Rethinking Fair Federated Learning from Parameter and Client View

Dear Reviewer bBPA:

Thank you very much for your thoughtful questions and concerns about our work. We have carefully considered each comment and provided responses.

Weaknesses

W1 & L1: Pareto stability guarantee.

A1: Thank you for your insightful comment. Since our method is not designed from a multi-objective optimization perspective, we did not explicitly provide a Pareto optimality analysis in the main paper. However, our approach satisfies the necessary conditions for achieving Pareto optimality under certain assumptions. Specifically, the global descent direction in our method is a weighted sum of individual client gradients. In the early stages of training, these gradients tend to be aligned (i.e., having positive pairwise inner products), and in later stages, they become nearly orthogonal. As long as the weights remain positive and not excessively large, the resulting global direction maintains a positive inner product with each client’s gradient, thereby qualifying as a Pareto Descent Direction. This property enables FedPW to approximate the Pareto frontier in practice, promoting a balanced trade-off between accuracy and fairness.

W2: The provided experimental code is incomplete.

A2: We sincerely apologize for the earlier incomplete release of our experimental code. The repository has now been fully updated to include all components necessary for reproduction, including complete datasets scripts, training and evaluation pipelines, and baseline implementations. We welcome you to re-evaluate the codebase, and we appreciate your understanding and feedback.

Questions

Q1: How is the redundancy value in the Fig. 2 (right) y-axis evaluated?

A3: We apologize for the confusion. The y-axis in Figure 2 (right, Page 4) does not represent the redundancy value itself. Each point corresponds to a particular experiment (as in Figure 2 left), where the x-axis denotes the redundancy ratio and the y-axis shows the resulting test accuracy. For instance, in the CIFAR-10 setting, when the redundancy ratio reaches around 0.85, the corresponding accuracy is approximately 70%.

Q2: Large std in Table 2 suggests a suboptimal fairness level.

A4: Thank you for your insights and concerns. As shown in Table 2 (Page 8), the performance varies noticeably across different domains. However, in multi-domain federated fairness settings, significant performance variation across domains is common due to extreme non-IID conditions. Our work focuses precisely on evaluating robustness under such challenging scenarios. Even state-of-the-art fairness methods struggle to achieve small standard deviations in this setting. Despite the seemingly large deviation values, our method achieves substantially lower disparity compared to SOTA baselines, highlighting its effectiveness and robustness in enforcing fairness under practical FL conditions.

Paper Formatting Concerns

F1: Incorrect reference of Equation (10) as Equation (9).

A5: Thank you for pointing this out. We sincerely apologize for the oversight. There was indeed a mix-up between the references to Equations (9) and (10). We will correct this citation in the final version.

F2 & F3: Explanation of equations and algorithmic flow.

A6: We appreciate your valuable suggestion. Due to the coupling between the two components of our method, some equations are cross-referenced, which may have disrupted the overall flow of the algorithm. To clarify the core workflow, we provide a simplified pseudocode that highlights the essential steps. We will include the complete pseudocode in the appendix of the final version and revise the corresponding descriptions to improve clarity.

For each client $k = 1, ..., K$:
//Adaptive Weighting:
$p_k^t, \Delta p_k^t \leftarrow (p_k^{t-1}, \Delta p_k^{t-1}, \beta)$ from Eq.(9)
$q_k^t, \Delta q_k^t \leftarrow (q_k^{t-1}, \Delta q_k^{t-1}, \beta)$ from Eq.(10)
$\lambda_k^t \leftarrow f(p_k^t, p_k^t)$ from Eq.(11)
//Parameter Adjustment:
For $i = 1, ..., G$:
$\mathcal{M}\_{k,i}^t \leftarrow$ mask computed from Eq.(5)
$\Delta \mathbf{w}\_{k,i}^t = \Delta w_{k,i}^t \cdot \mathcal{M}\_{k,i}^t$
$\alpha_i^t \leftarrow$ scaling from Eq.(7)
$\Delta \mathcal{W}\_i^t = \alpha_i^t \sum_{k=1}^K \lambda_k \Delta \mathbf{w}\_{k,i}^t$

F4: Clear definitions for $\sigma_p$ and $\sigma_q$.

