  Adversarial Training (AT) and Virtual Adversarial Training (VAT) are the
regularization techniques that train Deep Neural Networks (DNNs) with
adversarial examples generated by adding small but worst-case perturbations to
input examples. In this paper, we propose xAT and xVAT, new adversarial
training algorithms, that generate \textbf{multiplicative} perturbations to
input examples for robust training of DNNs. Such perturbations are much more
perceptible and interpretable than their \textbf{additive} counterparts
exploited by AT and VAT. Furthermore, the multiplicative perturbations can be
generated transductively or inductively while the standard AT and VAT only
support a transductive implementation. We conduct a series of experiments that
analyze the behavior of the multiplicative perturbations and demonstrate that
xAT and xVAT match or outperform state-of-the-art classification accuracies
across multiple established benchmarks while being about 30\% faster than their
additive counterparts. Furthermore, the resulting DNNs also demonstrate
distinct weight distributions.
