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Towards Practical Control of Singular Values of Convolutional Layers
Alexandra Senderovich · Ekaterina Bulatova · Anton Obukhov · Maxim Rakhuba

Wed Dec 07 05:00 PM -- 07:00 PM (PST) @

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/practicalsvdconv

Author Information

Alexandra Senderovich (Higher School of Economics)
Ekaterina Bulatova (Higher School of Economics)
Anton Obukhov (ETH Zurich)
Maxim Rakhuba (HSE University)

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