A7: Thank you for the feedback. Since the definitions of $\sigma_p$ and $\sigma_q$ are relatively straightforward, we only described them in words in the original manuscript. Specifically, $\sigma_p$ denotes the client-wise standard deviation of $p_k$ (defined in Eq. (9)), and $\sigma_q$ denotes the standard deviation of $q_k$ (defined in Eq. (10)). For completeness and clarity, we provide their explicit mathematical definitions below:

Thank you for your clarification and promised updates. I have considered these in my final score.

Dear Reviewer ixbu:

Thank you for your thorough review and insightful feedback. We sincerely appreciate your time and effort. We hope that the following responses effectively address your concerns.

Weaknesses

W1: Additional details on variance-based fairness metrics.

A1: As shown in the following table, We additionally evaluate fairness using max-loss, minimum accuracy, the group gap between top-10% and bottom-10% clients, Gini index, and Jain’s fairness index. These results show that our method substantially improves the performance of the most disadvantaged clients across diverse fairness definitions.

Table: Fairness Scores under Different Fairness Metrics in Digits

W2: Validation under more extreme FL conditions.

A2: We acknowledge the importance of evaluating performance under more challenging federated settings. Our original submission already includes experiments with 100 clients and Dirichlet allocation at $\alpha$ = 0.1 (see Tables 3 and 4). To further validate the robustness of FedPW, we have added new experiments covering larger client scales (from 120 to 300 clients) and more severe data heterogeneity with $\alpha$ ranging from 0.01 to 0.09. The updated results confirm that FedPW consistently outperforms other methods across all these extreme conditions, demonstrating strong scalability and adaptability.

Table: Sensitive Analysis on Number of Clients in Digits

Table: Sensitive Analysis on Dirichlet Heterogeneity in CIFAR-10

W3: Discussion on the limitations of assuming homogeneous model architecture.

A3: Using homogeneous models is a common and convenient setting for fairness-oriented methods. Most fairness-driven FL works adopt this setting, and we follow the same convention. Nonetheless, our approach is compatible with extensions to heterogeneous models. Specifically, our aggregation strategies do not require model alignment, and the pruning mechanism can be adapted to partially shared components, such as aligned layers. Therefore, our framework retains flexibility for broader applicability in non-iid or partially heterogeneous environments.

Question

Q1: What is the criterion for generating parameter masks?

A4: FedPW constructs client-specific parameter masks based on the magnitude of local updates. For each client $k$, we sort the elements of the update vector $\Delta w_k^t$ by absolute value and compute a threshold $\tau_k$ based on the client-specific mask ratio $r_k^t$. All parameters below this threshold are marked as redundant using a binary mask $M_k^t$, as described in Eq. (5). The mask ratio $r_k^t$ is determined by the inverse of the client’s smoothed training loss, meaning that underperforming clients retain more updates to aid their progress.

Q2: How is the transition between the two training phases defined?

A5: The transition between the two training phases in FedPW is not determined by a fixed round count or manually defined schedule. Instead, it is guided by an adaptive, data-driven mechanism. The transition is soft and continuous, governed by the dynamics of training signals rather than a clear boundary, allowing the optimization focus to shift gradually in response to the evolving state of training.

Q3: What communication settings were used in the experiments?

A6: For single-domain experiments, we used 3,000 communication rounds with local epoch = 1 and batch size = 50. For cross-domain experiments, we used 200 communication rounds with local epoch = 10. The batch size is 64 for the Digits dataset and 16 for Office-Caltech. Detailed communication and training configurations are described in the Implementation Details section of the paper (Page 8).

Dear Reviewer ixbu,

Thank you for your valuable comments and the time you spent reviewing our work. Your feedback has played an important role in helping us improve the paper, and we’re grateful for the opportunity to refine our work through this process.

Best regards,

Authors

Dear Reviewer Jzhw:

Thank you for the insightful comment. We appreciate your recognition of the innovative aspects of our motivation and the clarity of our writing. Thank you for your time and effort in reviewing our paper. We hope that our responses below will address your concerns and further affirm the quality of our research.

Weakness

W1 & Q1: Additional hyperparameter sensitivity analysis.

