1. A method performed by one or more computers, the method comprising: accessing, by the one or more computers, a first neural network that has been trained using speech data examples that are each assigned a context-dependent state by clustering context independent states based on activations at a hidden layer of a second neural network that was trained to provide outputs corresponding to context-independent states, the first neural network being configured to provide outputs corresponding to one or more context-dependent states; receiving, by the one or more computers, an audio signal encoding a portion of an utterance; providing, by the one or more computers, data corresponding to the audio signal to the first neural network that has been trained using the speech data examples that are each assigned a context-dependent state based on the activations at the hidden layer of the second neural network; generating, by the one or more computers, data indicating a transcription for the utterance based on an output of the first neural network that was generated in response to the data corresponding to the audio signal; and providing, by the one or more computers, the data indicating the transcription as output of an automated speech recognition service.