  Convolutional Neural Networks (CNNs) are a class of artificial neural
networks whose computational blocks use convolution, together with other linear
and non-linear operations, to perform classification or regression. This paper
explores the spectral response of CNNs and its potential use in diagnosing
problems with their training. We measure the gain of CNNs trained for image
classification on ImageNet and observe that the best models are also the most
sensitive to perturbations of their input. Further, we perform experiments on
MNIST and CIFAR-10 to find that the gain rises as the network learns and then
saturates as the network converges. Moreover, we find that strong gain
fluctuations can point to overfitting and learning problems caused by a poor
choice of learning rate. We argue that the gain of CNNs can act as a diagnostic
tool and potential replacement for the validation loss when hold-out validation
data are not available.
