The canonical Restricted Boltzmann Machine (RBM) is an energy-based model with binary visible and hidden units. Its energy function is:

$E(v,h) = -b^Tv - c^Th - v^TWh$

where $b$, $c$, and $W$ are unconstrained, real-valued, learnable parameters. It is easy to take its derivatives:

$\frac{\partial}{\partial W_{i,j}}E(v,h) = -v_ih_j$

There are no direct interactions between any two visible units or any two hidden units (restrictions). The restrictions on the RBM structure yield the properties:

$p(h|v)=\prod_ip(h_i|v)$ $p(v|h) = \prod_ip(v_i|h)$

The individual conditionals are simple to compute. For the binary RBM we obtain:

$P(h_i=1|v) = \rho(v^TW_{:,i} + b_i)$ $P(h_i=0|v) = 1 - \rho(v^TW_{:,i} + b_i)$

Together, these properties allow for efficient block Gibbs sampling and efficient derivatives, making training convenient. Samples generated by Gibbs sampling from an RBM model are shown below: