On the Geometry of Rectifier Convolutional Neural Networks

While recent studies have shed light on the expressivity, complexity and compositionality of convolutional networks, the real inductive bias of the family of functions reachable by gradient descent on natural data is still unknown. By exploiting symmetries in the preactivation space of convolutional layers, we present preliminary empirical evidence of regularities in the preimage of trained rectifier networks, in terms of arrangements of polytopes, and relate it to the nonlinear transformations applied by the network to its input.