We appreciate your detailed comments. Below, we address each of your concerns point by point.

Question1:what is the feasible domain of s?

Thank you for the question. The feasible domain of the total transfer quantity $s$ is defined as the interval from 0 to the total number of available source samples, i.e., $s\in[0, s_{\max}]$ where $s_{\max} = \sum\limits_{i=1}^{K} N_i$. In our experiments, we perform a uniform grid search over this interval using 1000 equally spaced steps (denoted as $stepnumber = 1000$). The computational complexity of this procedure depends solely on the value of $stepnumber$, and is independent of the size of the feasible domain. Therefore, a large feasible range does not pose a challenge to the efficiency of the algorithm. A detailed analysis of the computational complexity of this process can be found in our response to Reviewer 43HZ, Question 4.

Weakness1: Using “high-dimensional” is rather misleading.

Thank you for your suggestion. We agree that the term “high-dimensional” is misleading in our context, as our analysis is conducted in a fixed-dimensional regime. In the revised version of the paper, we will remove the term "high-dimensional statistics" and replace it with the more precise term "asymptotic analysis".

Weakness2: The assumption that all source tasks and the target task share the same parametric model is worrying, which is practically impossible.

Thank you for raising this important concern. We would like to clarify that our framework only assumes that the source and target tasks share the same parametric model class, but each task is associated with its own set of model parameters. As described in Section 3, the underlying model for the target task is $P\_{X;\underline{\theta}\_0}$, while the source tasks $\mathcal{S}\_1, \dots, \mathcal{S}\_K$ correspond to models $P\_{X;\underline{\theta}\_1}, \dots, P\_{X;\underline{\theta}\_K}$, respectively.

In transfer learning, it is common to select source and target tasks with the same input/output structure and similar feature spaces. This makes the use of a shared parameterized model a reasonable assumption, which is also widely adopted in the multi-source transfer learning literature [1][2].

Moreover, we do not impose any specific structural assumptions on the form of the underlying model $P_{X;\underline{\theta}}$. In fact, by the Universal Approximation Theorem [5], a feedforward neural network with sufficient width can approximate any continuous function on a compact domain. This ensures that our framework is applicable to a broad class of tasks and models, without being limited to a particular architecture.

In summary, while our theoretical derivation requires a shared model class, it allows full flexibility in parameterization across tasks. This assumption enables a general and tractable formulation, and our experiments further demonstrate the robustness and effectiveness of the proposed algorithm in realistic settings.

Weakness3:It has been too simple to provide helpful insight into the current transfer learning paradigm, i.e., pre-training and fine-tuning. Pooling both source and target data to obtain an estimator is never effective and efficient, as has been long demonstrated in the community.

Thank you for the comment. We respectfully clarify that the model-based paradigm you mentioned (e.g., fine-tuning) and the sample-based paradigm adopted in this paper represent two established approaches to transfer learning. While model-based methods have been more extensively studied, recent works—as well as our own results—demonstrate that sample-based strategies can also achieve competitive performance [3][4], both effectively and efficiently when properly designed.

We would also like to draw your attention to Table 2, where the runner-up method “AllSources $\cup$ Target” is a simple pooled estimator that uses all available source and target data for training. While naive, this baseline performs surprisingly well on certain datasets. The fact that more complex baselines do not consistently outperform such a simple pooling strategy suggests that they may not be universally suitable across all datasets.

Weakness4:The bounds in this paper are asymptotic and the authors require a “sufficient small models” assumption (line 139 or line 145) when derive these asymptotic results. However, in asymptotic regime, the “sufficient small models” actually indicates the source and target tasks/models are identical.

Thank you for the comment. We would like to clarify that the assumption of a “sufficiently small model distance” (i.e., $|\theta_0 - \theta_1| = O(1/\sqrt{N_0})$) is a technical condition introduced to control higher-order terms in the asymptotic analysis. Given that the source and target tasks used in transfer learning often share similar input-output structures and semantic spaces, this assumption is also reasonable in practice.

