  Neural network classifiers are vulnerable to misclassification of adversarial
samples, for which the current best defense trains classifiers with adversarial
samples. However, adversarial samples are not optimal for steering attack
convergence, based on the minimization at the core of adversarial attacks. The
minimization perturbation term can be minimized towards $0$ by replacing
adversarial samples in training with duplicated original samples, labeled
differently only for training. Using only original samples, Target Training
eliminates the need to generate adversarial samples for training against all
attacks that minimize perturbation. In low-capacity classifiers and without
using adversarial samples, Target Training exceeds both default CIFAR10
accuracy ($84.3$%) and current best defense accuracy (below $25$%) with $84.8$%
against CW-L$_2$($\kappa=0$) attack, and $86.6$% against DeepFool. Using
adversarial samples against attacks that do not minimize perturbation, Target
Training exceeds current best defense ($69.1$%) with $76.4$% against
CW-L$_2$($\kappa=40$) in CIFAR10.
