  Variational methods for revealing visual concepts learned by convolutional
neural networks have gained significant attention during the last years. Being
based on noisy gradients obtained via back-propagation such methods require the
application of regularization strategies. We present a mathematical framework
unifying previously employed regularization methods. Within this framework, we
propose a novel technique based on Sobolev gradients which can be implemented
via convolutions and does not require specialized numerical treatment, such as
total variation regularization. The experiments performed on feature inversion
and activation maximization demonstrate the benefit of a unified approach to
regularization, such as sharper reconstructions via the proposed Sobolev
filters and a better control over reconstructed scales.
