Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for a projection neural network. In one aspect, a projection neural network is configured to receive a projection network input and to generate a projection network output from the projection network input. The projection neural network includes a sequence of one or more projection layers. Each projection layer has multiple projection layer parameters, and is configured to receive a layer input, apply multiple projection layer functions to the layer input, and generate a layer output by applying the projection layer parameters for the projection layer to the projection function outputs.