On the magnitude of parameters of RBMs being universal approximators

This paper concentrates on the magnitude of parameters of restricted Boltzmann machines (RBMs) being universal approximators. It is known that when an RMB is used to compute a probability distribution with sufficient high accuracy, the magnitude of its parameters must tends to infinite unless the probability has a positive lower bound. In this paper, for any given error and probability, we provide a bound, by which there exits an RBM computing the the probability up to the error with parameters bounded. And the bound depends on the error and the input probability.