Methods, systems, and apparatus, including computer programs encoded on computer storage media, for training a neural network using consistency measures. One of the methods includes processing a particular training example from a mediator training data set using a first neural network to generate a first output for a first machine learning task; processing the particular training example in the mediator training data set using each of one or more second neural networks, wherein each second neural network is configured to generate a second output for a respective second machine learning task; determining, for each second machine learning task, a consistency target output for the first machine learning task; determining, for each second machine learning task, an error between the first output and the consistency target output corresponding to the second machine learning task; and generating a parameter update for the first neural network from the determined errors.