Clamping in Boltzmann machines

A certain assumption that appears in the proof of correctness of the standard Boltzmann machine learning procedure is investigated. The assumption, called the clamping assumption, concerns the behavior of a Boltzmann machine when some of its units are clamped to a fixed state. It is argued that the clamping assumption is essentially an assertion of the time reversibility of a certain Markov chain underlying the behavior of the Boltzmann machine. As such, the clamping assumption is generally false, though it is certainly true of the Boltzmann machines themselves. The author also considers how the concept of the Boltzmann machine may be generalized while retaining the validity of the clamping assumption