Gains: Fine-grained Federated Domain Adaptation in Open Set

We'd like to express our sincere gratitude to the reviewer for your careful reading and highly valuable feedback, which has been extremely beneficial to us. We have made every effort to address your concerns, and some of them will be included in the final version. The following is the the details:

Q1. Analysis of the $Diff$ thresholds

(1) Sensitivity analysis

Although the thresholds are manually set, the model exhibits strong robustness to threshold variations. As shown in Fig. 2, the changes in $Diff^F$ and $Diff^C$ are very significant, which means that the thresholds can take values over a wide range, with $Diff^F$ ranging from 700 to 3400 and $Diff^C$ from 0.05 to 0.27. We also conduct experiments on various thresholds under the mild shift scenario of DigitFive (source: MNIST-M; target: MNIST) as an example, with $T_F \in {800, 1000, 1200}$ and $T_C \in {0.20, 0.25, 0.27}$. The results are as follows:

It can be seen that the model performance remains stable when parameters fluctuate within reasonable ranges (performance variation < 1%).

(2) Alternative solutions

To automate the selection of thresholds, we can use a statistics-based approach. In the pre-experiment, we repeatedly introduce clients that carry new knowledge into the federated-learning system and, each time, record the resulting $Diff^F$ and $Diff^C$ values. After collecting many such samples, we compute the means ($\mu_F$, $\mu_C$) and standard deviations ($\sigma_F$, $\sigma_C$) of the two metrics. We then set the thresholds as:

• $T_F = \mu_F + \alpha\sigma_F$,
• $T_C = \mu_C + \beta\sigma_C$,

where $\alpha$ and $\beta$ are tunable coefficients that control how strict the thresholds should be.

Q2. Concerns about the public dataset

Public datasets are commonly utilized in FL to simulate shared server knowledge and enable cross-domain evaluations—e.g., FCCL[1] and SacFL[2] both rely on such resources to facilitate client model alignment. Our use aligns with this widespread and pragmatic practice.

In our experiments, the public data is sampled from the DigitFive and Amazon Review datasets, which are strictly disjoint from client data and only stored on the server. Generally speaking, it can be accessed from other datasets that are totally different from clients' data, such as Office-Home, thereby avoiding privacy leakage.

To address scenarios without public datasets, a lightweight client-encoder distillation mechanism can be adopted. Specifically, the server can collect statistical summaries (e.g., encoder outputs’ mean and covariance) from clients instead of raw data, ensuring privacy. By comparing these anonymized feature statistics, the server can approximate $Diff^F$ and $Diff^C$ for knowledge discovery. This part will be shown in the experimental setting and discussion.

• [1] Huang W, et al. Learn from others and be yourself in heterogeneous federated learning[C]//CVPR. 2022: 10143-10153.

• [2] Zhong Z, et al. SacFL: Self-Adaptive Federated Continual Learning for Resource-Constrained End Devices[J]. TNNLS, 2025.

Q3 & W1. Concerns about new knowledge discovery mechanism

(1) Empirical analysis

We conducted a detailed analysis of the DigitFive dataset. In the class increment scenario, the source domain data is MNIST with classes {0,1,2,3}, and we sequentially add data from {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, where the first four cases correspond to no increment and the latter six cases correspond to class increment. In the domain increment scenario, the source domain is SVHN, and we sequentially add MNIST, MNIST-M, and SynthDigits data. We obtained the mean and variance of $Diff^F$ and $Diff^C$ under different conditions, as shown in the table below:

As shown above, $Diff^F$ increases dramatically during domain and class increments, while $Diff^C$ exhibits clear peaks during class increments. Using a simple decision boundary (e.g., $Diff^F$ > 1000 → new knowledge, $Diff^C$ > 0.25 → new class), we can easily distinguish these two knowledge increment scenarios.

