The conditional probability of a binary hidden unit \( h_j \) being on or off again takes the form of a sigmoid function
$$ \begin{align*} p_{GB} (h_j =1 | \boldsymbol{x}) =& \frac{e^{b_j + (\frac{\boldsymbol{x}}{\boldsymbol{\sigma}^2})^T \boldsymbol{w}_{\ast j} } } {1 + e^{b_j + (\frac{\boldsymbol{x}}{\boldsymbol{\sigma}^2})^T \boldsymbol{w}_{\ast j}}} \nonumber \\ =& \frac{1}{1 + e^{-b_j - (\frac{\boldsymbol{x}}{\boldsymbol{\sigma}^2})^T \boldsymbol{w}_{\ast j}}} \\ p_{GB} (h_j =0 | \boldsymbol{x}) =& \frac{1}{1 + e^{b_j +(\frac{\boldsymbol{x}}{\boldsymbol{\sigma}^2})^T \boldsymbol{w}_{\ast j}}} . \end{align*} $$