### Boltzmann machine:  Each un-directed edge represents dependency. In this example there are 3 hidden units and 4 visible units.   This is not a restricted Boltzmann machine.Reconstruction is different from regression or classification in that it estimates the probability distribution of the original input instead of associating a continuous/discrete value to an input example.   The joint distribution is known in Physics as the Boltzmann Distribution which gives the probability that a particle can be observed in the state with the energy E.

As in Physics we assign a probability to observe a state of v and h, that depends on the overall energy of the model. Unfortunately it is very difficult to calculate the joint probability due to the huge number of possible combination of v and h in the partition function Z. Much easier is the calculation of the conditional probabilities of state h given the state v and conditional probabilities of state v given the state h and so on. the essential is here, energy-based probability  Reconstruction is different from regression or classification in that it estimates the probability distribution of the original input instead of associating a continuous/discrete value to an input example.

Boltzmann Machine     as a Pontryagin Observer in Sensor Network

The Pontryagin dual of a discrete abelian group is compact

Relationship between sums and  integrals

what are those conditions on "f"?

The Pontryagin dual of a discrete abelian group is compact

Einstein-Podolsky-Rosen paradox, has confounded physicists trying to understand how to interpret quantum measurements.

"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?" March9thv1a Boltzmann machine:  Each undirected edge represents dependency. In this example there are 3 hidden units and 4 visible units.  This is a restricted Boltzmann machine. Restricted Boltzmann Machines are probabilistic. As opposed to assigning discrete values the model assigns probabilities. At each point in time the RBM is in a certain state. The state refers to the values of neurons in the visible and hidden layers v and h.  This is the point where Restricted Boltzmann Machines meets Physics for the second time.

The joint distribution is known in Physics as the Boltzmann Distribution which gives the probability that a particle can be observed in the state with the energy E.

As in Physics we assign a probability to observe a state of v and h, that depends on the overall energy of the model. Unfortunately it is very difficult to calculate the joint probability due to the huge number of possible combination of v and h in the partition function Z. Much easier is the calculation of the conditional probabilities of state h given the state v and conditional probabilities of state v given the state h and so on. the essential is here, energy-based probability  Reconstruction is different from regression or classification in that it estimates the probability distribution of the original input instead of associating a continuous/discrete value to an input example.

Global Energy is

Learning Process