Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two\nimportant models at the interface of statistical physics, machine learning, and\nneuroscience. Recently, there has been interest in the relationship between HNs\nand RBMs, due to their similarity under the statistical mechanics formalism. An\nexact mapping between HNs and RBMs has been previously noted for the special\ncase of orthogonal (uncorrelated) encoded patterns. We present here an exact\nmapping in the case of correlated pattern HNs, which are more broadly\napplicable to existing datasets. Specifically, we show that any HN with $N$\nbinary variables and $p<N$ arbitrary binary patterns can be transformed into an\nRBM with $N$ binary visible variables and $p$ gaussian hidden variables. We\noutline the conditions under which the reverse mapping exists, and conduct\nexperiments on the MNIST dataset which suggest the mapping provides a useful\ninitialization to the RBM weights. We discuss extensions, the potential\nimportance of this correspondence for the training of RBMs, and for\nunderstanding the performance of deep architectures which utilize RBMs.\n