  In this work, we analyze the role of the network architecture in shaping the
inductive bias of deep classifiers. To that end, we start by focusing on a very
simple problem, i.e., classifying a class of linearly separable distributions,
and show that, depending on the direction of the discriminative feature of the
distribution, many state-of-the-art deep convolutional neural networks (CNNs)
have a surprisingly hard time solving this simple task. We then define as
neural anisotropy directions (NADs) the vectors that encapsulate the
directional inductive bias of an architecture. These vectors, which are
specific for each architecture and hence act as a signature, encode the
preference of a network to separate the input data based on some particular
features. We provide an efficient method to identify NADs for several CNN
architectures and thus reveal their directional inductive biases. Furthermore,
we show that, for the CIFAR-10 dataset, NADs characterize the features used by
CNNs to discriminate between different classes.
