Editing Boltzmann machine (section)

==Structure==
[[File:Boltzmannexamplev2.png|thumb|right|alt=A graphical representation of an example Boltzmann machine with weight labels.| A graphical representation of a Boltzmann machine with a few weights labeled. Each undirected edge represents dependency and is weighted with weight <math>w_{ij}</math>. In this example there are 3 hidden units (blue) and 4 visible units (white). This is not a restricted Boltzmann machine.]]

A Boltzmann machine, like a [[Spin glass#Sherrington–Kirkpatrick model|Sherrington–Kirkpatrick model]], is a network of units with a total "energy" ([[Hamiltonian function|Hamiltonian]]) defined for the overall network. Its units produce [[Binary number|binary]] results. Boltzmann machine weights are [[stochastic]]. The global energy <math>E</math> in a Boltzmann machine is identical in form to that of [[Hopfield network]]s and [[Ising model]]s:

:<math>E = -\left(\sum_{i<j} w_{ij} \, s_i \, s_j + \sum_i \theta_i \, s_i \right)</math>

Where:
* <math>w_{ij}</math> is the connection strength between unit <math>j</math> and unit <math>i</math>.
* <math>s_i</math> is the state, <math>s_i \in \{0,1\}</math>, of unit <math>i</math>.
* <math>\theta_i</math> is the bias of unit <math>i</math> in the global energy function. (<math>-\theta_i</math> is the activation threshold for the unit.)

Often the weights <math>w_{ij}</math> are represented as a symmetric matrix <math>W=[w_{ij}]</math> with zeros along the diagonal.