A1: Our method involves only two hyperparameters: the mask ratio $c$ and the momentum coefficient $\beta$. The mask ratio $c$ governs the average masking level in the PA component, where smaller values make FedPW resemble FedAvg and reduce potential gains, while excessively large values may cause instability due to insufficient trainable parameters. The coefficient $\beta$ controls the smoothness of adaptive updates in the AWA component; extremely small values degrade it to a non-momentum variant, while overly large values may delay the system’s responsiveness to training dynamics. To further examine sensitivity, we supplemented results across all datasets. Experiments indicate that the method performs robustly across a range of hyperparameter settings, showing stable behavior without strong sensitivity.

Table: Average Accuracy(and Standard Deviation) Under Varying $\beta$

Table: Average Accuracy(and Standard Deviation) Under Varying $c$

W2: Discussion on the limitations of assuming homogeneous model architecture.

A2: Using homogeneous models is a common and convenient setting for fairness-oriented methods. Most fairness-driven FL works adopt this setting, and we follow the same convention. Nonetheless, our approach is compatible with extensions to heterogeneous models. Specifically, our aggregation strategies do not require model alignment, and the pruning mechanism can be adapted to partially shared components, such as aligned layers. Therefore, our framework retains flexibility for broader applicability in non-iid or partially heterogeneous environments.

W3 & Q2: Discussion on implementation difficulty and resource costs.

A3: Thank you for your insights and concerns. Our method introduces two components, both operating at the aggregation stage, which are not difficult to implement in practice. These steps are lightweight and can be incorporated as plugins without modifying the client-side logic or disrupting existing FL frameworks. We demonstrate its ease of integration via multiple plug-in experiments in Table 2 (Page 8).

From a resource perspective, there is no extra client-side cost, either in computation or communication. The server-side overhead is also relatively small and acceptable. We measured the time and memory consumption on an NVIDIA 3090Ti, as shown in the following table. Additionally, we have supplemented a complexity analysis of our method, where the local epoch is denoted as $E$, batch size as $B$, number of parameters as $G$, number of clients as $K$, and dataset size as $D_k$. Although the complexity varies across these methods, their actual overhead in real-world scenarios is negligible and far smaller than the cost during training.

Table: Time (s) and Memory (GB) Costs on Digits Datasets

Table: Complexity Analysis.

Question

Q3: Impact of local training epoch.

A6: To evaluate how FedPW performs under different numbers of local training steps, we conducted experiments on the Digits cross-domain benchmark with local epochs varying from 5 to 20. The results, shown in the appended table, demonstrate that FedPW consistently outperforms baseline methods across all configurations. This suggests that our method maintains strong robustness to local training length.

Table: Sensitive Analysis on Local Epoch in Digits

Q4: Missing references for some related methods.

A7: We sincerely apologize for this oversight and thank the reviewer for the helpful reminder. The missing citations for FedCurve, Ditto, and other relevant works will be properly included in the final version of the paper.

Thank you for your valuable feedback and hope that our rebuttal adequately addresses your concerns!

Dear Reviewer Jzhw,

Thank you again for your time and thoughtful review. If you have any remaining concerns, we would sincerely appreciate the opportunity to address them and hope you might reconsider your evaluation. We truly value your feedback and hope our work can meet your expectations.

With sincere thanks,

Authors

Dear Reviewer NSd9:

We sincerely appreciate your time and effort in reviewing our paper. We hope that our responses below will address your concerns and further affirm the quality of our research.

Weaknesses & Questions

W1 & Q1: How to distinguish truly redundant parameter updates from temporarily small updates caused by noise or slow convergence?

A1: Thank you for your insights and concerns. Neural networks are known to contain subnetworks that are functionally equivalent to the full model, implying the presence of redundant parameters. In our work, we treat parameters with consistently small updates as redundant, since their contribution to loss reduction is minimal. This perspective has been widely supported in prior studies [1, 2]. To address the concern that some parameters may have small updates due to noise or slow convergence, we clarify the following:

(1) Temporarily small updates: Some parameters may have small updates due to gradient noise, stochasticity, or slow convergence. These temporarily small magnitudes do not reflect true redundancy. Such parameters are not persistently suppressed or discarded, so occasional masking of them does not cause significant negative impact.