Nevertheless, it does not imply that the source and target tasks are identical. Importantly, even under this assumption, our framework allows for meaningful differences between tasks. If the tasks were truly identical, all source samples would always benefit the target task. In contrast, both our theoretical analysis (lines 155–164) and experimental results (Section 5) demonstrate that using all available source samples is not always optimal. Furthermore, in the multi-source setting, the optimal transfer quantity from each source depends explicitly on its distance to the target task, as formally characterized in Theorem 7 and empirically validated in Appendix G.

Weakness5:Practical algorithm: The practical algorithm (QTAMS) replaced the true source parameters by their empirical version. While this is a compromise with reality where the true parameters are unknown in practice, we have to remember that, since the bounds are asymptotic, there could be error terms induced by the approximation.

Thank you for pointing out this important issue. We fully agree that the substitution of true source parameters $\theta_i$ with their empirical estimates $\hat{\theta}_i$ introduces approximation error. We acknowledge that this is a limitation of our current formulation, as the true source parameters are inaccessible in real-world scenarios. Despite this, we argue that our framework still provides a principled approximation scheme, and our empirical results (Section 5.2) show that it yields consistently strong performance across diverse settings. We will explicitly state this limitation in the revised version of paper. A more refined theoretical treatment that accounts for estimation error in source parameters is indeed an interesting direction for future work.

Moreover, it is important to note that our definition of $N_i$ refers only to the number of source samples available during the target training stage, rather than the full dataset used to obtain the empirical estimates $\hat{\theta}_i$. In many real-world scenarios—such as the use of large pretrained models including GPT-3 [6] and PaLM [7]—the parameters $\hat{\theta}_i$ are obtained by training on datasets that are significantly larger than the accessible source sample sizes $N_i$, often incorporating non-public or proprietary data sources. In such cases, the estimation error of $\hat{\theta}_i$ is smaller than the order of $1 / (N_0 + n_1)$, making it a highly reliable approximation to $\theta_i$ and thereby justifying our substitution.

Weakness6:The improvement over the runner-up is rather small. What is more interesting to the reviewer is that the efficiency improved by QTQMS.

Thank you for your thoughtful and balanced comment. We acknowledge that the performance gains of QTQMS over the strongest baselines are relatively modest in some cases. However, our goal is not only to pursue absolute accuracy, but also to develop a theoretically principled and practically efficient framework for multi-source transfer learning.

In fact, several components of our current implementation remain intentionally simple, in order to better isolate and verify the robustness of the theoretical framework. For instance, after obtaining the optimal transfer quantity for each source domain, we adopt a straightforward random sampling strategy to construct the joint dataset. This design choice allows us to focus on validating the effectiveness of the core theory. Nevertheless, we believe that incorporating more advanced sampling strategies—such as active sampling—could further improve the performance of the algorithm.

In addition, as shown in Section 5.4, QTQMS exhibits stable and superior performance across different shot settings, further demonstrating the robustness of the proposed method. As the reviewer kindly noted and as demonstrated in Section 5.5, QTQMS consistently achieves comparable or better accuracy while significantly reducing computational overhead, which we believe is one of the key advantages of our approach.

Thank you again for your valuable insights. We kindly request that the reviewer considers these points when assigning the final scores.

References：

[1]Wu, Y., Wang, J., Wang, W., and Li, Y. H-ensemble: An information theoretic approach to reliable few-shot multisource-free transfer. AAAI 2024

[2]Li Y, Yuan L, Chen Y, et al. Dynamic transfer for multi-source domain adaptation[C] CVPR2021

[3]Shui C, Li Z, Li J, et al. Aggregating from multiple target-shifted sources[C]//International conference on machine learning. PMLR, 2021: 9638-9648.

[4]Zhang W, Lv Z, Zhou H, et al. Revisiting the domain shift and sample uncertainty in multi-source active domain transfer[C] CVPR 2024

[5] Hornik K. Approximation capabilities of multilayer feedforward networks[J]. Neural networks, 1991

[6] Brown T, Mann B, Ryder N, et al. Language models are few-shot learners[J]. NeurIPS 2020

[7] Chowdhery A, Narang S, Devlin J, et al. Palm: Scaling language modeling with pathways[J]. Journal of Machine Learning Research, 2023, 24(240): 1-113.

