Editing Unsupervised learning (section)

=== Energy ===
An energy function is a macroscopic measure of a network's activation state.  In Boltzmann machines, it plays the role of the Cost function.  This analogy with physics is inspired by Ludwig Boltzmann's analysis of a gas' macroscopic energy from the microscopic probabilities of particle motion <math>p \propto e^{-E/kT}</math>, where k is the Boltzmann constant and T is temperature. In the [[Restricted Boltzmann machine|RBM]] network the relation is <math> p = e^{-E} / Z </math>,<ref name="Hinton2010" /> where <math>p</math> and <math>E</math> vary over every possible activation pattern and <math>\textstyle{Z = \sum_{\scriptscriptstyle{\text{All Patterns}}}  e^{-E(\text{pattern})}}</math>. To be more precise, <math>p(a) = e^{-E(a)} / Z</math>, where <math>a</math> is an activation pattern of all neurons (visible and hidden). Hence, some early neural networks bear the name Boltzmann Machine.  Paul Smolensky calls <math>-E\,</math> the ''Harmony''. A network seeks low energy which is high Harmony.