Before revision:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood,  and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameter of the weight distribution.
After revision:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood, and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameters of the weight distribution.