## 4 Conclusions  
This study has demonstrated the effectiveness of our proposed FedKD-WCL algorithm in addressing the challenges posed by statistical heterogeneity in FL, particularly in non-IID data settings. Experimental results show faster convergence and higher accuracy compared to state-of-the-art methods, particularly in high-heterogeneity settings. By integrating knowledge distillation with a bi-level optimization framework, FedKD-WCL successfully balances global model convergence and local personalization, outperforming established baseline methods across diverse datasets. The experimental results underscore the advantage of using the global model as a teacher to guide local training, with deeper models like multilayer perceptrons showing sensitivity to the KD weight parameter, highlighting the importance of model-specific tuning in non-IID environments. The algorithm performs well with both simple (MLR) and complex (MLP) models, demonstrating adaptability to varying model capacities. In addition, unlike methods like FedMD or FedDF, which rely on proxy or public datasets, pFedKD-WCL operates solely on clients' datasets, enhancing privacy and applicability in resource-constrained or privacy-sensitive scenarios. While these findings affirm the robustness of FedKD-WCL, its reliance on centralized coordination and potential computational demands present areas for improvement, especially in large-scale deployments. Although pFedKD-WCL performs well across MLR and MLP models, deeper architectures (e.g., MLPs) are more sensitive to \(\gamma\), exhibiting sharper accuracy drops with suboptimal settings. Future research could explore adaptive tuning strategies for the KD weight, thereby enhancing the algorithm's applicability to real-world FL scenarios.  
Conceptualization, H.H.; methodology, H.H.; software, H.H.; validation, H.H. and A.B.; formal analysis, H.H.; writing--original draft preparation, H.H.; writing--review and editing, H.H., A.N.K. and A.B.; visualization, H.H.; supervision, A.B. All authors have read and agreed to the published version of the manuscript.  
The project described was supported partly by the National Center for Advancing Translational Sciences, National Institutes of Health, Award Number UL1 TR001436. The content is solely the responsibility of the author(s) and does not necessarily represent the official views of the NIH.  
The code and datasets are available online [[https://github.com/[PERSON]/pFedKD](https://github.com/[PERSON]/pFedKD)]([https://github.com/[PERSON]/pFedKD](https://github.com/[PERSON]/pFedKD)) (accessed on 16 March 2025).  
We appreciate the editors and reviewers for their constructive comments and suggestions.  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Algorithm** & **Model** & **Accuracy** \\ \hline FedAvg & MLR & 67.76 \(\pm\) 0.09 \\ FedProx & MLR & 69.11 \(\pm\) 0.02 \\ PerfedAvg & MLR & 81.86 \(\pm\) 0.03 \\ pFedMe & MLR & 83.84 \(\pm\) 0.02 \\ FedCKD & MLR & 30.14 \(\pm\) 0.30 \\ pFedKD-WCL & MLR & **89.48 \(\pm\) 0.01** \\ \hline FedAvg & MLP & 72.22 \(\pm\) 0.09 \\ FedProx & MLP & 73.22 \(\pm\) 0.09 \\ PerfedAvg & MLP & 76.51 \(\pm\) 0.10 \\ pFedMe & MLP & 79.71 \(\pm\) 0.10 \\ FedGKD & MLP & 22.78 \(\pm\) 0.01 \\ pFedKD-WCL & MLP & **89.12 \(\pm\) 0.02** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparisons of the average test accuracy on synthetic data.