## 5 Conclusions  
To jointly reduce communication overhead and achieve competitive model accuracy as emerging edge devices, we proposed a novel communication-efficient federated learning framework, DualPFL. In this framework, we consider the statistical heterogeneity and varying state of the device and propose a dual sparsity pruning method. In the first stage, we introduce the inverse of KL divergence to initialize the sparse rate of each device. On this basis, sparse ratio-based binary matrix M is generated to implement channel pruning of the model. In the second stage, the auxiliary evaluation component of the server is used to dynamically adjust the sparsity rate contained in each device to complete the pruning requirements of subsequent rounds. To ensure the utility of the global model, we propose an adaptive model aggregation strategy based on sparse ratio scaling. Meanwhile, we construct a server-side assisted dynamic sparse adjustment component to fine-tune the sparse ratio by evaluating the gradient change rate so as to realize the sparse pruning adaptive adjustment in different training stages. Subsequently, our proposed DualPFL can achieve a significant reduction in traffic while maintaining the accuracy of the model. The experimental results, including 2\(\times\) speedup in convergence speed on the CIFAR-10 dataset, a mean average precision (mAP) of 95% on the COCO dataset, and a mean average precision of 96% on the TT100K dataset, confirmed that our framework is able to facilitate efficient collaborative computing in federated learning applications.  
Since most deep neural networks are sparse, our DualPFL framework can potentially be applied to other problems like natural language processing or reinforcement learning, where over-parametrization is common. However, the specific implementation details might vary depending on the characteristics of the hardware and the heterogeneity of the devices whose network bandwidth and resources are not allocated an equal share. Future work will explore these extensions and validate the generalizability of our approach.  
Methodology, S.S.; software, S.S.; validation, S.S.; formal analysis, S.D.; investigation, Y.S.; writing--original draft preparation, S.S.; writing--review and editing, Y.Z.; supervision, Y.Z.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China (Grant No. 12475196) and the Science and Technology Service Network Initiative of Chinese Academy of Sciences (Grant No. 2023T3005).  
Not applicable.  
The dataset used in this study is publicly available. The CIFAR10 dataset can be obtained from the following link: [[http://www.cs.toronto.edu/~kriz/cifar.html](http://www.cs.toronto.edu/~kriz/cifar.html)]([http://www.cs.toronto.edu/~kriz/cifar.html](http://www.cs.toronto.edu/~kriz/cifar.html)) accessed on 17 August 2024. The COCO dataset is achieved from [[https://cocodataset.org/#detection-2020](https://cocodataset.org/#detection-2020)]([https://cocodataset.org/#detection-2020](https://cocodataset.org/#detection-2020)) accessed on 3 September 2024.  
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Schemes**} & \multirow{2}{*}{**Accuracy**} & **Average Communication** & \multirow{2}{*}{**Param. Saving**} \\  & & **Time per Round** & \\ \hline FedAvg [1] & 92.89 & 54.46 s & 0 \\ \hline FedLP [48] & 94.25 & 47.70 s & 26\% \\ \hline DualPFL & 96.87 & 30.24 s & 43\% \\ \hline \end{tabular}
\end{table}
Table 4: Comparisons of detection performance on TT100K dataset.