1. A computer-implemented method, comprising: receiving training data comprising a respective training data set for each of two or more languages; processing a monolingual deep neural network (DNN) acoustic model on a given training data set of the two or more languages; initializing one or more weights of a multilingual DNN acoustic model based on the processing of the monolingual DNN acoustic model, wherein the multilingual DNN acoustic model comprises a feedforward neural network having multiple layers of one or more nodes, wherein each node of a given layer connects with a respective weight to each node of a subsequent layer, and wherein the multiple layers of one or more nodes comprise one or more hidden layers of nodes that are shared between at least two of the two or more languages and a language-specific output layer of nodes corresponding to each of the two or more languages; after initializing the one or more weights of the multilingual DNN acoustic model based on the processing of the monolingual DNN acoustic model, processing, by one or more computing devices, the multilingual DNN acoustic model based on the training data to generate a trained multilingual DNN acoustic model; and using the trained multilingual DNN acoustic model in an automatic speech recognition (ASR) system.