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, along with varying
 hyperparameters of a deep convolutional network, comparing our bounds
 with practical generalization gaps.
We prove generalization bounds for convolutional neural networks that take account of weight-tying Studies the generalization power of CNNs and improves the upper bounds of generalization errors, showing correlation between the generalization error of learned CNNs and the upper bound's dominant term. This paper presents a generalization bound for convolutional neural networks based on the number of parameters, the Lipschitz constant, and the distance of the final weights from initialization.