Inserting into the expression for \( E_{RBM}(\boldsymbol{x},\boldsymbol{h},\boldsymbol{\Theta}) \) in equation results in the energy
$$ \begin{align*} E_{GB}(\boldsymbol{x}, \boldsymbol{h},\boldsymbol{\Theta}) =& \sum_i^M \frac{(x_i - a_i)^2}{2\sigma_i^2} - \sum_j^N b_j h_j -\sum_{ij}^{M,N} \frac{x_i w_{ij} h_j}{\sigma_i^2} \nonumber \\ =& \vert\vert\frac{\boldsymbol{x} -\boldsymbol{a}}{2\boldsymbol{\sigma}}\vert\vert^2 - \boldsymbol{b}^T \boldsymbol{h} - (\frac{\boldsymbol{x}}{\boldsymbol{\sigma}^2})^T \boldsymbol{W}\boldsymbol{h} . \end{align*} $$