  In this work, we explain the working mechanism of MixUp in terms of
adversarial training. We introduce a new class of adversarial training schemes,
which we refer to as directional adversarial training, or DAT. In a nutshell, a
DAT scheme perturbs a training example in the direction of another example but
keeps its original label as the training target. We prove that MixUp is
equivalent to a special subclass of DAT, in that it has the same expected loss
function and corresponds to the same optimization problem asymptotically. This
understanding not only serves to explain the effectiveness of MixUp, but also
reveals a more general family of MixUp schemes, which we call Untied MixUp. We
prove that the family of Untied MixUp schemes is equivalent to the entire class
of DAT schemes. We establish empirically the existence of Untied Mixup schemes
which improve upon MixUp.