We sincerely thank the reviewer for the time and effort spent in evaluating our work and for the constructive feedback provided throughout the discussion. We fully respect the reviewer’s final judgment regarding the score. The following clarification is offered not to dispute your assessment, but to further explain our reasoning and address potential misunderstandings.

Reason1: The revision for this manuscript could be too much

We do not consider such revisions to be “too much”. In our discussion with you, only Weakness 1 and Weakness 5 involve modifications. Across the discussions with the other three reviewers, there are only two additional questions where we proposed modifications for the revised version. Moreover, the corresponding revised text has already been completed and presented in this rebuttal, and the only remaining work for the revised paper is the substitution of text. We also assure you and all other reviewers that all the modifications mentioned in rebuttal will be fully implemented in the final version of the paper.

Reason2: Some assumptions/settings are strong. Some theory are intuitive result using real application setting

First, we would like to clarify that our reference to realistic scenarios serves to define our assumptions and research scope, ensuring that the framework remains applicable to real-world settings. However, our theoretical framework is derived from formal statistical principles under these assumptions, rather than from intuitive reasoning.

For example, in our response to Weakness 5, we referred to real-world cases—such as the use of large pretrained models including GPT-3 and PaLM—where the parameters $\hat{\theta}_i$ are obtained by training on datasets whose sizes are significantly larger than the accessible source sample sizes $N_i$. This reference was intended solely to motivate the assumptions, but the conclusion that “the estimation error of $\hat{\theta}_i$ is smaller than the order of $1 / (N_0 + n_1)$” is firmly grounded in established statistical theory. Specifically, when the source parameters $\hat{\theta}_i$ are obtained from pretraining on $M_i \gg (N_0 + n_1)$ samples, the asymptotic MSE of the MLE scales as $O(1/M_i)$ using Lemma 1, which is negligible compared to the $O(1/(N_0 + n_1))$ term in our asymptotic bounds. Therefore, substituting $\hat{\theta}_i$ for $\theta_i$ does not introduce error terms of the same order, and this conclusion is derived from rigorous theoretical analysis rather than from simply asserting, based on real-world examples, that additional higher-order terms are negligible.

For the “identical” assumption and the use of pooled MLE, we would like to clarify that our “identical” assumption—interpreted as a small source–target parameter distance—is not “strong”; rather, It is motivated by realistic transfer learning scenarios in which the source and target tasks typically share similar input–output structures and semantic spaces. The fact that the theory based on pooled MLE works in our experiments is because this assumption matches the characteristics of widely used real-world datasets such as Office-Home and DomainNet, making our theory applicable, rather than this “strong” assumption directly causing favorable experimental results. Importantly, having the parameter distance be asymptotically small does not imply the trivial conclusion that the pooled MLE using all available source samples is always optimal. On the contrary, both our theoretical analysis (lines 155–164) and experimental results (Section 5) demonstrate that using all available source samples is not always optimal.

Reason3: Sample-level methods can be very restrictive in practice

First, we would like to reiterate that sample-based transfer learning constitutes a meaningful and active research direction, whose significance and effectiveness has been confirmed by several recent works [1][2][3]. Our own experimental results further demonstrate that this approach can perform competitively across diverse settings. We acknowledge that our method requires accessing source data; however, this limitation is inherent to a broad class of sample-based transfer learning approaches, and scenarios in which source data can be accessed do occur in practice. Second, our framework can be integrated with strategies such as LoRA (Section 5.6), which can greatly reduce retraining overhead by avoiding full-model updates when switching tasks.

Reference:

[1]Shui C, Li Z, Li J, et al. Aggregating from multiple target-shifted sources[C]//International conference on machine learning. PMLR, 2021: 9638-9648.

[2]Zhang W, Lv Z, Zhou H, et al. Revisiting the domain shift and sample uncertainty in multi-source active domain transfer[C] CVPR 2024

[3]Li D, Zhang Z, Wang L, et al. Scalable Fine-tuning from Multiple Data Sources: A First-Order Approximation Approach[C]// EMNLP 2024 Findings

We are grateful to you for taking the time to review our paper and provide thoughtful insights. Below, we address each of your concerns point by point.

