Algorithm 1. Generalized federated learning train process.

1:Initialize ${\mathbf{\theta }}_0$ based on He normal weight initialization method   2:${\mathbf{g}}_0\leftarrow \mathbf{0}$   3:for$t\leftarrow 1$ to T do   4:      (Clients) ${\mathbf{\theta }}_t^{\left(l\right)}\leftarrow {\mathbf{\theta }}_{t-1}^{\left(l\right)}+{\mathbf{g}}_{t-1}$   5:      (Clients) Update ${\mathbf{g}}_t^{\left(l\right)}$ from the datasets ${\Phi }_{tr}^{\left(l\right)}$   6:      (Clients) Report ${\mathbf{g}}_t^{\left(l\right)}$ to the server via the backhaul link   7:      (Server) ${\mathbf{g}}_t\leftarrow {\mathbf{f}}_g({\mathbf{g}}_t^{\left(l\right)},l=1,\dots ,L)$ as in (7)   8:      (Server) Broadcast ${\mathbf{g}}_t$ to multi-clients   9:end for