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.