# boltzmann machine; from logistic function to boltzmann distribution [closed]

I'm trying to understand Boltzmann machines. Tutorials explain it with two formulas.

Logistic function for the probability of single units:

 $p(unit=1)=\frac{1}{1+e^{-\sum_{x}wx } }$


and, when the machine is running, every state of the machine goes to the probability:

$p(State= state\ with\ energy\ E_i )=\frac{e^{-E_i}}{\sum_i e^{-E_i}}$


so, the state depends on the units, and then if I understand correctly, the second formula is a consequence of the first; so, how can it be the proof that the distribution of $p(state)$ is a consequence of $p(unit)$?

## closed as off-topic by Franck Dernoncourt, kenorb, user58, Ben N♦Nov 25 '16 at 3:59

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• "This question does not appear to be about artificial intelligence, within the scope defined in the help center." – Franck Dernoncourt, kenorb, user58, Ben N
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