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Hopfield NNs are iterative autoassociative networks that are composed of a single layer . The network is also contains  fully connected processing elements and they are used  as  associative memory ( an MLP can in principle be converted to an associative memory by making the outputs the same as the inputs). The learning algorithm of the Hopfield network is based on the analogy of energy minimization as opposed to BP. Hopfield networks can also be trained  in a single pass as opposed to BP that takes many iterations through the data..