\begin{equation}
\mathcal L_a(\mathbf{\mathbf{z}_a, \tilde{x}}_a) = \frac{1}{\alpha_a n_a} \sum_{i \in \mathcal{M}_a} || \text{Decode}(\mathbf{z}_{a, i}) - \tilde{\mathbf{x}}_{a, i} ||^{2},
\label{eq:reconstruction}
\end{equation}