(2) Theoretical supports

This work is based on experimental findings that the Decoder (especially the classification head) is more sensitive to changes in classes, while the features extracted by the Encoder are sensitive to changes in knowledge. Therefore, we detect new knowledge by observing changes in the features extracted by the Encoder and the parameters of the Decoder. This approach is well supported by previous studies. For example, Rebuffi et al. [1] found that an increase in the number of classes leads to changes in the structure and parameters of the classifier, indicating that the classifier is sensitive to class changes. Zhong et al. [2] proposed that when new knowledge is introduced, the features extracted by the Encoder undergo significant changes. Therefore, the findings of previous research provide strong theoretical support for the knowledge discovery method proposed in this paper.

• [1] Rebuffi S A, Kolesnikov A, Sperl G, et al. icarl: Incremental classifier and representation learning[C]//CVPR. 2017: 2001-2010.

• [2] Zhong Z, Bao W, Wang J, et al. SacFL: Self-Adaptive Federated Continual Learning for Resource-Constrained End Devices[J]. TNNLS, 2025.

Q4 & W2. Concerns about baselines

(1) FOSDA and SemiFDA

Although FOSDA and SemiFDA are not specifically designed for class+domain shift scenarios, in our experiments, our method has been compared with them in both individual class increment and domain increment scenarios (Table 1), demonstrating excellent superiority. This further illustrates that Gains possesses good adaptation capabilities.

(2) FCL baselines

While our work is primarily situated in the open-set federated domain adaptation (FDA) setting, which differs in several key aspects from FCL (illustrated in the discussion), we agree that including FCL baselines addressing class-incremental scenarios would enrich our evaluation. To address this, we conducted additional experiments incorporating FedWeIT and FedCIL as baselines in the class-incremental scenario under mild data shift (DigitFive dataset, target client introduces new classes {1,5}).

Gains achieves significantly higher T-Acc while maintaining S-Acc, demonstrating both effective new class integration and source knowledge retention. These baselines will be included in the final version.

Q5 & W1. More complex models

We test the ResNet18 model in the DigitFive dataset under the medium data shift scenario (source: SVHN, target: MNIST). All baselines are reimplemented with ResNet18 as backbone for fair comparison.

We can see that Gains maintains strong generalization on both source and target domains. It outperforms all baselines across all metrics, confirming robustness across architecture types. Meanwhile, under the condition of equivalent learning effectiveness, the computational resources consumed by Gains are lower than those of most other methods (comparable to FedHEAL). Although the calculation of server-side contribution degree will consume more computing resources during the aggregation compared to traditional FL, this process will accelerate the model convergence, thereby reducing the training time. Therefore, it will not result in significant computational resource overhead. This part will be included in the final version.

L1. Experiments in complex scenarios

When both domain shift and class shift occur simultaneously in the target domain, our method still works. We can combine Domain-incremental and Class-incremental contribution-driven aggregation strategies. The aggregation strategy is as follows:

• Encoder: Contribution calculated by Eq. (2), aggregated by Eq. (4).
• Classifier:
  • Old-class channels aggregated via Eq. (3) and Eq. (5),
  • New-class channels are directly adopted from the target domain model, as described in Line 176 of the manuscript.

To this end, we validated the scenario where both class increment and domain increment occur simultaneously. Specifically, using the DigitFive dataset medium shift as an example, the source domain client data is MNIST with classes {0,2,3,4,6,7,8,9}; the target client includes two types of data: one is MNIST classes {1,5}, and the other is SVHN dataset classes {0,2,3,4,6,7,8,9}. The experimental results obtained are as follows:

The results indicate that under the mixed incremental scenario, the performance achieved by Gains is comparable to scenarios with only domain or class increments, without significant degradation. For more complex task-increment scenarios, such as extending from image classification tasks to object detection tasks, adaptive architectures can be designed by incorporating meta-learning techniques. This allows the model to autonomously identify and handle task space expansion, automatically differentiate parameters, and adapt independently, thereby ensuring continual knowledge growth and effective control of unlearning. We will include the above experimental validation and discussion in the final version.

Thank you sincerely for your valuable comments. We are sorry for not providing a clear clarification. In the previous version, we had already conducted a thorough empirical analysis. Hence, we made the best efforts to conduct a theoretical analysis in this version and kindly hope this justification addresses the issue you raised. Your discussion is greatly appreciated.

1. Justification Objective

We aim to prove:

Discovery 1. Both domain increment and class increment significantly disturb the encoder $E$'s feature extraction, causing $Diff^F$ increases.

Discovery 2. In contrast, class increment leads to a greater disturbance in classifier parameters $C$, i.e., $Diff^C_{class}>Diff^C_{domain}$.

2. Analysis of Discovery 1 ($Diff^F$)

2.1 Basic Definitions and Assumptions

Definitions

Let:

• $x \in D_P$: Public input sample from server

• $E^S$, $E^T$: Encoders from source and target domains

• Feature change is defined as:

  $Diff^F = \frac{1}{||D_P||} \sum_{x \in D_P} ||E^T(x) - E^S(x)||_1.$

Assumptions

• The Original input distribution is $\mathbb{P}_S(x)$, and the new client input distribution is $\mathbb{P}_T(x)$, where:

  $\text{domain shift: } \mathbb{P}_T(x) \neq \mathbb{P}_S(x)$ or $\text{class shift: } \mathbb{P}_T(y) \neq \mathbb{P}_S(y)$.

• Encoder is $E$ is $L_E$-Lipschitz.

We aim to analyze why this quantity increases in both class and domain increment scenarios.

2.2 Domain/Class increment

Domain increment case

Since $E$ is $L_E$-Lipschitz, we can get:

$||E(x_1) - E(x_2)||_1 \leq L_E \cdot ||x_1 - x_2||_1.$

Using the Wasserstein-1 distance:

$$W_1(\mathbb{P}\_T, \mathbb{P}\_S) := \inf_{\gamma \in \Pi(\mathbb{P}\_T, \mathbb{P}\_S)} \mathbb{E}\_{(x,x') \sim \gamma} ||x - x'||_1.$$

It measures the distance between two domains. Then, from Kantorovich-Rubinstein Duality, for Lipschitz $f$:

$$||\mathbb{E}\_{x \sim \mathbb{P}\_T}[f(x)] - \mathbb{E}\_{x \sim \mathbb{P}\_S}[f(x)]|| \leq L\_f \cdot W_1(\mathbb{P}\_T, \mathbb{P}\_S).$$

Let $f(x) = ||E^T(x) - E^S(x)||_1$, thus:

$$\mathbb{E}{x \sim D_P}[||E^T(x) - E^S(x)||_1] \propto L_E \cdot W_1(\mathbb{P}_T, \mathbb{P}_S).$$

As long as $\mathbb{P}_T \ne \mathbb{P}_S$ (i.e., domain increment occurs), the Wasserstein distance $W_1 > 0$, which leads to a significant increase in the feature discrepancy, i.e., $Diff^F$ rises sharply.

Class increment case

Even if input style remains unchanged $( \mathbb{P}\_T(x) = \mathbb{P}\_S(x) )$, new labels emerge:

• Original labels: $\mathcal{Y}\_S = \{1,...,K\}$
• New client labels: $\mathcal{Y}\_T = \mathcal{Y}\_S \cup \Delta \mathcal{Y}$

Training on new labels:

$$\min_{E, C} \mathbb{E}\_{(x,y) \sim \mathbb{P}\_T(x,y)} \left[ \mathcal{L}\_{\text{CE}}(C(E(x)), y) \right].$$

In the above process, we focus on the parameter updates of $E$, which are dominated by gradients:

$$\Delta E = -\eta \cdot \mathbb{E}_{(x,y) \sim \mathbb{P}_T} \left[ \frac{\partial \mathcal{L}\_{CE}(C(E(x)), y)}{\partial E} \right].$$

Specifically, for the newly added class $\Delta \mathcal{Y}$, its corresponding samples may account for a large proportion of the loss gradient. Since the model had not encountered these classes initially, the prediction deviation is greater, resulting in a higher loss and steeper gradient. Hence, it will cause $E$ to be more inclined to update towards the new class, thereby leading to significant changes in the extracted feature values.

