From statistical mechanics, the Boltzmann distribution over a system's energy states arises from the assumption that many replicas of the system are exchanging energy with each other. The distribution of these replicas in each energy level is the maximum entropy distribution subject to the constraint that their total energy is fixed, and that any one assignment of energy levels to each replica, a "microstate", satisfying this constraint, is equally probable.

From machine learning, the so-called Energy-based model defines a Hamiltonian (energy function) to its various configurations, and uses Boltzmann's distribution to convert an "energy" to a probability over these configurations. Thus, an EBM can model a probability distribution over some data domain.

Is there some viewpoint by which one can interpret the EBM as a "system" exchanging energy with many other replicas of that system? What semantic interpretation of EBMs connects them to the Boltzmann distribution's assumptions?



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