Let's see the expressions that we will need to make our RBM:

Forward pass: The information at visible units (V) is passed via weights (W) and biases (c) to the hidden units (h₀). The hidden unit may fire or not depending on the stochastic probability (σ is stochastic probability):

Backward pass: The hidden unit representation (h₀) is then passed back to the visible units through the same weights W, but different bias c, where they reconstruct the input. Again, the input is sampled:

These two passes are repeated for k-steps or till the convergence is reached. According to researchers, k=1 gives good results, so we will keep k = 1.

The joint configuration of the visible vector V and the hidden vector has an energy given as follows:

Also associated with each visible vector V is free energy, the energy that a single configuration would need to have in order to have the same probability as all of the configurations that contain V:

Using the Contrastive Divergence objective function, that is, Mean(F(V_original))- Mean(F(V_{reconstructed})), the change in weights is given by:

Here, η is the learning rate. Similar expressions exist for the biases b and c.