In summary, we can conclude that input distribution shift (either from new classes or new domains) leads to larger $Diff^F$.

3. Analysis of Discovery 2 ($Diff^C$)

3.1 Definition

$$Diff^C = ||C_T - C_S||_2 = \sqrt{ \sum _{i} ||w_i^{(T)} - w_i^{(S)}||_2^2 }.$$

3.2 Domain/Class increment

• Assume $C_S \in \mathbb{R}^{d \times K}$, $C_T \in \mathbb{R}^{d \times (K + \Delta K)}$
• New class heads $w_j^{(T)}$ are initialized at zero and updated with large gradients due to untrained logits
• Let $\mu = \mathbb{E}[||w_j^{(T)}||_2]$ for $j \in \Delta K$
• Inputs change but label supervision remains stable, classifier fine-tuned slightly around $w_i^{(S)}$:

$$||w_i^{(T)} - w_i^{(S)}||_2 \approx \varepsilon,\quad \forall i \in \{1,...,K\}.$$

Class increment case

$${Diff^C_{\text{class}}}^2 = \sum _{j=1}^K ||w_j^{(T)} - w_j^{(S)}||_2^2 + \sum _{j=K+1}^{K+\Delta K} ||w_j^{(T)}||_2^2 \approx K \cdot \varepsilon^2 + \Delta K \cdot \mu^2.$$

Domain increment case

$${Diff^C_{\text{domain}}}^2 \approx K \cdot \varepsilon^2.$$

Comparative Inequality

Given $\mu \gg \varepsilon$:

$$Diff^C_{\text{class}} \gg Diff^C_{\text{domain}}.$$

This inequality theoretically confirms that class increments yield substantially higher classifier parameter variation, justifying our use of $Diff^C$ to detect new class knowledge.

Thank you sincerely for your valuable comments. We have made every effort to respond to each point individually, addressing your concerns to the best of our ability. We hope these revisions adequately address all the issues you raised. Your input is greatly appreciated.

Q1 & W1. Sensitivity analysis of the $Diff^F$ and $Diff^C$ thresholds

Although the thresholds are manually set, the model exhibits strong robustness to threshold variations. As can be seen from Figure 2, the changes in $Diff^F$ and $Diff^C$ are very significant, which means that the thresholds can take values over a wide range, with $Diff^F$ ranging from 700 to 3400 and $Diff^C$ from 0.05 to 0.27. We also conduct experiment tests on various thresholds using the mild shift scenario in the DigitFive dataset as an example. Assuming the source domain data is MNIST-M and the target domain data is MNIST, with $T_F \in {800, 1000, 1200}$ and $T_C \in {0.20, 0.25, 0.27}$. The experimental results obtained are shown in the following table:

From the above two tables, it can be seen that the model performance remains stable when parameters fluctuate within reasonable ranges (performance variation < 1%).

Q2 & W2. Mixed incremental scenarios

When both domain shift and class shift occur simultaneously in the target domain, we can combine Domain-incremental and Class-incremental contribution-driven aggregation strategies. The aggregation strategy is as follows:

• Encoder: Contribution calculated by Eq. (2), aggregated by Eq. (4).
• Classifier:
  • Old-class channels aggregated via Eq. (3) and Eq. (5),
  • New-class channels are directly adopted from the target domain model, as described in Line 176 of the manuscript.

