Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for neural network compression. In one aspect, a method comprises receiving a neural network and identifying a particular set of multiple weights of the neural network. Multiple anchor points are determined based on current values of the particular set of weights of the neural network. The neural network is trained by, at each of multiple training iterations, performing operations comprising adjusting the values of the particular set of weights by backpropagating gradients of a loss function. The loss function comprises a first loss function term based on a prediction accuracy of the neural network and a second loss function term based on a similarity of the current values of the particular set of weights to the anchor points. After training, the values of the particular set of weights are quantized based on the anchor points.