Gaussian RBM
For the Gaussian-Binary RBM the conditional probabilities are
$$
\begin{align}
P(x_i|\mathbf{h}) &= \mathcal{N}(x_i; a_i+ \sum_j h_j w_{ij}, \sigma^2)
\tag{11}\\
P(h_j=1|\mathbf{x}) &= \frac{1}{1+e^{-b_j-\frac{1}{\sigma^2} \sum_i x_i w_{ij}}},
\tag{12}
\end{align}
$$
while the visible units now follow a normal distribution, we see the hidden units again follow the logistic sigmoid function.