A neural network system is configured to receive an input image and to generate a classification output for the input image. The neural network system includes: a separable convolution subnetwork comprising a plurality of separable convolutional neural network layers arranged in a stack one after the other, in which each separable convolutional neural network layer is configured to: separately apply both a depthwise convolution and a pointwise convolution during processing of an input to the separable convolutional neural network layer to generate a layer output.