## 5 Enforced Synchronization Strategy Based on Model Dropout
Once the edge reconstructs all clients' local models, it can proceed with synchronous aggregation. The proposed enforced synchronization strategy based on model dropout, as described in Algorithm 2, is designed to mitigate the impact of heterogeneous computing capabilities among terminal clients in a three-tier FL architecture. By selectively transmitting masked sub-models and enforcing synchronous local updates, the algorithm ensures that all clients--regardless of computing capacity--complete their updates within a fixed number of iterations, thereby aligning their upload timings to the edge servers. This structured synchronization, together with dropout-based model reconstruction at the edge level, enhances the consistency of aggregation and reduces the staleness of updates. Consequently, the method improves convergence stability and ensures the contribution of weak clients without degrading the global model quality. When built upon convergent federated optimization algorithms such as FedAvg, this strategy preserves theoretical convergence while empirically accelerating the training process by reducing idle waiting time and minimizing gradient variance during aggregation. The computational complexity of Algorithm 2 can be broken down as follows. Each client performs \(\tau_{1}\) local updates on a partial model of size \(\alpha d\), where \(d\) is the dimensionality of the global model and \(\alpha\) in (0, 1] is the dropout ratio. The local update cost is thus \(\mathcal{O}(\tau_{1}\alpha d)\). Dropout masking and identifier encoding incur negligible overhead. Each edge server reconstructs \(K/N\) masked models per round, with a reconstruction cost of \(\mathcal{O}(\alpha d)\) per model. Aggregation and weighting involve an additional \(\mathcal{O}(Kd)\) across all edges. The total complexity per round is \(\mathcal{O}(K\tau_{1}\alpha d+K\alpha d+Nd)\), which is significantly lower than full-model synchronous updates. Moreover, the model compression via dropout reduces communication cost and training latency, making the algorithm well-suited for resource-constrained edge environments. ```
Input: The global model \(W_{cloud}^{T-1}\) for round \(T-1\); the number of clients \(K\); the number of edges \(N\); the number of local update training iterations \(\tau_{1}\); and the number of edge aggregations \(\tau_{2}\). Output: The global model \(W_{cloud}^{T}\) for round \(T\). 1 for\(edge\)\(j=1,2,\cdots,N\)in paralleldo
2 Calculate the model dropout ratio \(q_{i}^{M}\) for each paired client according to Equation (1). 3 end for
4 for\(t=1,2,\cdots,\tau_{2}\)do// Synchronous Aggregation Stage
5 forclient\(i=1,2,\cdots,K\)in paralleldo
6 for\(ep=1,\cdots,\tau_{1}\)do
7\(W_{local_{i}}^{T,tep}\) \(W_{local_{i}}^{T,tep-1}-\eta\
abla F_{i}(W_{local_{i}}^{T,tep-1})\)
8 end for
9 Generate the identifier of the mask \(M_{i}^{T,t}\) based on the dropout ratio \(q_{i}^{M}\);
10 Transmit the masked model \(W_{local_{i}}^{T,t}\) along with the identifier to the paired edge;
11 end for
12 for\(edge\)\(j=1,2,\cdots,N\)in paralleldo
13 for\(i=1,2,\cdots,K/N\)do// Model Completion
14 Reconstruct each client's mask based on the identifier \(M_{i}^{T,t}\);
15\(\tilde{W}_{local_{i}}^{T,t}\) \(\leftarrow\)\(W_{local_{i}}^{T,t}\)\(\odot\)\(M_{i}^{T,t}\)\(+\)\(\
u\cdot W_{edge_{j}}^{T,t-1}\)\(\odot\)\(\left(M_{i}^{T,t}\right)^{c}\)
16 end for
17\(W_{edge_{j}}^{T,t}\) \(=\)\(\frac{1}{\underset{i\in K_{j}}{\sum}D_{i}}\)\(\times\)\(\underset{i\in K_{j}}{\sum}\)\(\left(D_{i}\times\tilde{W}_{local_{i}}^{T,t}\right)\)
18 end for
19 Obtain the edge's weight \(\omega_{j}^{T}\) using the algorithm in [18];
20 end for
21\(W_{cloud}^{T}\) \(=\)\(\underset{j=1}{\overset{N}{\sum}}\)\(\omega_{j}^{T}\)\(W_{e_{j}}^{T,t=\tau_{2}}\)
```  
**Algorithm 2**Enforored Synchronization Strategy Based on Model dropout  
6 Contribution-Based Aggregation Strategy Optimization Based on Heterogeneous Computing Capabilities  
A high-contribution edge model essentially reflects the characteristics of the local dataset more effectively.