Texas->Cornell (0.024) have the smallest values among all the scenarios. In this case, closed-set models leverage the full target space for alignment without needing to separate unknown classes, resulting in a performance improvement. We will include this analysis and a brief discussion of these observations in the final version to help readers better understand our approach.

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Q6. How is the value of the budget $B$ determined?

A6. Thanks for pointing this out. The budget $B$ is treated as a hyperparameter that controls the sparsity of the reprogrammed graph structure. In our experiments, we set $B$ to a fixed proportion (e.g., 20%) of the total possible edges. We further analyze the sensitivity of the model to different values of $B$ through an ablation study, as shown in Figure 2(b).

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Q7. How is the learning of $\Delta{A}$ achieved in practice?

A7. Thanks for pointing this out. To learn $\Delta A$ in practice, we treat each entry in $\Delta A$ as a Bernoulli random variable, where the probability of an edge being present is learned. During training, we sample the learned graph structure from these Bernoulli distributions, allowing the model to adaptively reprogram the input graph while keeping the structure binary. The learning process is further constrained by a budget $B$ via projected gradient descent, which limits the number of added or modified edges. This formulation enables stochastic but learnable structure refinement in a principled manner. We will add a more detailed description in the final version.

Dear Reviewer 2LyR,

As the deadline for author-reviewer discussion is approaching, could you please check the authors' rebuttal and post your response?

Thank you!

Best,

AC

We greatly appreciate Reviewer ny1J for the insightful review to help us improve the paper. We address the reviewer’s concerns as follows:

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Q1. The authors should provide a more detailed introduction to the datasets used in the experiments. For example, it would be helpful to clarify how open-set classes are selected within each dataset.

A1. Thank you for your suggestion. In our experiments, we follow the common practice used in prior works such as SDA and G2Pxy by selecting the first several classes (based on label indices) as known classes, and the remaining classes as open-set (unknown) classes. We will provide a more detailed description of this setup in the final version of the paper to improve clarity.

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Q2. One of the recent baselines appears to be missing from the discussion and experimental comparison.

A2. Thank you for bringing this work to our attention. The UAGA method you mentioned is a two-stage framework. It first separates known and unknown classes by training a graph neural network, and then it applies unknown-excluded adversarial domain alignment across different classes. Notably, these operations are performed entirely in the representation space. In contrast, our proposed GraphRTA introduces model reprogramming and graph reprogramming from dual perspectives, which enhances generalization capabilities by explicitly modeling the model space and the graph space. Following your suggestion, we have compared UAGA with GraphRTA on citation datasets. The results of H-score are as follows:

As can be seen, our method demonstrates superior performance over the baseline in 5 out of 6 evaluated scenarios, indicating strong generalization and robustness.

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Q3. It would be helpful to explore alternative strategies for open-set detection—such as using an entropy-based threshold—and compare their performance with the proposed approach.

A3. Thank you for the insightful suggestion. We agree that exploring alternative open-set detection strategies provides valuable perspective. Based on your suggestion, we implemented an entropy-based thresholding variant and compared its performance with our proposed approach. The results of H-score show that our approach consistently outperforms it across all settings.

We will include these results and discussion in the final version of the paper to provide a more comprehensive evaluation.

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Q4. Some of the ablation studies currently placed in the appendix are crucial for understanding the core contributions of the paper and should be moved to the main content.

A4. Thank you for your helpful feedback. We agree that some of the ablation studies (e.g., Table 5 and Table 6) are important for understanding the core contributions of our work. In the final version of the paper, we will move these ablation results from the appendix to the main text to improve the clarity of our contributions.

Dear Reviewer ny1J,

As the deadline for author-reviewer discussion is approaching, could you please check the authors' rebuttal and post your response?

Thank you!

Best,

AC

We sincerely thank Reviewer bwmJ for the constructive feedback. We address the reviewer’s concerns as follows.

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Q1. Model complexity raises concerns. The combination of adversarial training, multiple loss functions, and dual reprogramming may lead to training instability and convergence difficulties.

A1. Thank you for raising this point. For model complexity, we have provided a detailed model complexity analysis in the Appendix D, which shows that the overall computational overhead remains manageable and comparable to existing domain adaptation methods. For training instability, we mitigate potential instability by using the gradient reversal layer (GRL), a well-established technique in adversarial training that enables stable joint optimization without requiring alternating updates. In our experiments, we did not observe instability or convergence issues during training across all datasets. We will include additional training details and convergence plots in the final version to demonstrate the stability of our method.

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Q2. Core techniques (entropy-based known/unknown separation, adversarial domain alignment) are adaptations of existing methods from non-graph open-set domains. The incremental contribution does not sufficiently advance the state-of-the-art.

