\begin{equation}
    \label{prompted encoder}
    \begin{aligned}
    {\left[\mathbf{x}_{1}, \mathbf{Z}_{1}, \mathbf{E}_{1}\right] } & =L_{1}\left(\left[\mathbf{x}_{0}, \mathbf{P_{v}}, \mathbf{E}_{0}\right]\right), \\
    {\left[\mathbf{x}_{i}, \mathbf{Z}_{i}, \mathbf{E}_{i}\right] } & =L_{i}\left(\left[\mathbf{x}_{i-1}, \mathbf{Z}_{i-1}, \mathbf{E}_{i-1}\right]\right) \quad i=2,3, \ldots, N_L, \\
    \mathbf{Output} & =\operatorname{Head}\left(\mathbf{x}_{N_L}\right),
    \end{aligned}
\end{equation}
