  In general, convolutional neural networks (CNNs) are easy to train, but their
essential properties, such as generalization error and adversarial robustness,
are hard to control. Recent research demonstrated that singular values of
convolutional layers significantly affect such elusive properties and offered
several methods for controlling them. Nevertheless, these methods present an
intractable computational challenge or resort to coarse approximations. In this
paper, we offer a principled approach to alleviating constraints of the prior
art at the expense of an insignificant reduction in layer expressivity. Our
method is based on the tensor-train decomposition; it retains control over the
actual singular values of convolutional mappings while providing structurally
sparse and hardware-friendly representation. We demonstrate the improved
properties of modern CNNs with our method and analyze its impact on the model
performance, calibration, and adversarial robustness. The source code is
available at: https://github.com/WhiteTeaDragon/practical_svd_conv
