  We investigate the geometric properties of the functions learned by trained
ConvNets in the preactivation space of their convolutional layers, by
performing an empirical study of hyperplane arrangements induced by a
convolutional layer. We introduce statistics over the weights of a trained
network to study local arrangements and relate them to the training dynamics.
We observe that trained ConvNets show a significant statistical bias towards
regular hyperplane configurations. Furthermore, we find that layers showing
biased configurations are critical to validation performance for the
architectures considered, trained on CIFAR10, CIFAR100 and ImageNet.
