In one aspect, this specification describes a recurrent neural network system implemented by one or more computers that is configured to process input sets to generate neural network outputs for each input set. The input set can be a collection of multiple inputs for which the recurrent neural network should generate the same neural network output regardless of the order in which the inputs are arranged in the collection. The recurrent neural network system can include a read neural network, a process neural network, and a write neural network. In another aspect, this specification describes a system implemented as computer programs on one or more computers in one or more locations that is configured to train a recurrent neural network that receives a neural network input and sequentially emits outputs to generate an output sequence for the neural network input.