## 5 Enforced Synchronization Strategy Based on Model Dropout  
In the previous section, we re-paired the clients based on model similarity and computing capabilities. Although the computing capabilities of clients under the same edge are similar, they are not identical, resulting in some waiting time. This section proposes an enforced synchronization method based on model dropout for client transmissions. Clients with higher computing capability can transmit the entire model, while clients with lower computing capability perform dropout operations on the model using the algorithm in this section, ensuring that all clients' local models reach the edge simultaneously, as shown in Figure 2.  
As a regularization technique, dropout was first introduced in neural network methods to prevent overfitting by making some neurons' activation values stop working with a certain probability during forward propagation. This prevents the model from relying too heavily on local features and thus improves model generalization [17]. In this section, a fixed proportion of neuron values are set to zero to reduce the pressure and delay of model transmission. We assume that all edges can beforehand know the computing capabilities of each client. Taking a specific edge as an example, when clients complete local updates, if all clients have equal computing capabilities, the entire model can be directly transmitted. If the computing capabilities are unequal, the client with the highest computing capability is used as the baseline. Since each client is allocated equal bandwidth, the time to transmit the entire model is equal, denoted as \(T^{cmp}\). The dropout proportion \(q_{i}^{M}\) for each client's model can be obtained using the following formula:  
\[q_{i}^{M}=\frac{T_{i}^{\text{com}}}{T_{*}^{\text{com}}}=1-\frac{T_{i}^{\text {cmp}}-T_{*}^{\text{cmp}}}{T_{*}^{\text{com}}} \tag{1}\]  
where \(T_{*}^{com}\) and \(T_{*}^{cmp}\) represent the time required for the client with the highest computing capability under that edge to perform local updates and model transmission, respectively. To ensure the effectiveness of this method, it is necessary to guarantee that \(q_{i}^{M}\in(0,1]\)  
Figure 2: Enforced synchronization strategy based on model dropout. Therefore, the number of local updates needs to be controlled within a reasonable range to avoid the situation where \(T_{i}^{cmp}>T_{*}^{com}+T_{*}^{cmp}\). When clients transmit model parameters to the edge, they follow the agreed-upon protocol using the dropout proportion \(q_{i}^{M}\) calculated by Equation (1) to apply dropout to the local model parameters before retransmitting. This selection of dropout parameters is referred to as the mask \(M_{i}^{T,t}\). The generation of this mask can achieve an approximately pseudo-random effect based on some client identifier (such as version number or timestamp of the sent model). In the mask, the parameters to be sent are set to one and those not to be sent are set to zero, with the same dimensions as the model. This work employs lightweight identifiers--such as random seeds or hash signatures--instead of explicitly transmitting masks. Edge nodes can reconstruct the corresponding masks based on the client identifiers and use them to complete the missing portions of the uploaded model parameters. Bandwidth estimation indicates that the overhead introduced by this mechanism constitutes only a minimal fraction of the total uplink data volume, making its transmission latency negligible on typical IoT devices. The completed client model parameters \(\tilde{W}_{local,i}^{T,t}\) are  
\[\tilde{W}_{local,i}^{T,t}\gets W_{local,i}^{T,t}\odot M_{i}^{T,t}+\
u \cdot W_{edge,i}^{T,t-1}\odot\left(M_{i}^{T,t}\right)^{c} \tag{2}\]  
where \((M_{i}^{T,t})^{c}\) denotes the complement of the mask; \(\odot\) denotes the Hadamard product between matrices; the unsent model parameters are replaced with the previous round's edge model \(W_{edge,i}^{T,t-1}\). The proportion is controlled by the hyper-parameter \(\
u\in[0,1]\).