I'm learning about RBM and I try to understand the notation used for it. We have the input vector $v=(v_i)$ and the output vector $h=(h_j)$, a weight matrix $W=(W_{ij})$ and finally two bias vectors - $a,b$.
Normally for an ANN we would say that - $$h=\sigma(v^TW+a)$$ where $\sigma$ is the network's activation function.
does this relation not hold for RBM? How does $b $ fit in here? Why is it common to talk about $h$ as a vector that stand for itself and not a deterministic result of the input? What part of this definition makes the network stochastic?