We prove bounds on the generalization error of convolutional networks. The bounds are in terms of the training loss, the number of
parameters, the Lipschitz constant of the loss and the distance from the weights to the initial weights. They are independent of the number of pixels in the input, and the height and width of hidden feature maps. We present experiments with CIFAR-10 and a scaled-down variant, along with varying hyperparameters of a deep convolutional network, comparing our bounds with practical generalization gaps.