To this end, we validated the scenario where both class increment and domain increment occur simultaneously. Specifically, using the DigitFive dataset medium shift as an example, the source domain client data is MNIST with classes {0,2,3,4,6,7,8,9}; the target client includes two types of data: one is MNIST classes {1,5}, and the other is SVHN dataset classes {0,2,3,4,6,7,8,9}. The experimental results obtained are as follows:

These results indicate that under the mixed incremental scenario, the performance achieved by Gains is comparable to scenarios with only domain or class increments, without significant degradation. We will include this new experiment and clarify the support for mixed-increment scenarios in the final version.

Q3. Algorithm 1

When no new knowledge is introduced, the original model can be directly applied to newly joined clients for inference tasks without requiring training. We will complete this explanation in the final version of the algorithm.

Q4. Explanations of Table 1

(1) The T-Acc of FOSDA and SemiFDA

FOSDA is designed for open-set scenarios by leveraging an uncertainty-aware mechanism to distinguish known from unknown classes. Under a mild domain shift, the inter-domain discrepancy is too small to activate the unknown class detector properly, causing a large number of target samples to be incorrectly rejected, which leads to T-Acc approaching zero. As the domain shift increases (Medium/Strong), the feature distribution discrepancy becomes more pronounced, enabling FOSDA to perform effective domain separation.

SemiFDA employs an unsupervised feature alignment strategy (based on CORAL) with a frozen classification head. In the Mild setting, the target distribution is extremely close to the source, resulting in insufficient feature updates and poor adaptation of the classifier—hence a T-Acc of 0.00. As the domain gap widens, stronger distributional shifts provide more adaptation signals, improving alignment and classification performance.

(2) The S-Acc of AutoFedGP and FedAVG

In the Mild scenario, AutoFedGP suffers from scarce and noisy target data. Its auto-weighting mechanism overemphasizes the limited target gradients and suppresses source gradient contributions, leading to severe source forgetting.

FedAVG assumes fully IID data and lacks any domain adaptation mechanism. Under Mild conditions, the introduction of new target-domain classes exacerbates data distribution skew across clients, resulting in unstable training dynamics (as shown in Fig. 4(a)). Consequently, FedAVG fails to balance performance between source and target domains. The reported results reflect only the final training round.

Q5 & W3. Sensitivity analysis of $\lambda$

We test the performance on the DigitFive dataset under the medium shift scenario (task: USPS → MNIST) with $\lambda$ ∈ {0.0, 0.1, 0.3, 0.5, 0.7, 1.0}. Each $\lambda$ is tested with three repeated training runs, taking the average. The results are as follows:

From the above experimental results, it can be seen that when $\lambda$ approaches 0, new knowledge dominates aggregation, leading to old knowledge forgetting (S-Acc decreases). When $\lambda$ is too large, target domain performance is limited (T-Acc decreases). Overall, $\lambda=0.5$ achieves optimal balance, and subsequent experiments are set accordingly.

Q6. Results under no domain shift conditions.

In the table below, we present the accuracy of the source domain clients without the entry of new clients. Compare with Table 1 of the paper, it can be seen that almost all baselines show a decline in performance on the source domain, while Gains has the smallest decline. We will include these results in Table 1 in the final version.

Q7. Concerns about the training time.

Inevitably, extra computational costs occur when calculating the contributions on the server. However, by calculating the weights based on contribution, more efficient aggregation can be achieved, thereby significantly reducing the number of federated iterations. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations are as shown in the table below:

Although Gains consumes more computational resources per round, it reduces the number of communication rounds by approximately 84.8%, resulting in lower overall computation costs. Moreover, since the contribution calculation is performed on the server, it does not impose an additional computational burden on the clients. On the contrary, the significantly reduced number of rounds substantially lowers the communication overhead for clients. The above results will be shown in the final version.

Thank you for your time and efforts. We hope this has addressed your concerns and answered your questions. Please don’t hesitate to reach out if you have any further questions.

