  Adversarial examples are augmented data points generated by imperceptible
perturbation of input samples. They have recently drawn much attention with the
machine learning and data mining community. Being difficult to distinguish from
real examples, such adversarial examples could change the prediction of many of
the best learning models including the state-of-the-art deep learning models.
Recent attempts have been made to build robust models that take into account
adversarial examples. However, these methods can either lead to performance
drops or lack mathematical motivations. In this paper, we propose a unified
framework to build robust machine learning models against adversarial examples.
More specifically, using the unified framework, we develop a family of gradient
regularization methods that effectively penalize the gradient of loss function
w.r.t. inputs. Our proposed framework is appealing in that it offers a unified
view to deal with adversarial examples. It incorporates another
recently-proposed perturbation based approach as a special case. In addition,
we present some visual effects that reveals semantic meaning in those
perturbations, and thus support our regularization method and provide another
explanation for generalizability of adversarial examples. By applying this
technique to Maxout networks, we conduct a series of experiments and achieve
encouraging results on two benchmark datasets. In particular,we attain the best
accuracy on MNIST data (without data augmentation) and competitive performance
on CIFAR-10 data.