Question1：As the learning objective of many problems are not limited to negative log likelihood, I am interested in the optimal quantities with general learning objectives, such as cross-entropy loss in classification problems and mean square error in regression problems, or at least some error analysis when the proposed method is applied in general settings.

Thank you for your valuable suggestion. For the case of cross-entropy loss in classification problems, it is essentially equivalent to the negative log-likelihood when softmax outputs and one-hot encoded labels are used. This corresponds precisely to the setup adopted in the main experiments of our paper.

For other learning objectives, such as mean squared error in regression tasks, we acknowledge that there is a gap compared to the negative log-likelihood formulation assumed in our theoretical analysis. While our framework does not directly cover these cases, we believe the core idea can be extended to broader loss functions under certain regularity conditions. We will clarify this limitation in the revised version of paper, and include additional experiments with other loss functions to empirically demonstrate the robustness and broader applicability of our method.

Question2：How can the proposed method combine with other parts of the transfer learning? For examples, the sample selection and domain alignment.

Thank you for the insightful suggestion, which points to a valuable direction for future work. In this paper, after obtaining the optimal transfer quantity of each source domain, we adopt a straightforward random sampling strategy to construct the joint dataset in our algorithm implementation. As our theoretical analysis is based on average-case assumptions, random sampling is sufficient to validate the robustness of both the theoretical framework and the proposed algorithm. Nonetheless, we anticipate that more advanced sample selection strategies, such as active sampling, could further enhance the algorithm’s performance. We plan to explore this possibility in future work.

Once again, we thank you for the constructive feedback.

We sincerely appreciate the reviewer’s thoughtful observation. Below, we address each of your concerns point by point.

Question1：How does the framework behave, and could it be extended to formally account for larger parameter distances?

Thank you for the valuable feedback. We agree that the assumption of a small parameter distance (i.e., $|\theta_0 - \theta_1| = O(\frac{1}{\sqrt{N_0}})$) is a strong condition underlying the asymptotic derivation in Theorem 4 and its extensions. This assumption is necessary for controlling higher-order terms in the theoretical analysis. Nevertheless, the optimal transfer quantity derived from the framework remains consistent with intuition even when the assumption does not strictly hold. In particular, as shown in lines 160–162, when the parameter distance becomes large, the optimal transfer quantity naturally reduces to zero, reflecting the expected behavior under significant domain shift. This suggests that the theoretical formulation still captures the correct transfer tendency even for less related tasks. Moreover, our empirical results in Section 5 demonstrate that the proposed algorithm remains robust across a wide range of transfer scenarios.

Question2：Can the framework be decomposed to provide more granular insights into how different types of shift (e.g., covariate shift vs. concept shift) individually impact the optimal transfer quantity?

Thank you for the insightful comment. Our framework models task divergence as a unified parametric distance between $\underline{\theta}_0$ and $\underline{\theta}_i$, which implicitly captures different types of domain shift (e.g., covariate shift and concept shift). This design reflects our goal of constructing a task-agnostic framework that determines the optimal transfer quantity without relying on prior knowledge of task-specific structure or decomposition.

On the other hand, in scenarios where such prior knowledge is available and the model architecture explicitly separates covariate and concept shifts, for example by assigning them to different layers for processing, the parametric difference vector $\underline{\theta}_0 - \underline{\theta}_i$ naturally reflects these distinctions across different subsets of parameters. In such cases, our method can effectively incorporate both types of shift during optimization without requiring explicit separation.

Question3：How sensitive is the final model performance to the quality of this initial, and potentially noisy, estimation?

As discussed in Section 5.4, we investigate the performance of OTQMS under different shot settings. The results show that increasing the number of target samples indeed improves the quality of the initial estimation, which in turn leads to better model performance. Nevertheless, across the vast majority of settings, our method consistently outperforms the baselines, demonstrating its robustness to the quality of the initial estimation.

Question4：The paper highlights significant reductions in training time. However, the OTQMS algorithm introduces a selection step in each epoch that involves solving a constrained quadratic program. Could you provide an analysis of the computational overhead of this selection process itself, particularly as the number of source domains $K$ increases?

