Methods, systems, and apparatus, including computer programs encoded on computer storage media, for augmenting neural networks to generate additional outputs. One of the systems includes a neural network and a sequence processing subsystem, wherein the sequence processing subsystem is configured to perform operations comprising, for each of the system inputs in a sequence of system inputs: receiving the system input; generating an initial neural network input from the system input; causing the neural network to process the initial neural network input to generate an initial neural network output for the system input; and determining, from a first portion of the initial neural network output for the system input, whether or not to cause the neural network to generate one or more additional neural network outputs for the system input.