Methods, systems, and apparatus, including computer programs encoded on computer storage media, for processing a network input using a neural network to generate a network output for the network input. One of the methods includes maintaining, for each of the plurality of neural network layers, a respective look-up table that maps each possible combination of a quantized input index and a quantized weight index to a multiplication result; and generating a network output from a network input, comprising, for each of the neural network layers: receiving data specifying a quantized input to the neural network layer, the quantized input comprising a plurality of quantized input values; and generating a layer output for the neural network layer from the quantized input to the neural network layer using the respective look-up table for the neural network layer.