Differential Contrastive Divergence

We formulate a differential version of contrastive divergence for continuous configuration spaces by considering a limit of MCMC processes in which the proposal distribution becomes infinitesimal. This leads to a deterministic differential contrastive divergence update -- one in which no stochastic sampling is required. We prove convergence of differential contrastive divergence in general and prove convergence to the optimal parameter value under natural but restrictive assumptions.