Boltzmann Machine
A Boltzmann machine is a thermodynamic system
, which has binary units as its microstates, with each state is a vector Its energy function is given by where are called symmetric weights, and are biases.
Restricted Boltzmann Machine
A restricted Boltzmann machine is a special case of a Boltzmann machine that imposes a bipartite structure on the units. It is represented as
, where and denote the number of visible and hidden units, respectively. The parameters of satisfy the constraint for all , ensuring no intra-layer connections. We can explicitly write each state vector as Then energy function of can be written as where , and and are the biases of visible and hidden units respectively.