Thank you for the question. The detailed procedure of the selection step is provided in Appendix F. Here, we provide an analysis of its computational complexity. Specifically, the procedure involves optimizing over two variables: a scalar variable $s$ representing the total transfer quantity, and a vector variable $\underline{\alpha}$ representing the proportion of samples drawn from each source domain. We perform a uniform grid search over the feasible range of $s$, i.e., $[0, s_{\max}]$, using 1000 uniform steps (denoted as $stepnumber = 1000$), where $s_{\max}= \sum\limits_{i=1}^{K} N_i$. For each candidate value $s'$, we solve a constrained optimization problem over $\underline{\alpha}$ under the constraint set $A(s')$, which corresponds to a $K \times K$ quadratic program (QP) with complexity $\mathcal{O}(K^3)$. Thus, the overall time complexity of the selection process is $\mathcal{O}(stepnumber \cdot K^3)$. In our experiments on the Office-Home dataset, where $stepnumber = 1000$ and $K = 3$, the total computational cost of the selection step is approximately $2.7 \times 10^4$ basic operations per epoch. Empirically, the selection step takes around 3.19 seconds per epoch on average, accounting for only 1.1% of the total training time. We acknowledge the reviewer’s concern regarding the growth of computational overhead with respect to $K$. In practice, the number of source domains in standard transfer learning benchmarks is typically small (e.g., $K \leq 10$), making the $\mathcal{O}(stepnumber \cdot K^3)$ complexity acceptable for most practical applications. Moreover, for scenarios with a large number of source domains, one possible extension is to cluster or merge similar domains before applying our algorithm.

Question5：Does this averaging potentially mask the impact of large discrepancies in a small subset of critical parameters? Would a dimension-weighted approach offer further improvements?

Under the high-dimensional setting in Eq. (13) and Eq. (15), the Fisher information matrix $J$ within the $t$ term naturally plays a role similar to dimension-weighted averaging. Specifically, the Fisher matrix captures the model’s sensitivity to perturbations in different dimensions of the parameter vector, thereby implicitly assigning greater importance to more influential parameters.

Question6：Could you elaborate on how the cited work [20] specifically justifies this scaling law for parameter distance in the context of transfer learning?

Thank you for the question. [20] provides empirical evidence that supports this assumption. The paper shows that during fine-tuning, model parameters—especially in the lower layers—change very little from their pretrained values. This suggests that for related domains or similar data distributions, the corresponding optimal parameters lie close in parameter space. Since transfer learning typically involves source and target tasks with some degree of similarity, we interpret this as indirect support for our assumption that the parameter distance between source and target models is small in transfer learning settings.

Thank you for your insightful comment!

Thank you for your insightful feedback on our paper. Below, we address each of your concerns point by point.

Q1:Fisher Information Estimation: Given that the Fisher information matrix is estimated using only a small number of target samples, how do the authors ensure the stability and reliability of this estimate?

The dynamic strategy proposed in lines 210–212 can address this issue. Specifically, in the first epoch, we train a $\underline{\theta}_0$ using only the target data, and get the $J(\underline{\theta}_0)$ using the gradient of loss. This $\underline{\theta}_0$ and $J(\underline{\theta}_0)$ is then used to determine the optimal transfer quantity from each source task, and we use random sampling to form a new resampled training dataset. Finally, we continue training $\underline{\theta}_0$ and get new $J(\underline{\theta}_0)$ on this new dataset, and this procedure is repeated in each subsequent epoch to iteratively update the training dataset. In brief, only in the algorithm’s initial epoch do we use a small number of target samples to train the Fisher information matrix; in subsequent epochs, we incorporate additional source samples to assist in training the Fisher information matrix, and the inclusion of more samples helps ensure its stability. Introducing source samples to assist in training the Fisher information matrix can ensure its stability without incurring significant error, because, as stated in line~533, the difference between ${J}(\theta_0)$ and ${J}(\theta_1)$ is of the order $O\left(\frac{1}{\sqrt{N_0}}\right)$. We will include the proof of this result in the revision version of the paper.