Thank you sincerely for your thoughtful comments and valuable insights on our manuscript. We have carefully addressed each of your concerns, dedicating significant effort to revise and clarify the points you raised. The following is our response:

W1. Large-scale experiments

Taking the medium shift in the DigitFive dataset (source: SVHN; target: MNIST) as an example, we respectively increase the number of source domain clients from 50 to 100, and increase the number of newly joined clients each time from 1 to 10, obtaining the following experimental results:

From the above table, it can be seen that when the number of source domain and target domain clients increases, the method proposed in the paper still maintains a good performance. This part will be included in the final version.

W2. Explanations of formulas

Formulas (2) and (3) are the foundation of our contribution-driven aggregation mechanism, designed to adaptively weigh each source client’s encoder and classifier during aggregation, depending on both their similarity to the target domain and their sample size.

Formula (2) is as follows:

$CD^E_n(i) = \frac{1}{(1 + \mathrm{Diff}^F_n(i)) \times \sum_{n=1}^{N} \left( \frac{1}{1 + \mathrm{Diff}^F_n(i)} \right)} \times \frac{\sum_{n=1}^{N} |\mathcal{D}^S_n|}{|\mathcal{D}^T| + \sum_{n=1}^{N} |\mathcal{D}^S_n|}$,

where $\frac{1}{1 + Diff^F_{n}(i)}$ assigns a higher contribution to source clients whose encoder features are more similar to the target domain (i.e., with a smaller $Diff^F_n(i)$); the normalization $\frac{1}{\sum_{n=1}^{N} \frac{1}{1 + Diff^F_{n}(i)} }$ ensures fairness among all clients; the sample proportion component $\frac{\sum_{n=1}^{N} |\mathcal{D}^S_n|}{|\mathcal{D}^T| + \sum_{n=1}^{N} |\mathcal{D}^S_n|}$ ensures that source clients with more data have an appropriate level of influence. Formula (3) follows a similar logic but focuses on the classifier parameters ($Diff^C_n(i)$). A lower distance indicates a better fit to the target domain; thus, a higher contribution weight is assigned. We apologize for the inconvenience and will include explanations in the final version.

W3. Concerns about the discussion

(1) Solutions to automated knowledge discovery

To automate the selection of thresholds, we can use a statistics-based approach. In the pre-experiment, we repeatedly introduce clients that carry new knowledge into the federated-learning system and, each time, record the resulting $Diff^F$ and $Diff^C$ values. After collecting many such samples, we compute the means ($\mu_F$, $\mu_C$) and standard deviations ($\sigma_F$, $\sigma_C$) of the two metrics. We then set the thresholds as:

• $T_F = \mu_F + \alpha\sigma_F$,
• $T_C = \mu_C + \beta\sigma_C$,

where $\alpha$ and $\beta$ are tunable coefficients that control how strict the thresholds should be.

(2) Solutions to complex increment scenarios

When both domain shift and class shift occur simultaneously in the target domain, our method still works. We can combine Domain-incremental and Class-incremental contribution-driven aggregation strategies. The aggregation strategy is as follows:

• Encoder: Contribution calculated by Eq. (2), aggregated by Eq. (4).
• Classifier:
  • Old-class channels aggregated via Eq. (3) and Eq. (5),
  • New-class channels are directly adopted from the target domain model, as described in Line 176 of the manuscript.

To this end, we validated the scenario where both class increment and domain increment occur simultaneously. Specifically, using the DigitFive dataset medium shift as an example, the source domain client data is MNIST with classes {0,2,3,4,6,7,8,9}; the target client includes two types of data: one is MNIST classes {1,5}, and the other is SVHN dataset classes {0,2,3,4,6,7,8,9}. The experimental results obtained are as follows:

These results indicate that under the mixed incremental scenario, the performance achieved by Gains is comparable to scenarios with only domain or class increments, without significant degradation. For more complex task-increment scenarios, such as extending from image classification tasks to object detection tasks, adaptive architectures can be designed by incorporating meta-learning techniques. This allows the model to autonomously identify and handle task space expansion, automatically differentiate parameters, and adapt independently, thereby ensuring continual knowledge growth and effective control of unlearning.

