## 5 Enforced Synchronization Strategy Based on Model Dropout
In homogeneous client scenarios [19], since each client performs the same number of computations, the SV can directly reflect the importance of the dataset to the global model. However, when clients have different computing capabilities and can perform different numbers of local training iterations, directly using the SV as a measure of contribution is inappropriate, as it violates the principle of collaborative fairness in FL. Therefore, this section aims to design a contribution-based aggregation optimization strategy. In the previous section, we grouped clients with similar computing capabilities into clusters, ensuring that the clients paired with each edge have similar computing capability. Through the dropout method, we also maintained consistent local iteration counts within each cluster, although the iteration counts differ between clusters. If we directly use the SV as the consideration for contribution weight, it may result in a loss of global model accuracy due to insufficient computing capability from originally high-contributing clients. Therefore, this section introduces a reward-punishment mechanism into the weights. Figure 3 presents a quadrant chart, where the horizontal axis represents client contribution and the vertical axis represents client computing resources. By calculating the contribution within each cluster (i.e., SV) and the average computing capability of each cluster, we can influence the weights. The specific explanation is as follows. Clients within clusters with lower average computing capability have performed fewer local iterations compared to those with higher computing capability; thus, their local models should be less effective at feature extraction. Similarly, clients within clusters with higher average computing capability have performed more iterations and should have better feature extraction capabilities. Therefore, in the upper left and lower right quadrants of the quadrant chart, the SV can be directly used as a weight reference without any rewards or penalties. However, if a cluster with lower average computing capability has an SV higher than the average SV, it indicates that the local data within that cluster are of higher quality and better represents the global model. Thus, a reward factor \(\chi_{i}\) (corresponding to the upper right quadrant in the chart) can be introduced to increase the proportion of this edge model in the subsequent weighting, thereby tilting the global model towards this edge model. Conversely, if a cluster with higher average computing capability has an SV lower than the average SV, it is the least desirable situation. It implies that the local data under high-computing-capability clients are of lower quality, offering limited features for the model to learn from. Thus, a penalty factor \(\xi_{i}\) (corresponding to the lower left quadrant in the chart) can be introduced to decrease the proportion of this edge model in the subsequent weighting, causing the global model to slightly diverge from this edge model. Note that this method is limited to appropriate adjustments of SV. If the reward and penalty factors are too large, it may lead to overcorrection, making it difficult for the global model to converge. After analyzing the rewards and penalties for each edge model, we can start optimizing the aggregation weights with the following formula:  
\[\omega_{i}^{T}=\left\{ \begin{array}{l}\frac{\chi_{i}\xi_{i}\text{as}\
u_{i}} {\sum_{i=0}^{i=k}\sum_{i=0}^{i=k}\chi_{i}\xi_{i}\text{as}\
u_{i}},asv_{i}\geq 0,\\ 0,asv_{i}<0.\end{array} \right. \tag{3}\]  
where \(asv_{i}\) is accumulative SV for client \(i\). If no rewards or penalties are applied to the model, then \(\chi_{i}\) and \(\xi_{i}\) are both 1. Figure 3: Contribution-based aggregation strategy optimization.