Q2:Negative Transfer Evidence: While the theoretical analysis suggests that transferring too many source samples may lead to negative transfer, the experimental results do not explicitly show this. Can the authors provide empirical evidence demonstrating performance degradation when the transfer quantity exceeds the theoretical optimum?

We have addressed this issue at two points in the paper. First, in Figure 1, we observe that when the quantity of target samples is large, training with both target task samples and all source samples may perform worse than using target task samples only. Second, in Table 2, the method "AllSources $\cup$ Target", which uses all available source and target data for training, gain worse performance than our proposed optimal transfer quantity method, OTQMS.

Furthermore, to better address your concern, we conducted additional experiments. Specifically, over the feasible domain of the total transfer quantity $s \in [0, s_{\max}]$, where $s_{\max}= \sum\limits_{i=1}^{K} N_i$, we evaluated the training performance corresponding to the transfer quantity at each decile point of $s_{\max}$. The results demonstrate that none of these transfer quantities achieve better performance than our proposed optimal transfer quantity $s^{*}$. This experiment is conducted on the Office-Home dataset, and the table reports the average accuracy across all domains when each is used as the target domain.

Q3:Optimal Transfer Quantity in Practice: The framework is designed to compute the optimal number of samples to transfer from each source, but the paper does not state what these optimal quantities actually are in practical settings. Could the authors report or visualize the learned transfer quantities to enhance interpretability?

Your suggestion is very helpful. In Figure 5(b) of Appendix G, we provide a domain preference heatmap for transfer on the DomainNet dataset, which reflects the normalized transfer proportion of each source domain. Your comment made us realize the importance of also reporting the raw transfer quantities. We hereby supplement the actual average transfer quantities on both the Office-Home and DomainNet datasets, and will include them in the revised version of the paper. In the table below, each row corresponds to a target domain, while each column represents a source domain.

Q4:Existence and Solvability of the Optimum: Has the existence and uniqueness of the solution to the optimization problem in Theorem 7 been formally analyzed or empirically verified? Are there conditions under which the solution may not exist?

Here, we provide a more detailed explanation of the optimization method of Theorem 7 described in Appendix F, and prove the existence of a globally optimal solution. The minimization problem of the objective function in Theorem 7 is Eq. (74), i.e.,

$$(s^\*, \underline{\alpha}^\*) \gets \arg \min_{(s, \underline{\alpha})} \frac{d}{2}\left(\frac{1}{N_0+s}+\frac{s^2}{(N_0+s)^2}\frac{\underline{\alpha}^T\Theta^T{J}({{\underline{\theta}}_0})\Theta\underline{\alpha}}{d}\right).$$

We decompose this problem and explicitly formulate the constraints as Eq. (75), i.e.,

$$(s^\*, \underline{\alpha}^\*) \gets \arg\min_{s\in[0,\sum\limits_{i=1}^{K}N_i]} \frac{d}{2}\left(\frac{1}{N_0+s}+\frac{s^2}{(N_0+s)^{2}d}\arg\min\limits_{\underline{\alpha}\in\mathcal{A}(s)}\underline{\alpha}^T\Theta^T{J}({{\underline{\theta}}_0})\Theta\underline{\alpha}\right),$$

where

\mathcal{A}(s)=\bigg\\{\underline{\alpha}\Bigg|\sum_{i=1}^{K}\alpha_i=1, s*\alpha_i \le N_i, \alpha_i \ge0,i=1,\dots,K \bigg\\}.

This problem requires optimizing the objective function over two variables: a scalar variable $s$ representing the total transfer quantity, and a vector variable $\underline{\alpha}$ representing the proportion of samples drawn from each source domain. For $s$ which is restricted to integer values, we perform a exhaustive search over its feasible domain $[0, s_{\max}]$，where $s_{\max}= \sum\limits_{i=1}^{K} N_i$. For each candidate $s'$ in the search, we compute the optimal $\underline{\alpha}'$ under the constraint $\mathcal{A}(s')$, which is a $K\times K$ quadratic programming problem with respect to $\underline{\alpha}$

$$\underline{\alpha}'=\arg\min\limits_{\underline{\alpha}\in\mathcal{A}(s')}\underline{\alpha}^T\Theta^T{J}({{\underline{\theta}}_0})\Theta\underline{\alpha}.$$

The quadratic coefficient matrix in this optimization problem is given by $\Theta^\top J(\underline{\theta}_0) \Theta$. Since the Fisher information matrix $J(\underline{\theta}_0)$ is positive semi-definite, the quadratic coefficient matrix is also positive semi-definite. This guarantees the existence of a global optimal solution. After getting $s'$ and $\underline{\alpha}'$, the function is then evaluated at $(s', \underline{\alpha}')$.