A2. Thank you for your feedback. We believe our proposed dual reprogramming provides a new and meaningful direction for open-set graph domain adaptation that goes beyond adapting existing ideas. By reprogramming the model and the graph from dual perspectives, the method effectively reshapes the learning objective to focus on domain-invariant and known-class-relevant information. This is a novel strategy that contributes to the method’s strong performance under open-set conditions. To summarize, we would like to emphasize our contributions as follows:

(1) For problem, we explore the challenging yet practical problem of unsupervised open-set graph domain adaptation, which remains relatively uninvestigated within the graph community. (2) For model, we propose a dual reprogramming framework named GraphRTA that jointly reprograms the model and the graph structure to better handle the open-set setting in graphs. This is fundamentally different from conventional methods that operate solely in the representation space. (3) For evaluation, we conduct extensive comparisons with 14 baselines to validate the effectiveness of our proposed GraphRTA. The baselines encompass various categories, such as no-adaptation methods, closed-set graph domain adaptation, and open-set graph domain adaptation methods.

We believe these contributions offer a substantive advancement in the field of open-set graph domain adaptation.

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Q3. Potential of LLM Integration: Given datasets with text-describable nodes (e.g., Citation networks), have you considered leveraging LLMs for unknown class detection? LLMs could generate semantic explanations for classification decisions and handle the open-set classification.

A3. Thank you for the insightful suggestion. We agree that integrating large language models (LLMs) into open-set graph domain adaptation holds great potential, especially for datasets with text-describable nodes. To explore the impact of LLM generated semantic explanations on unknown class detection, we follow the prompt strategy from TAPE [1] to generate semantic explanations for each node in the ogbn-arxiv dataset. The node features are then constructed by combining the title, abstract, and the LLM-generated explanation. We evaluate the effectiveness of these enhanced features using three models. Each experiment is run 5 times, and we report the average H-score along with the standard deviation as follows:

As shown in the table, incorporating LLM-generated explanations leads to performance improvements across the evaluated models. This suggests that LLMs can enhance the models and provide additional semantic signals beneficial for open-set classification. We consider this a promising direction for future research and will include a brief discussion of this potential extension in the final version of the paper.

Reference:

[1] He X, Bresson X, Laurent T, et al. Harnessing Explanations: LLM-to-LM Interpreter for Enhanced Text-Attributed Graph Representation Learning[C]// ICLR 2024.

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Q4. There is an inconsistency in reported baselines: Table 4 cites GCN HS metric as 56.91%, while Table 2 lists as 59.41%. Please verify and correct all numerical results.

A4. Thank you for pointing this out. We have carefully reviewed all numerical results and confirm that the discrepancy is due to a typo in Table 4, where the accuracy value (56.91%) was mistakenly placed in the H-score for GCN backbone. The correct H-score is 59.41%, as reported in Table 2. We have verified all other results, and this is the only such error. The correction will be made in the final version.

Dear Reviewer bwmJ,

As the deadline for author-reviewer discussion is approaching, could you please check the authors' rebuttal and post your response?

Thank you!

Best,

AC

We greatly appreciate Reviewer s6Bn for the insightful review to help us improve the paper. We address the reviewer’s concerns as follows:

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Q1. The authors should discuss and compare with the following AAAI 2025 paper.

A1. Thank you for bringing this work to our attention. The UAGA method you mentioned is a two-stage framework. It first separates known and unknown classes by training a graph neural network, and then it applies unknown-excluded adversarial domain alignment across different classes. Notably, these operations are performed entirely in the representation space. In contrast, our proposed GraphRTA introduces model reprogramming and graph reprogramming from dual perspectives, which enhances generalization capabilities by explicitly modeling the model space and the graph space. Following your suggestion, we have compared UAGA with GraphRTA on citation datasets. The results of H-score are as follows:

As can be seen, our method demonstrates superior performance over the baseline in 5 out of 6 evaluated scenarios, indicating strong generalization and robustness.

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Q2. The effect of varying the number of known classes—from 2 up to 4—on the model’s performance remains unexplored.

A2. Thanks for this suggestion. Following your suggestion, we have conducted additional ablation studies to evaluate the impact of varying the number of known classes (from 2 to 4) on model performance. The results of H-score on citation dataset are presented below:

When the number of known classes is very small (e.g., only 2 known classes), open-set models have less supervision to guide feature alignment and separation. In contrast, when enough known classes is available, our model becomes more robust and less sensitive is to the number of unknown classes.

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Q3. The organization of the paper could be further improved by simplifying Section 3.5.

A3. Thank you for the constructive feedback regarding the organization of the paper. We agree that simplifying Section 3.5 would improve clarity and overall coherence. We will revise and streamline this section in the final version to enhance readability and make the key concepts more accessible.

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Q4. How does graph reprogramming affect the feature distribution of unknown classes?

A4. Thank you for your insightful comment. To analyze how graph reprogramming affects the feature distribution of unknown classes, we measure the distributional divergence between known and unknown classes using Maximum Mean Discrepancy (MMD). This allows us to quantitatively assess whether our approach enhances the separation between these two groups. The results are as follows:

The results indicate that graph reprogramming increases the distributional distance between known and unknown classes after graph reprogramming, suggesting improved feature separation. We will include this analysis in the final version of the paper.