We will include the above experimental validation and discussion in the final version.

W4. Concerns about method effect

In fact, rapid adaptation is reflected not only in fewer iterations but also in shorter computation time. Inevitably, extra computational costs occur when calculating the contributions on the server. However, by calculating the weights based on contribution, more efficient aggregation can be achieved, thereby significantly reducing the number of federated iterations and reducing the overall training time. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations are as shown in the table below:

Although Gains consumes more computational resources per round, it reduces the number of communication rounds by approximately 84.8%, resulting in lower overall training time. We will further emphasize this point in the paper.

W5. Missing table lines

Thank you for your correction. We will revise the formats of Table 2 and Table 3 in the final version.

Q1. Doubts about Figure 2

As shown in Figure 2, in the class-incremental scenario, when the number of new classes is 1, the change in the encoder parameters is significantly lower than in the case where the new client does not experience a shift; when the number of new classes is 4, the amount of change is comparable to that when the new client does not experience a shift. This change increases as the number of new classes increases. This indicates that the amount of change in the encoder is closely related to the number of new classes, but not obviously related to whether new class knowledge is introduced. In addition, in the domain-incremental scenario, the change in the encoder is also comparable to that without increment. Therefore, the variation of the encoder does not show a clear fluctuation trend.

Q2. Doubts about Line 22

“new clients, i.e., target domain” refers to new clients from the target domain. We usually consider the data carried by newly joined clients as belonging to the target domain, and the target domain may or may not be the same as the source domain.

Greatly thank the reviewer for your time and valuable feedback. We have made every effort to solve your problem and sincerely hope to meet your requirements. The responses are as follows:

W1 & Q1. Notations

In the paper, $\hat{I}$ refers to the number of local training iterations performed on the new client after joining the federated learning. The updated model is then uploaded to the server for fine-grained identification of new knowledge types. If new knowledge is detected, global federated training is conducted for $I$ rounds. To avoid confusion, we will denote this local training epoch as $Q$ in the final version.

W2 & Q2 & Q3. Superscript error & Concerns about the public dataset

(1) Superscript error

Yes, the superscript of encoder E should be capital S. Thank you for your careful reading. We will correct the superscript of Encoder E in line 130 in the final version.

(2) Public dataset

In our experiments, the public data is sampled from the DigitFive and Amazon Review datasets, which are strictly disjoint from client data and only stored on the server. Generally speaking, it can be accessed from other datasets that are totally different from clients' data, such as Office-Home, thereby avoiding direct privacy leakage.

To address scenarios without public datasets, a lightweight client-encoder distillation mechanism can be adopted. Specifically, the server can collect statistical summaries (e.g., encoder outputs’ mean and covariance) from clients instead of raw data, ensuring privacy. By comparing these anonymized feature statistics, the server can approximate $Diff^F$ and $Diff^C$ for knowledge discovery.

W3. Computing complexity analysis

Compared with traditional federated learning, Gains mainly increases the computational load during the server-side contribution calculation. Its complexity is 𝑂(N⋅P⋅d), where N is the number of source domain clients, P is the size of the public dataset, and d is the number of model parameters. Inevitably, extra computational costs occur during the above process. However, by calculating the weights based on contribution, more efficient aggregation can be achieved, thereby significantly reducing the number of federated iterations and reducing the overall training time. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations are as shown in the table below:

Among the methods with comparable learning effects, although Gains consumes more computing resources in each round, it reduces the number of iterations by 84.8%, thereby reducing the overall training time. We will show this result in the experiment section.

W4. Concerns about Fig.3

Sorry, it is a mistake. Figure 3 should be cited in line 117:

"Framework. Inspired by the above empirical discoveries, we propose a fine-grained federated domain adaptation framework in open set, Gains (as shown in Fig. 3). Specifically, it consists of two main components: knowledge discovery and knowledge adaptation."

In the final version, we will simplify the characters in Figure 3 to make them clearer and easier to understand.