In brief, for each $s'$, we solve for the corresponding optimal $\underline{\alpha}'$, yielding a finite collection of candidate solutions $(s', \underline{\alpha}')$ and their associated objective function values. After completing the search, the optimal solution $(s^\*, \underline{\alpha}^\*)$ is chosen as the pair that achieves the lowest objective function values among all candidate $(s', \underline{\alpha}')$. Since the feasible set of $s$ is finite and enumerable, and for each fixed $s'$ the optimization over $\underline{\alpha}'$ has a solution, the overall optimization problem is guaranteed to have at least one global solution. Hence, the optimal pair $(s^\*, \underline{\alpha}^\*)$ exists.

It is worth noting that, for the sake of computational efficiency, we do not exhaustively enumerate all possible values of $s$ in our experiments. Instead, we perform a grid search using 1000 uniformly spaced steps over the feasible range of $s$, where the number of steps is denoted as $stepnumber = 1000$. Experimental results in Section 5 demonstrate that this strategy does not compromise the effectiveness or stability of the method.

Thank you again for your valuable insights. We kindly request that the reviewer considers these points when assigning the final scores.

Thank you for the detailed responses. I find the answers to Q2–Q4 satisfactory.

Regarding Q1, I appreciate the explanation of the dynamic update strategy. However, I still have some concerns about the stability of the Fisher information estimate, particularly in the initial epoch when only a small number of target samples are used. Clarifying its robustness would further strengthen the method.

That said, given that the empirical results are promising and my concerns in Q2–Q4 have been adequately addressed, I am willing to raise my score.

Thank you for your thoughtful response and your positive recognition of our work. We will provide a clarification regarding your remaining concern on Q1.

Question: The robustness of the algorithm and the initial Fisher information estimation.

We understand the reviewer’s concern regarding the impact of the variance of the initial Fisher information matrix on the robustness of our algorithm OTQMS. We believe that Sections 5.3 and 5.4 help clarify this issue. As discussed in Section 5.4, we evaluate the performance of OTQMS under varying shot settings, which correspond to different quantities of target samples. A higher shot setting leads to better initial estimates of both the target model parameters and the Fisher information matrix. Nevertheless, OTQMS demonstrates stable performance and consistently outperforms the baselines across most shot settings, including those with very limited target samples, highlighting its robustness to the quality of the initial Fisher information. This robustness is largely attributable to the proposed dynamic strategy, which incorporates additional source samples to assist in training the Fisher information matrix in subsequent epochs, and whose effectiveness is further validated in Section 5.3.

To further support the robustness of our algorithm, we supplement the main result table (Table 2 in the paper) by reporting the standard deviations of OTQMS and selected baselines, computed over 10 runs with different random seeds. Since each seed results in a different randomly sampled 10-shot target dataset, the relatively small standard deviations suggest that OTQMS remains robust despite variations arising from different target-data samplings and corresponding initial Fisher information estimates.

Performance on the Office-Home dataset under the same setting as Table 2 in the paper. The horizontal axis lists the target domains, where the arrow notation (e.g., →Ar) indicates transferring to that domain from all others. The vertical axis lists the compared methods.

Performance on the DomainNet dataset under the same setting of Table 2 in the paper

Thank you again for your thoughtful and constructive feedback. We kindly hope these clarifications demonstrate the robustness of our algorithm. We are truly grateful for your willingness to raise your score. Considering that the discussion phase is about to end, we would like to kindly remind you that—if you have no further concerns—you may click the “Edit” button at the top of your initial review to update your final score.