(2) Persistent redundancy: Truly redundant parameters tend to have consistently small updates over the long term. Our masking strategy captures this pattern and consistently discards such parameters.

(3) Long-term mask: Our masking strategy operates continuously over the long term. This long-term perspective ensures that only persistently inactive parameters are consistently masked, while temporarily small updates may be masked occasionally but are not systematically suppressed.

This distinction between temporarily small updates and persistent redundancy allows us to identify and mask unimportant parameters in a robust manner.

[1] Picking winning tickets before training by preserving gradient flow. In International Conference on Learning Representations (ICLR), 2021.

[2] Gradient flow in sparse neural networks and how lottery tickets win. In Proceedings of the AAAI Conference on Artificial Intelligence, 2022.

W2 & Q2: Convergence bound and bias analysis.

A2: Our current masking strategy is not strictly unbiased, as it favors the preservation of high-magnitude parameters. However, the resulting bias remains limited. We decompose the global update as:

and define the total bias as:

with bounds:

Assuming $F(w)$ is $L$-smooth and $\mu$-strongly convex, we obtain the convergence bound:

In typical settings, $\sqrt{c_{\max}} < 1$, $\frac{m_d}{m_a} \ll 1$, and $\eta G \ll 1$, implying that the bias term $b$ remains significantly smaller than $1/T$. This guarantees convergence to a bounded neighborhood with controlled directional bias.

W3 & Q3: Dual-phase scheduler robustness and sensitive justification.

A3: To assess the scheduler’s sensitivity, we focus on two key aspects:
(1) Stability: whether the dual-phase phenomenon that the scheduler relies on is consistently observable and stable across settings, and
(2) Effectiveness: whether the scheduler can consistently achieve the intended objectives in both phases under different configurations.

For (1), we confirm the presence of the dual-phase behavior in all tested settings and report the proportion of training epochs in each phase, denoted as $E_{\text{Phase I}}$ and $E_{\text{Phase II}}$. In general, $E_{\text{Phase II}}$ accounts for a larger portion of the training, indicating that the scheduler tends to prioritize fairness for most of the time.
For (2), we quantify how concentrated the scheduler’s selection is in each phase. Specifically, we report $K \cdot \lambda_{\text{top-25\%-p}}$ and $K \cdot \lambda_{\text{top-25\%-q}}$, which represent the average weight assigned to the top 25% of clients (in terms of $p_k^t$ and $q_k^t$, respectively), scaled by the total number of clients $K$. Clients with higher $p_k$ (or $q_k$) values are those more beneficial for generalization (or fairness), and they are expected to be favored in the corresponding phase. A stable value of $K \cdot \lambda_{\text{top-25\%}}$ greater than 1 indicates that the scheduler consistently prioritizes these top clients as intended.

The following tables present our results. The first two rows present the accuracy and corresponding standard deviation (in parentheses) for our method and FedAvg. These results suggest that the scheduler is not overly sensitive to batch stochasticity or system heterogeneity, and its decision rule remains stable and reliable across different settings.

Table: Sensitive Analysis on Bacth Size in Digits

Table: Sensitive Analysis on Number of Clients in Digits

Table: Sensitive Analysis on Variance Scaling (Max Value of $\sigma_p$ and $\sigma_q$)

W4 & Q4: Additional details on variance-based fairness metrics.

A4: As shown in the following table, We additionally evaluate fairness using max-loss, minimum accuracy, the group gap between top-10% and bottom-10% clients, Gini index, and Jain’s fairness index. These results show that our method substantially improves the performance of the most disadvantaged clients across diverse fairness definitions.

Table: Fairness Scores under Different Fairness Metrics

W5: Further clarification on Figure 2 and the x-axis.

A5: We apologize for your confusion caused. The x-axis labeled "mask rate" indeed refers to the percentage of parameters (ranked by magnitude) that are pruned. This definition aligns with the meaning of $r_k^t$ in our paper, representing the percentage of parameters being discarded. The left plot illustrates how performance varies across different domains as the mask ratio increases, where the inflection point indicates the maximum tolerable pruning ratio. The right plot displays the corresponding mask ratios and accuracy levels at which these inflection points occur across different datasets.